# Publications

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## 2019

Franz Baader:

Abstract BibTeX Entry PDF File

**Expressive Cardinality Constraints on**\(\mathcal{ALCSCC}\)**Concepts**. In*Proceedings of the 34th Annual ACM Symposium on Applied Computing (SAC'19)*, pages 1123–1131. ACM, 2019.Abstract BibTeX Entry PDF File

In two previous publications we have, on the one hand, extended the description logic (DL) ALCQ by more expressive number restrictions using numerical and set constraints expressed in the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA). The resulting DL was called ALCSCC. On the other hand, we have extended the terminological formalism of the well-known description logic ALC from concept inclusions (CIs) to more general cardinality constraints expressed in QFBAPA, which we called extended cardinality constraints. Here, we combine the two extensions, i.e., we consider extended cardinality constraints on ALCSCC concepts. We show that this does not increase the complexity of reasoning, which is NExpTime-complete both for extended cardinality constraints in ALC and ALCSCC. The same is true for a restricted version of such cardinality constraints, where the complexity of reasoning decreases to ExpTime, not just for ALC, but also for ALCSCC.

@inproceedings{ BaaderSAC19, author = {Franz {Baader}}, booktitle = {Proceedings of the 34th Annual {ACM} Symposium on Applied Computing ({SAC}'19)}, pages = {1123--1131}, publisher = {{ACM}}, title = {Expressive Cardinality Constraints on {$\mathcal{ALCSCC}$} Concepts}, year = {2019}, }

Franz Baader and Filippo De Bortoli:

Abstract BibTeX Entry PDF File DOI (The final publication is available at link.springer.com) ©Springer Nature Switzerland AG 2019

**On the Expressive Power of Description Logics with Cardinality Constraints on Finite and Infinite Sets**. In Andreas Herzig and Andrei Popescu, editors,*Proc. of the 12th International Symposium on Frontiers of Combining Systems (FroCoS 2019)*, volume 11715 of*Lecture Notes in Computer Science*, pages 203–219. Springer, 2019.Abstract BibTeX Entry PDF File DOI (The final publication is available at link.springer.com) ©Springer Nature Switzerland AG 2019

In recent work we have extended the description logic (DL) by means of more expressive number restrictions using numerical and set constraints stated in the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA). It has been shown that reasoning in the resulting DL, called \(\mathcal{ALCSCC}\), is PSpace-complete without a TBox and ExpTime-complete w.r.t. a general TBox. The semantics of \(\mathcal{ALCSCC}\) is defined in terms of finitely branching interpretations, that is, interpretations where every element has only finitely many role successors. This condition was needed since QFBAPA considers only finite sets. In this paper, we first introduce a variant of \(\mathcal{ALCSCC}\), called \(\mathcal{ALCSCC}^\infty\), in which we lift this requirement (inexpressible in first-order logic) and show that the complexity results for \(\mathcal{ALCSCC}\) mentioned above are preserved. Nevertheless, like \(\mathcal{ALCSCC}\), \(\mathcal{ALCSCC}^\infty\) is not a fragment of first-order logic. The main contribution of this paper is to give a characterization of the first-order fragment of \(\mathcal{ALCSCC}^\infty\). The most important tool used in the proof of this result is a notion of bisimulation that characterizes this fragment.

@inproceedings{ BaDeBo-FroCoS19, author = {Franz {Baader} and Filippo {De Bortoli}}, booktitle = {Proc. of the 12th International Symposium on Frontiers of Combining Systems ({FroCoS} 2019)}, doi = {https://doi.org/10.1007/978-3-030-29007-8_12}, editor = {Andreas {Herzig} and Andrei {Popescu}}, pages = {203--219}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {On the Expressive Power of Description Logics with Cardinality Constraints on Finite and Infinite Sets}, volume = {11715}, year = {2019}, }

Franz Baader, Andreas Ecke, Gabriele Kern-Isberner, and Marco Wilhelm:

Abstract BibTeX Entry PDF File (The final publication is available at link.springer.com)

**The Complexity of the Consistency Problem in the Probabilistic Description Logic**\(\mathcal{ALC}^{\mathsf{ME}}\). In Andreas Herzig and Andrei Popescu, editors,*Proc. of the 12th International Symposium on Frontiers of Combining Systems (FroCoS 2019)*, volume 11715 of*Lecture Notes in Computer Science*, pages 167–184. Springer, 2019.Abstract BibTeX Entry PDF File (The final publication is available at link.springer.com)

The probabilistic Description Logic ALC^{M}^{E}is an extension of the Description Logic ALC that allows for uncertain conditional statements of the form "if C holds, then D holds with probability p," together with probabilistic assertions about individuals. In ALC^{M}^{E}, probabilities are understood as an agent's degree of belief. Probabilistic conditionals are formally interpreted based on the so-called aggregating semantics, which combines a statistical interpretation of probabilities with a subjective one. Knowledge bases of ALC^{M}^{E}are interpreted over a fixed finite domain and based on their maximum entropy (ME) model. We prove that checking consistency of such knowledge bases can be done in time polynomial in the cardinality of the domain, and in exponential time in the size of a binary encoding of this cardinality. If the size of the knowledge base is also taken into account, the combined complexity of the consistency problem is NP-complete for unary encoding of the domain cardinality and NExpTime-complete for binary encoding.

@inproceedings{ BaEKW19, author = {Franz {Baader} and Andreas {Ecke} and Gabriele {Kern{-}Isberner} and Marco {Wilhelm}}, booktitle = {Proc. of the 12th International Symposium on Frontiers of Combining Systems ({FroCoS} 2019)}, editor = {Andreas {Herzig} and Andrei {Popescu}}, pages = {167--184}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {The Complexity of the Consistency Problem in the Probabilistic Description Logic {$\mathcal{ALC}^{\mathsf{ME}}$}}, volume = {11715}, year = {2019}, }

Franz Baader, Oliver Fernández Gil, and Pavlos Marantidis:

Abstract BibTeX Entry PDF File

**Matching in the Description Logic FL0 with respect to General TBoxes (Extended abstract)**. In Mantas Simkus and Grant Weddell, editors,*Proceedings of the 32nd International Workshop on Description Logics (DL'19)*, volume 2373 of*CEUR Workshop Proceedings*. CEUR-WS, 2019.Abstract BibTeX Entry PDF File

Matching concept descriptions against concept patterns was introduced as a new inference task in Description Logics two decades ago, motivated by applications in the Classic system. Shortly afterwards, a polynomial-time matching algorithm was developed for the DL FL0. However, this algorithm cannot deal with general TBoxes (i.e., finite sets of general concept inclusions). Here we show that matching in FL0 w.r.t. general TBoxes is in ExpTime, which is the best possible complexity for this problem since already subsumption w.r.t. general TBoxes is ExpTime-hard in FL0. We also show that, w.r.t. a restricted form of TBoxes, the complexity of matching in FL0 can be lowered to PSpace.

@inproceedings{ BaFeMa-DL19, author = {Franz {Baader} and Oliver {Fern\'andez Gil} and Pavlos {Marantidis}}, booktitle = {Proceedings of the 32nd International Workshop on Description Logics (DL'19)}, editor = {Mantas {Simkus} and Grant {Weddell}}, publisher = {CEUR-WS}, series = {CEUR Workshop Proceedings}, title = {Matching in the Description Logic {FL0} with respect to General TBoxes (Extended abstract)}, volume = {2373}, year = {2019}, }

Franz Baader, Francesco Kriegel, and Adrian Nuradiansyah:

Abstract BibTeX Entry PDF File DOI ©Springer-Verlag Extended Technical Report

**Privacy-Preserving Ontology Publishing for**\(\mathcal{EL}\)**Instance Stores**. In Francesco Calimeri, Nicola Leone, and Marco Manna, editors,*16th European Conference on Logics in Artificial Intelligence, JELIA 2019, Rende, Italy, May 7-11, 2019, Proceedings*, volume 11468 of*Lecture Notes in Computer Science*, pages 323–338. Springer, 2019.Abstract BibTeX Entry PDF File DOI ©Springer-Verlag Extended Technical Report

We make a first step towards adapting an existing approach for privacy-preserving publishing of linked data to Description Logic (DL) ontologies. We consider the case where both the knowledge about individuals and the privacy policies are expressed using concepts of the DL \(\mathcal{EL}\), which corresponds to the setting where the ontology is an \(\mathcal{EL}\) instance store. We introduce the notions of compliance of a concept with a policy and of safety of a concept for a policy, and show how optimal compliant (safe) generalizations of a given \(\mathcal{EL}\) concept can be computed. In addition, we investigate the complexity of the optimality problem.

@inproceedings{ BaKrNu-JELIA19, author = {Franz {Baader} and Francesco {Kriegel} and Adrian {Nuradiansyah}}, booktitle = {16th European Conference on Logics in Artificial Intelligence, {JELIA} 2019, Rende, Italy, May 7-11, 2019, Proceedings}, doi = {https://dx.doi.org/10.1007/978-3-030-19570-0_21}, editor = {Francesco {Calimeri} and Nicola {Leone} and Marco {Manna}}, pages = {323--338}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {{Privacy-Preserving Ontology Publishing for $\mathcal{EL}$ Instance Stores}}, volume = {11468}, year = {2019}, }

Franz Baader and Adrian Nuradiansyah:

Abstract BibTeX Entry PDF File

**Mixing Description Logics in Privacy-Preserving Ontology Publishing**. In Christoph Benzmüller and Heiner Stuckenschmidt, editors,*KI 2019: Advances in Artificial Intelligence - 42nd German Conference on AI, Kassel, Germany, September 23 - 26, 2019, Proceedings*. Springer, 2019. To AppearAbstract BibTeX Entry PDF File

In previous work, we have investigated privacy-preserving publishing of Description Logic (DL) ontologies in a setting where the knowledge about individuals to be published is an \(\mathcal{EL}\) instance store, and both the privacy policy and the possible background knowledge of an attacker are represented by concepts of the DL \(\mathcal{EL}\). We have introduced the notions of compliance of a concept with a policy and of safety of a concept for a policy, and have shown how, in the context mentioned above, optimal compliant (safe) generalizations of a given \(\mathcal{EL}\) concept can be computed. In the present paper, we consider a modified setting where we assume that the background knowledge of the attacker is given by a DL different from the one in which the knowledge to be published and the safety policies are formulated. In particular, we investigate the situations where the attacker’s knowledge is given by an \(\mathcal{FL}_0\) or an \(\mathcal{FLE}\) concept. In both cases, we show how optimal safe generalizations can be computed. Whereas the complexity of this computation is the same (ExpTime) as in our previous results for the case of \(\mathcal{FL}_0\), it turns out to be actually lower (polynomial) for the more expressive DL \(\mathcal{FLE}\).

@inproceedings{ BaNu-KI19, author = {Franz {Baader} and Adrian {Nuradiansyah}}, booktitle = {KI 2019: Advances in Artificial Intelligence - 42nd German Conference on AI, Kassel, Germany, September 23 - 26, 2019, Proceedings}, editor = {Christoph {Benzm{\"u}ller} and Heiner {Stuckenschmidt}}, note = {To Appear}, publisher = {Springer}, title = {Mixing Description Logics in Privacy-Preserving Ontology Publishing}, year = {2019}, }

Stefan Borgwardt, Ismail Ilkan Ceylan, and Thomas Lukasiewicz:

Abstract BibTeX Entry PDF File PDF File (Extended Technical Report) DOI

**Ontology-Mediated Query Answering over Log-linear Probabilistic Data**. In Pascal Van Hentenryck and Zhi-Hua Zhou, editors,*Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI'19)*, pages 2711–2718. Honolulu, USA, AAAI Press, 2019.Abstract BibTeX Entry PDF File PDF File (Extended Technical Report) DOI

Large-scale knowledge bases are at the heart of modern information systems. Their knowledge is inherently uncertain, and hence they are often materialized as probabilistic databases. However, probabilistic database management systems typically lack the capability to incorporate implicit background knowledge and, consequently, fail to capture some intuitive query answers. Ontology-mediated query answering is a popular paradigm for encoding commonsense knowledge, which can provide more complete answers to user queries. We propose a new data model that integrates the paradigm of ontology-mediated query answering with probabilistic databases, employing a log-linear probability model. We compare our approach to existing proposals, and provide supporting computational results.

@inproceedings{ BoCL-AAAI19, address = {Honolulu, USA}, author = {Stefan {Borgwardt} and Ismail Ilkan {Ceylan} and Thomas {Lukasiewicz}}, booktitle = {Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI'19)}, doi = {https://doi.org/10.1609/aaai.v33i01.33012711}, editor = {Pascal Van {Hentenryck} and Zhi-Hua {Zhou}}, pages = {2711--2718}, publisher = {AAAI Press}, title = {Ontology-Mediated Query Answering over Log-linear Probabilistic Data}, year = {2019}, }

Stefan Borgwardt, Ismail Ilkan Ceylan, and Thomas Lukasiewicz:

Abstract BibTeX Entry PDF File

**Ontology-Mediated Query Answering over Log-linear Probabilistic Data (Abstract)**. In Mantas Simkus and Grant Weddell, editors,*Proceedings of the 32nd International Workshop on Description Logics (DL'19)*, volume 2373 of*CEUR Workshop Proceedings*. Oslo, Norway, CEUR-WS, 2019.Abstract BibTeX Entry PDF File

@inproceedings{ BoCL-DL19, address = {Oslo, Norway}, author = {Stefan {Borgwardt} and Ismail Ilkan {Ceylan} and Thomas {Lukasiewicz}}, booktitle = {Proceedings of the 32nd International Workshop on Description Logics (DL'19)}, editor = {Mantas {Simkus} and Grant {Weddell}}, publisher = {CEUR-WS}, series = {CEUR Workshop Proceedings}, title = {Ontology-Mediated Query Answering over Log-linear Probabilistic Data (Abstract)}, volume = {2373}, year = {2019}, }

Stefan Borgwardt and Walter Forkel:

Abstract BibTeX Entry PDF File PDF File (Extended Technical Report) DOI ©Springer-Verlag

**Closed-World Semantics for Conjunctive Queries with Negation over**\(\mathcal{ELH}_\bot\)**Ontologies**. In Francesco Calimeri, Nicola Leone, and Marco Manna, editors,*Proc. of the 16th European Conf. on Logics in Artificial Intelligence (JELIA'19)*, volume 11468 of*Lecture Notes in Artificial Intelligence*, pages 371–386. Rende, Italy, Springer, 2019.Abstract BibTeX Entry PDF File PDF File (Extended Technical Report) DOI ©Springer-Verlag

Ontology-mediated query answering is a popular paradigm for enriching answers to user queries with background knowledge. For querying the absence of information, however, there exist only few ontology-based approaches. Moreover, these proposals conflate the closed-domain and closed-world assumption, and therefore are not suited to deal with the anonymous objects that are common in ontological reasoning. We propose a new closed-world semantics for answering conjunctive queries with negation over ontologies formulated in the description logic \(\mathcal{ELH}_\bot\), which is based on the minimal canonical model. We propose a rewriting strategy for dealing with negated query atoms, which shows that query answering is possible in polynomial time in data complexity.

@inproceedings{ BoFo-JELIA19, address = {Rende, Italy}, author = {Stefan {Borgwardt} and Walter {Forkel}}, booktitle = {Proc.\ of the 16th European Conf.\ on Logics in Artificial Intelligence (JELIA'19)}, doi = {https://doi.org/10.1007/978-3-030-19570-0_24}, editor = {Francesco {Calimeri} and Nicola {Leone} and Marco {Manna}}, pages = {371--386}, publisher = {Springer}, series = {Lecture Notes in Artificial Intelligence}, title = {Closed-World Semantics for Conjunctive Queries with Negation over {$\mathcal{ELH}_\bot$} Ontologies}, volume = {11468}, year = {2019}, }

Stefan Borgwardt and Walter Forkel:

Abstract BibTeX Entry PDF File

**Closed-World Semantics for Conjunctive Queries with Negation over**\(\mathcal{ELH}_\bot\)**Ontologies (Extended Abstract)**. In Mantas Simkus and Grant Weddell, editors,*Proceedings of the 32nd International Workshop on Description Logics (DL'19)*, volume 2373 of*CEUR Workshop Proceedings*. Oslo, Norway, CEUR-WS, 2019.Abstract BibTeX Entry PDF File

Ontology-mediated-query-answering is a popular paradigm for enriching answers to user queries with background knowledge. For querying the absence of information, however, there exist only few ontology-based approaches. Moreover, these proposals conflate the closed-domain and closed-world assumption, and therefore are not suited to deal with the anonymous objects that are common in ontological reasoning. We propose a new closed-world semantics for answering conjunctive queries with negation over ontologies formulated in the description logic \(\mathcal{ELH}_\bot\), which is based on the minimal canonical model. We propose a rewriting strategy for dealing with negated query atoms, which shows that query answering is possible in polynomial time in data complexity.

@inproceedings{ BoFo-DL19, address = {Oslo, Norway}, author = {Stefan {Borgwardt} and Walter {Forkel}}, booktitle = {Proceedings of the 32nd International Workshop on Description Logics (DL'19)}, editor = {Mantas {Simkus} and Grant {Weddell}}, publisher = {CEUR-WS}, series = {CEUR Workshop Proceedings}, title = {Closed-World Semantics for Conjunctive Queries with Negation over {$\mathcal{ELH}_\bot$} Ontologies (Extended Abstract)}, volume = {2373}, year = {2019}, }

Stefan Borgwardt, Walter Forkel, and Alisa Kovtunova:

Abstract BibTeX Entry PDF File PDF File (Extended Technical Report) ©Springer-Verlag

**Finding New Diamonds: Temporal Minimal- World Query Answering over Sparse ABoxes**. In Paul Foder, Marco Montali, Diego Calvanese, and Dumitru Roman, editors,*Proc. of the 3rd International Joint Conference on Rules and Reasoning (RuleML+RR'19)*. Bolzano, Italy, Springer, 2019. To appear.Abstract BibTeX Entry PDF File PDF File (Extended Technical Report) ©Springer-Verlag

Lightweight temporal ontology languages have become a very active field of research in recent years. Many real-world applications, like processing electronic health records (EHRs), inherently contain a temporal dimension, and require efficient reasoning algorithms. Moreover, since medical data is not recorded on a regular basis, reasoners must deal with sparse data with potentially large temporal gaps. In this paper, we introduce a temporal extension of the tractable language ELH bottom, which features a new class of convex diamond operators that can be used to bridge temporal gaps. We develop a completion algorithm for our logic, which shows that entailment remains tractable. Based on this, we develop a minimal-world semantics for answering metric temporal conjunctive queries with negation. We show that query answering is combined first-order rewritable, and hence in polynomial time in data complexity.

@inproceedings{ BoFoKo-RRML, address = {Bolzano, Italy}, author = {Stefan {Borgwardt} and Walter {Forkel} and Alisa {Kovtunova}}, booktitle = {Proc.\ of the 3rd International Joint Conference on Rules and Reasoning (RuleML+RR'19)}, editor = {Paul {Foder} and Marco {Montali} and Diego {Calvanese} and Dumitru {Roman}}, note = {To appear.}, publisher = {Springer}, title = {Finding New Diamonds: Temporal Minimal- World Query Answering over Sparse ABoxes}, year = {2019}, }

Camille Bourgaux, Patrick Koopmann, and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File

**Ontology-mediated query answering over temporal and inconsistent data**.*Semantic Web*, 10(3):475–521, 2019.Abstract BibTeX Entry PDF File

Stream-based reasoning systems process data stemming from different sources that are received over time. In this kind of applications, reasoning needs to cope with the temporal dimension and should be resilient against inconsistencies in the data. Motivated by such settings, this paper addresses the problem of handling inconsistent data in a temporal version of ontology-mediated query answering. We consider a recently proposed temporal query language that combines conjunctive queries with operators of propositional linear temporal logic (LTL), and consider these under three inconsistency-tolerant semantics that have been introduced for querying inconsistent description logic knowledge bases. We investigate their complexity for temporal \(\mathcal{EL}_\bot\) and \(\text{DL-Lite}_\mathcal{R}\) knowledge bases. In particular, we consider two different cases, depending on the presence of negations in the query. Furthermore, we complete the complexity picture for the consistent case. We also provide two approaches toward practical algorithms for inconsistency-tolerant temporal query answering.

@article{ BouKooTur2019, author = {Camille {Bourgaux} and Patrick {Koopmann} and Anni-Yasmin {Turhan}}, journal = {Semantic Web}, number = {3}, pages = {475--521}, title = {Ontology-mediated query answering over temporal and inconsistent data}, volume = {10}, year = {2019}, }

David Carral, Larry González, and Patrick Koopmann:

Abstract BibTeX Entry PDF File

**From Horn-**\(\mathcal{SRIQ}\)**to Datalog: A Data-Independent Transformation that Preserves Assertion Entailment (Abstract)**. In Mantas Simkus and Grant Weddell, editors,*Proceedings of the 32nd International Workshop on Description Logics (DL'19)*, volume 2373 of*CEUR Workshop Proceedings*. Oslo, Norway, CEUR-WS, 2019.Abstract BibTeX Entry PDF File

Ontology-based access to large data-sets has recently gained a lot of attention. To access data efficiently, one approach is to rewrite the ontology into Datalog, and then use powerful Datalog engines to compute implicit entailments. Existing rewriting techniques support Description Logics (DLs) from \(\mathcal{ELH}\) to Horn-\(\mathcal{SHIQ}\). We go one step further and present one such data-independent rewriting technique for Horn-\(\mathcal{SRIQ}_\sqcap\), the extension of Horn-\(\mathcal{SHIQ}\) that supports role chain axioms, an expressive feature prominently used in many real-world ontologies. We evaluated our rewriting technique on a large known corpus of ontologies. Our experiments show that the resulting rewritings are of moderate size, and that our approach is more efficient than state-of-the-art DL reasoners when reasoning with data-intensive ontologies.

@inproceedings{ CaGoKo-DL19, address = {Oslo, Norway}, author = {David {Carral} and Larry {Gonz\'alez} and Patrick {Koopmann}}, booktitle = {Proceedings of the 32nd International Workshop on Description Logics (DL'19)}, editor = {Mantas {Simkus} and Grant {Weddell}}, publisher = {CEUR-WS}, series = {CEUR Workshop Proceedings}, title = {From {Horn}-{$\mathcal{SRIQ}$} to {Datalog}: A Data-Independent Transformation that Preserves Assertion Entailment (Abstract)}, volume = {2373}, year = {2019}, }

David Carral, Larry González, and Patrick Koopmann:

Abstract BibTeX Entry PDF File PDF File (Extended Technical Report) Evaluation Files

**From Horn-**\(\mathcal{SRIQ}\)**to Datalog: A Data-Independent Transformation that Preserves Assertion Entailment**. In Pascal Van Hentenryck and Zhi-Hua Zhou, editors,*Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI'19)*, pages 2736–2743. AAAI Press, 2019.Abstract BibTeX Entry PDF File PDF File (Extended Technical Report) Evaluation Files

@inproceedings{ CaGoKo-AAAI-19, author = {David {Carral} and Larry {Gonz\'alez} and Patrick {Koopmann}}, booktitle = {Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI'19)}, editor = {Pascal Van {Hentenryck} and Zhi-Hua {Zhou}}, pages = {2736--2743}, publisher = {{AAAI} Press}, title = {From {Horn}-{$\mathcal{SRIQ}$} to {Datalog}: {A} Data-Independent Transformation that Preserves Assertion Entailment}, year = {2019}, }

Patrick Koopmann:

Abstract BibTeX Entry PDF File PDF File (Extended Technical Report)

**Maybe Eventually? Towards Combining Temporal and Probabilistic Description Logics and Queries**. In Mantas Simkus and Grant Weddell, editors,*Proceedings of the 32nd International Workshop on Description Logics (DL'19)*, volume 2373 of*CEUR Workshop Proceedings*. Oslo, Norway, CEUR-WS, 2019.Abstract BibTeX Entry PDF File PDF File (Extended Technical Report)

We present some initial results on ontology-based query answering with description logic ontologies that may employ temporal and probabilistic operators on concepts and axioms. Specifically, we consider description logics extended with operators from linear temporal logic (LTL), as well as subjective probability operators, and an extended query language in which conjunctive queries can be combined using these operators. We first show some complexity results for the setting in which either only temporal operators or only probabilistic operators may be used, both in the ontology and in the query, and then show a TwoExpSpace lower bound for the setting in which both types of operators can be used together.

@inproceedings{ Ko-DL19b, address = {Oslo, Norway}, author = {Patrick {Koopmann}}, booktitle = {Proceedings of the 32nd International Workshop on Description Logics (DL'19)}, editor = {Mantas {Simkus} and Grant {Weddell}}, publisher = {CEUR-WS}, series = {CEUR Workshop Proceedings}, title = {Maybe Eventually? Towards Combining Temporal and Probabilistic Description Logics and Queries}, volume = {2373}, year = {2019}, }

Patrick Koopmann:

Abstract BibTeX Entry PDF File PDF File (Extended Technical Report)

**Ontology-Based Query Answering for Probabilistic Temporal Data**. In Pascal Van Hentenryck and Zhi-Hua Zhou, editors,*Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI'19)*, pages 2903–2910. AAAI Press, 2019.Abstract BibTeX Entry PDF File PDF File (Extended Technical Report)

We investigate ontology-based query answering for data that are both temporal and probabilistic, which might occur in contexts such as stream reasoning or situation recognition with uncertain data. We present a framework that allows to represent temporal probabilistic data, and introduce a query language with which complex temporal and probabilistic patterns can be described. Specifically, this language combines conjunctive queries with operators from linear time logic as well as probability operators. We analyse the complexities of evaluating queries in this language in various settings. While in some cases, combining the temporal and the probabilistic dimension in such a way comes at the cost of increased complexity, we also determine cases for which this increase can be avoided.

@inproceedings{ Ko-AAAI-19, author = {Patrick {Koopmann}}, booktitle = {Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI'19)}, editor = {Pascal Van {Hentenryck} and Zhi-Hua {Zhou}}, pages = {2903--2910}, publisher = {{AAAI} Press}, title = {Ontology-Based Query Answering for Probabilistic Temporal Data}, year = {2019}, }

Patrick Koopmann:

Abstract BibTeX Entry PDF File

**Ontology-Based Query Answering for Probabilistic Temporal Data (Abstract)**. In Mantas Simkus and Grant Weddell, editors,*Proceedings of the 32nd International Workshop on Description Logics (DL'19)*, volume 2373 of*CEUR Workshop Proceedings*. Oslo, Norway, CEUR-WS, 2019.Abstract BibTeX Entry PDF File

@inproceedings{ Ko-DL19, address = {Oslo, Norway}, author = {Patrick {Koopmann}}, booktitle = {Proceedings of the 32nd International Workshop on Description Logics (DL'19)}, editor = {Mantas {Simkus} and Grant {Weddell}}, publisher = {CEUR-WS}, series = {CEUR Workshop Proceedings}, title = {Ontology-Based Query Answering for Probabilistic Temporal Data (Abstract)}, volume = {2373}, year = {2019}, }

Francesco Kriegel:

Abstract BibTeX Entry PDF File DOI ©Springer-Verlag Extended Technical Report

**Joining Implications in Formal Contexts and Inductive Learning in a Horn Description Logic**. In Diana Cristea, Florence Le Ber, and Barış Sertkaya, editors,*15th International Conference on Formal Concept Analysis, ICFCA 2019, Frankfurt, Germany, June 25-28, 2019, Proceedings*, volume 11511 of*Lecture Notes in Computer Science*, pages 110–129. Springer, 2019.Abstract BibTeX Entry PDF File DOI ©Springer-Verlag Extended Technical Report

A joining implication is a restricted form of an implication where it is explicitly specified which attributes may occur in the premise and in the conclusion, respectively. A technique for sound and complete axiomatization of joining implications valid in a given formal context is provided. In particular, a canonical base for the joining implications valid in a given formal context is proposed, which enjoys the property of being of minimal cardinality among all such bases. Background knowledge in form of a set of valid joining implications can be incorporated. Furthermore, an application to inductive learning in a Horn description logic is proposed, that is, a procedure for sound and complete axiomatization of \(\textsf{Horn-}\mathcal{M}\) concept inclusions from a given interpretation is developed. A complexity analysis shows that this procedure runs in deterministic exponential time.

@inproceedings{ Kr-ICFCA19, author = {Francesco {Kriegel}}, booktitle = {15th International Conference on Formal Concept Analysis, {ICFCA} 2019, Frankfurt, Germany, June 25-28, 2019, Proceedings}, doi = {https://dx.doi.org/10.1007/978-3-030-21462-3_9}, editor = {Diana {Cristea} and Florence {Le Ber} and Bar\i{}\c{s} {Sertkaya}}, pages = {110--129}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {{Joining Implications in Formal Contexts and Inductive Learning in a Horn Description Logic}}, volume = {11511}, year = {2019}, }

Francesco Kriegel:

Abstract BibTeX Entry PDF File DOI ©Springer-Verlag Extended Technical Report

**Learning Description Logic Axioms from Discrete Probability Distributions over Description Graphs**. In Francesco Calimeri, Nicola Leone, and Marco Manna, editors,*16th European Conference on Logics in Artificial Intelligence, JELIA 2019, Rende, Italy, May 7-11, 2019, Proceedings*, volume 11468 of*Lecture Notes in Computer Science*, pages 399–417. Springer, 2019.Abstract BibTeX Entry PDF File DOI ©Springer-Verlag Extended Technical Report

Description logics in their standard setting only allow for representing and reasoning with crisp knowledge without any degree of uncertainty. Of course, this is a serious shortcoming for use cases where it is impossible to perfectly determine the truth of a statement. For resolving this expressivity restriction, probabilistic variants of description logics have been introduced. Their model-theoretic semantics is built upon so-called probabilistic interpretations, that is, families of directed graphs the vertices and edges of which are labeled and for which there exists a probability measure on this graph family.

Results of scientific experiments, e.g., in medicine, psychology, or biology, that are repeated several times can induce probabilistic interpretations in a natural way. In this document, we shall develop a suitable axiomatization technique for deducing terminological knowledge from the assertional data given in such probabilistic interpretations. More specifically, we consider a probabilistic variant of the description logic \(\mathcal{E\mkern-1.618mu L}^{\!\bot}\), and provide a method for constructing a set of rules, so-called concept inclusions, from probabilistic interpretations in a sound and complete manner.

@inproceedings{ Kr-JELIA19, author = {Francesco {Kriegel}}, booktitle = {16th European Conference on Logics in Artificial Intelligence, {JELIA} 2019, Rende, Italy, May 7-11, 2019, Proceedings}, doi = {https://dx.doi.org/10.1007/978-3-030-19570-0_26}, editor = {Francesco {Calimeri} and Nicola {Leone} and Marco {Manna}}, pages = {399--417}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {{Learning Description Logic Axioms from Discrete Probability Distributions over Description Graphs}}, volume = {11468}, year = {2019}, }

Francesco Kriegel:

Abstract BibTeX Entry PDF File DOI ©Elsevier

**Most Specific Consequences in the Description Logic**\(\mathcal{E\mkern-1.618mu L}\).*Discrete Applied Mathematics*, 2019. To appear.Abstract BibTeX Entry PDF File DOI ©Elsevier

The notion of a most specific consequence with respect to some terminological box is introduced, conditions for its existence in the description logic \(\mathcal{E\mkern-1.618mu L}\) and its variants are provided, and means for its computation are developed. Algebraic properties of most specific consequences are explored. Furthermore, several applications that make use of this new notion are proposed and, in particular, it is shown how given terminological knowledge can be incorporated in existing approaches for the axiomatization of observations. For instance, a procedure for an incremental learning of concept inclusions from sequences of interpretations is developed.

@article{ Kr-DAM19, author = {Francesco {Kriegel}}, doi = {https://doi.org/10.1016/j.dam.2019.01.029}, journal = {Discrete Applied Mathematics}, note = {To appear.}, title = {{Most Specific Consequences in the Description Logic $\mathcal{E\mkern-1.618mu L}$}}, year = {2019}, }

Friedrich Michel, Anni-Yasmin Turhan, and Benjamin Zarrieß:

Abstract BibTeX Entry PDF File

**Efficient TBox Reasoning with Value Restrictions—Introducing the Flower Reasoner**. In Paul Fodor and Marco Montalil, editors,*Proceedings of the 3rd International Joint Conference on Rules and Reasoning (RuleML+RR 2019)*, volume to appear of*LNCS*. Bolzano, Italy, Springer, 2019.Abstract BibTeX Entry PDF File

The Description Logic (DL) FL0 uses universal quantification, whereas its well-known counter-part EL uses the existential one. While for EL deciding subsumption in the presence of general TBoxes is tractable, this is no the case for FL0. We present a novel algorithm for solving the ExpTime-hard subsumption problem in FL0 w.r.t. general TBoxes, which is based on the computation of so-called least functional models. To build a such a model our algorithm treats TBox axioms as rules that are applied to objects of the interpretation domain. This algorithm is implemented in the FLower reasoner, which uses a variant of the Rete pattern matching algorithm to find applicable rules. We present an evaluation of FLower on a large set of TBoxes generated from real world ontologies. The experimental results indicate that our prototype implementation of the specialised technique for FL0 leads in most cases to a huge performance gain in comparison to the highly-optimised tableau reasoners.

@inproceedings{ MiTuZa-RuleML19, address = {Bolzano, Italy}, author = {Friedrich {Michel} and Anni-Yasmin {Turhan} and Benjamin {Zarrie{\ss}}}, booktitle = {Proceedings of the 3rd International Joint Conference on Rules and Reasoning (RuleML+RR 2019)}, editor = {Paul {Fodor} and Marco {Montalil}}, publisher = {Springer}, series = {LNCS}, title = {Efficient TBox Reasoning with Value Restrictions---Introducing the Flower Reasoner}, volume = {to appear}, year = {2019}, }

Satyadharma Tirtarasa and Benjamin Zarrieß:

Abstract BibTeX Entry PDF File

**Projection in a Description Logic of Context with Actions**. In Mantas Simkus and Grant Weddell, editors,*Proceedings of the 32nd International Workshop on Description Logics (DL'19)*, volume 2373 of*CEUR Workshop Proceedings*. Oslo, Norway, CEUR-WS, 2019.Abstract BibTeX Entry PDF File

Projection is the problem of checking whether the execution of a given sequence of actions will achieve its goal starting from some initial state. In this paper, we study a setting where we combine a two-dimensional Description Logic of context (ConDL) with an action formalism. We choose a well-studied ConDL where both: the possible states of a dynamical system itself (object level) and also different context-dependent views on this system state (context level) are organised in relational structures and can be described using usual DL constructs. To represent how such a system and its views evolve we introduce a suitable action formalism. It allows one to describe change on both levels. Furthermore, the observable changes on the object level due to an action execution can also be context-dependent. We show that the formalism is well-behaved in the sense that projection has the same complexity as standard reasoning tasks in case \( \mathcal{ALCO} \) is the underlying DL.

@inproceedings{ TiZa-DL-19, address = {Oslo, Norway}, author = {Satyadharma {Tirtarasa} and Benjamin {Zarrie{\ss}}}, booktitle = {Proceedings of the 32nd International Workshop on Description Logics (DL'19)}, editor = {Mantas {Simkus} and Grant {Weddell}}, publisher = {CEUR-WS}, series = {CEUR Workshop Proceedings}, title = {Projection in a Description Logic of Context with Actions}, volume = {2373}, year = {2019}, }

Marco Wilhelm, Gabriele Kern-Isberner, Andreas Ecke, and Franz Baader:

Abstract BibTeX Entry PDF File DOI ©Springer-Verlag

**Counting Strategies for the Probabilistic Description Logic**\(\mathcal{ALC}^{\mathsf{ME}}\)**Under the Principle of Maximum Entropy**. In Francesco Calimeri, Nicola Leone, and Marco Manna, editors,*16th European Conference on Logics in Artificial Intelligence, JELIA 2019, Rende, Italy, May 7-11, 2019, Proceedings*, volume 11468 of*Lecture Notes in Computer Science*, pages 434–449. Springer, 2019.Abstract BibTeX Entry PDF File DOI ©Springer-Verlag

We present \(\mathcal{ALC}^{\mathsf{ME}}\), a probabilistic variant of the Description Logic \(\mathcal{ALC}\) that allows for representing and processing conditional statements of the form ``if \(E\) holds, then \(F\) follows with probability \(p\)'' under the principle of maximum entropy. Probabilities are understood as degrees of belief and formally interpreted by the aggregating semantics. We prove that both checking consistency and drawing inferences based on approximations of the maximum entropy distribution is possible in \(\mathcal{ALC}^{\mathsf{ME}}\) in time polynomial in the domain size. A major problem for probabilistic reasoning from such conditional knowledge bases is to count models and individuals. To achieve our complexity results, we develop sophisticated counting strategies on interpretations aggregated with respect to the so-called conditional impacts of types, which refine their conditional structure.

@inproceedings{ WiKeEcBa-JELIA19, author = {Marco {Wilhelm} and Gabriele {Kern-Isberner} and Andreas {Ecke} and Franz {Baader}}, booktitle = {16th European Conference on Logics in Artificial Intelligence, {JELIA} 2019, Rende, Italy, May 7-11, 2019, Proceedings}, doi = {https://dx.doi.org/10.1007/978-3-030-19570-0_28}, editor = {Francesco {Calimeri} and Nicola {Leone} and Marco {Manna}}, pages = {434--449}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {{Counting Strategies for the Probabilistic Description Logic $\mathcal{ALC}^{\mathsf{ME}}$ Under the Principle of Maximum Entropy}}, volume = {11468}, year = {2019}, }

Chao Xu, Walter Forkel, Stefan Borgwardt, Franz Baader, and Beihai Zhou:

Abstract BibTeX Entry PDF File

**Automatic Translation of Clinical Trial Eligibility Criteria into Formal Queries**. In Frank Loebe, editor,*Proc. of the 9th Workshop on Ontologies and Data in Life Sciences (ODLS'19), part of The Joint Ontology Workshops (JOWO'19)*, 2019. To appear.Abstract BibTeX Entry PDF File

Selecting patients for clinical trials is very labor-intensive. Our goal is to develop an automated system that can support doctors in this task. This paper describes a major step towards such a system: the automatic translation of clinical trial eligibility criteria from natural language into formal, logic-based queries. First, we develop a semantic annotation process that can capture many types of clinical trial criteria. Then, we map the annotated criteria to the formal query language. We have built a prototype system based on state-of-the-art NLP tools such as Word2Vec, Stanford NLP tools, and the MetaMap Tagger, and have evaluated the quality of the produced queries on a number of criteria from clinicaltrials.gov. Finally, we discuss some criteria that were hard to translate, and give suggestions for how to formulate eligibility criteria to make them easier to translate automatically.

@inproceedings{ XFB-ODLS15, address = {Graz, Austria}, author = {Chao {Xu} and Walter {Forkel} and Stefan {Borgwardt} and Franz {Baader} and Beihai {Zhou}}, booktitle = {Proc.\ of the 9th Workshop on Ontologies and Data in Life Sciences (ODLS'19), part of The Joint Ontology Workshops (JOWO'19)}, editor = {Frank {Loebe}}, note = {To appear.}, title = {Automatic Translation of Clinical Trial Eligibility Criteria into Formal Queries}, year = {2019}, }

## 2018

Christian Alrabbaa, Sebastian Rudolph, and Lukas Schweizer:

Abstract BibTeX Entry PDF File

**Faceted Answer-Set Navigation**. In Christoph Benzmüller and Francesco Ricca and Xavier Parent and Dumitru Roman, editors,*Proceedings of Rules and Reasoning - Second International Joint Conference, RuleML+RR 2018*, volume 11092 of*Lecture Notes in Computer Science*, pages 211–225. Springer, 2018.Abstract BibTeX Entry PDF File

Even for small logic programs, the number of resulting answer-sets can be tremendous. In such cases, users might be incapable of comprehending the space of answer-sets as a whole nor being able to identify a specific answer-set according to their needs. To overcome this difficulty, we propose a general formal framework that takes an arbitrary logic program as input, and allows for navigating the space of answer- sets in a systematic interactive way analogous to faceted browsing. The navigation is carried out stepwise, where each step narrows down the remaining solutions, eventually arriving at a single one. We formulate two navigation modes, one stringent conflict avoiding, and a “free” mode, where conflicting selections of facets might occur. For the latter mode, we provide efficient algorithms for resolving the conflicts. We provide an implementation of our approach and demonstrate that our framework is able to handle logic programs for which it is currently infeasible to retrieve all answer sets.

@inproceedings{ AlRuSc-RR18, author = {Christian {Alrabbaa} and Sebastian {Rudolph} and Lukas {Schweizer}}, booktitle = {Proceedings of Rules and Reasoning - Second International Joint Conference, RuleML+RR 2018}, editor = {Christoph Benzm{\"{u}}ller and Francesco Ricca and Xavier {Parent} and Dumitru {Roman}}, pages = {211--225}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Faceted Answer-Set Navigation}, volume = {11092}, year = {2018}, }

Franz Baader, Stefan Borgwardt, and Walter Forkel:

Abstract BibTeX Entry PDF File DOI

**Patient Selection for Clinical Trials Using Temporalized Ontology-Mediated Query Answering**. In*Proc. of the 1st Int. Workshop on Hybrid Question Answering with Structured and Unstructured Knowledge (HQA'18), Companion of the The Web Conference 2018*, pages 1069–1074. ACM, 2018.Abstract BibTeX Entry PDF File DOI

Finding suitable candidates for clinical trials is a labor-intensive task that requires expert medical knowledge. Our goal is to design (semi-)automated techniques that can support clinical researchers in this task. We investigate the issues involved in designing formal query languages for selecting patients that are eligible for a given clinical trial, leveraging existing ontology-based query answering techniques. In particular, we propose to use a temporal extension of existing approaches for accessing data through ontologies written in Description Logics. We sketch how such a query answering system could work and show that eligibility criteria and patient data can be adequately modeled in our formalism.

@inproceedings{ BaBF-HQA18, author = {Franz {Baader} and Stefan {Borgwardt} and Walter {Forkel}}, booktitle = {Proc.\ of the 1st Int.\ Workshop on Hybrid Question Answering with Structured and Unstructured Knowledge (HQA'18), Companion of the The Web Conference 2018}, doi = {https://dx.doi.org/10.1145/3184558.3191538}, pages = {1069--1074}, publisher = {ACM}, title = {Patient Selection for Clinical Trials Using Temporalized Ontology-Mediated Query Answering}, year = {2018}, }

Franz Baader, Oliver Fernández Gil, and Pavlos Marantidis:

Abstract BibTeX Entry PDF File DOI

**Matching in the Description Logic**\(\mathcal{FL}_0\)**with respect to General TBoxes**. In Gilles Barthe, Geoff Sutcliffe, and Margus Veanes, editors,*LPAR-22. 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning*, volume 57 of*EPiC Series in Computing*, pages 76–94. EasyChair, 2018.Abstract BibTeX Entry PDF File DOI

@inproceedings{ BaFeMa18-LPAR, author = {Franz {Baader} and Oliver {Fern\'andez Gil} and Pavlos {Marantidis}}, booktitle = {LPAR-22. 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning}, doi = {https://dx.doi.org/10.29007/q74p}, editor = {Gilles {Barthe} and Geoff {Sutcliffe} and Margus {Veanes}}, pages = {76--94}, publisher = {EasyChair}, series = {EPiC Series in Computing}, title = {Matching in the Description Logic $\mathcal{FL}_0$ with respect to General TBoxes}, volume = {57}, year = {2018}, }

Franz Baader, Oliver Fernández Gil, and Maximilian Pensel:

Abstract BibTeX Entry PDF File DOI

**Standard and Non-Standard Inferences in the Description Logic**\(\mathcal{FL}_0\)**Using Tree Automata**. In Daniel Lee, Alexander Steen, and Toby Walsh, editors,*GCAI 2018, 4th Global Conference on Artificial Intelligence, Luxembourg, September 2018.*, volume 55 of*EPiC Series in Computing*, pages 1–14. EasyChair, 2018.Abstract BibTeX Entry PDF File DOI

Although being quite inexpressive, the description logic (DL) FL0, which provides only conjunction, value restriction and the top concept as concept constructors, has an intractable subsumption problem in the presence of terminologies (TBoxes): subsumption reasoning w.r.t. acyclic FL0 TBoxes is coNP-complete, and becomes even ExpTime-complete in case general TBoxes are used. In the present paper, we use automata working on infinite trees to solve both standard and non-standard inferences in FL0 w.r.t. general TBoxes. First, we give an alternative proof of the ExpTime upper bound for subsumption in FL0 w.r.t. general TBoxes based on the use of looping tree automata. Second, we employ parity tree automata to tackle non-standard inference problems such as computing the least common subsumer and the difference of FL0 concepts w.r.t. general TBoxes.

@inproceedings{ BaFePe-GCAI-18, author = {Franz {Baader} and Oliver {Fern\'andez Gil} and Maximilian {Pensel}}, booktitle = {{GCAI} 2018, 4th Global Conference on Artificial Intelligence, Luxembourg, September 2018.}, doi = {https://dx.doi.org/10.29007/scbw}, editor = {Daniel {Lee} and Alexander {Steen} and Toby {Walsh}}, pages = {1--14}, publisher = {EasyChair}, series = {EPiC Series in Computing}, title = {Standard and Non-Standard Inferences in the Description Logic {$\mathcal{FL}_0$} Using Tree Automata}, volume = {55}, year = {2018}, }

Franz Baader, Francesco Kriegel, Adrian Nuradiansyah, and Rafael Peñaloza:

BibTeX Entry PDF File PDF File (ceur-ws.org) Full Conference Paper

**Making Repairs in Description Logics More Gentle (Extended Abstract)**. In Magdalena Ortiz and Thomas Schneider, editors,*Proceedings of the 31st International Workshop on Description Logics, Tempe, Arizona, October 27-29, 2018*, volume 2211 of*CEUR Workshop Proceedings*. CEUR-WS.org, 2018.BibTeX Entry PDF File PDF File (ceur-ws.org) Full Conference Paper

@inproceedings{ BaKrNuPe-DL2018, author = {Franz {Baader} and Francesco {Kriegel} and Adrian {Nuradiansyah} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 31st International Workshop on Description Logics, Tempe, Arizona, October 27-29, 2018}, editor = {Magdalena {Ortiz} and Thomas {Schneider}}, publisher = {CEUR-WS.org}, series = {{CEUR} Workshop Proceedings}, title = {{Making Repairs in Description Logics More Gentle (Extended Abstract)}}, volume = {2211}, year = {2018}, }

Franz Baader, Francesco Kriegel, Adrian Nuradiansyah, and Rafael Peñaloza:

Abstract BibTeX Entry PDF File ©AAAI Extended Abstract Extended Technical Report

**Making Repairs in Description Logics More Gentle**. In Frank Wolter, Michael Thielscher, and Francesca Toni, editors,*Principles of Knowledge Representation and Reasoning: Proceedings of the Sixteenth International Conference, KR 2018, Tempe, Arizona, 30 October - 2 November 2018*, pages 319–328. USA, AAAI Press, 2018.Abstract BibTeX Entry PDF File ©AAAI Extended Abstract Extended Technical Report

The classical approach for repairing a Description Logic ontology \(\mathfrak{O}\) in the sense of removing an unwanted consequence \(\alpha\) is to delete a minimal number of axioms from \(\mathfrak{O}\) such that the resulting ontology \(\mathfrak{O}'\) does not have the consequence \(\alpha\). However, the complete deletion of axioms may be too rough, in the sense that it may also remove consequences that are actually wanted. To alleviate this problem, we propose a more gentle notion of repair in which axioms are not deleted, but only weakened. On the one hand, we investigate general properties of this gentle repair method. On the other hand, we propose and analyze concrete approaches for weakening axioms expressed in the Description Logic \(\mathcal{E\mkern-1.618mu L}\).

@inproceedings{ BaKrNuPe-KR2018, address = {USA}, author = {Franz {Baader} and Francesco {Kriegel} and Adrian {Nuradiansyah} and Rafael {Pe{\~n}aloza}}, booktitle = {Principles of Knowledge Representation and Reasoning: Proceedings of the Sixteenth International Conference, {KR} 2018, Tempe, Arizona, 30 October - 2 November 2018}, editor = {Frank {Wolter} and Michael {Thielscher} and Francesca {Toni}}, pages = {319--328}, publisher = {{AAAI} Press}, title = {{Making Repairs in Description Logics More Gentle}}, year = {2018}, }

Franz Baader, Pavlos Marantidis, and Antoine Mottet:

Abstract BibTeX Entry PDF File

**ACUI Unification modulo Ground Theories**. In Mauricio Ayala-Rincón and Philippe Balbiani, editors,*Proceedings of the 32th International Workshop on Unification (UNIF 2018)*, 2018.Abstract BibTeX Entry PDF File

It is well-known that the unification problem for a binary associative-commutative-idempotent function symbol with a unit (ACUI-unification) is polynomial for unification with constants and NP-complete for general unification. We prove that the same is true if we add a finite set of ground identities. To be more precise, we first show that not only unification with constants, but also unification with linear constant restrictions is in P for any extension of ACUI with a finite set of ground identities. Using well-known combination results for unification algorithms, this then yields an NP-upper bound for general unification modulo such a theory. The matching lower bound can be shown as in the case without ground identities.

@inproceedings{ BaMaMo-UNIF2018, address = {Oxford, UK}, author = {Franz {Baader} and Pavlos {Marantidis} and Antoine {Mottet}}, booktitle = {Proceedings of the 32th International Workshop on Unification ({UNIF 2018})}, editor = {Mauricio {Ayala-Rinc{\'o}n} and Philippe {Balbiani}}, title = {ACUI Unification modulo Ground Theories}, year = {2018}, }

Franz Baader, Pavlos Marantidis, and Maximilian Pensel:

Abstract BibTeX Entry PDF File DOI

**The Data Complexity of Answering Instance Queries in**\(\mathcal{FL}_0\). In*Proc. of the Reasoning on Data Workshop (RoD'18), Companion of the The Web Conference 2018*, pages 1603–1607. ACM, 2018.Abstract BibTeX Entry PDF File DOI

Ontology-mediated query answering can be used to access large data sets through a mediating ontology. It has drawn considerable attention in the Description Logic (DL) community where both the complexity of query answering and practical query answering approaches based on rewriting were investigated in detail. Surprisingly, there is still a gap in what is known about the data complexity of query answering w.r.t. ontologies formulated in the inexpressive DL FL0. While it is known that the data complexity of answering conjunctive queries w.r.t. FL0 ontologies is coNP-complete, the exact complexity of answering instance queries was open until now. In the present paper, we show that answering instance queries w.r.t. FL0 ontologies is in P for data complexity. Together with the known lower bound of P-completeness for a fragment of FL0, this closes the gap mentioned above.

@inproceedings{ BaMaPe-RoD-18, author = {Franz {Baader} and Pavlos {Marantidis} and Maximilian {Pensel}}, booktitle = {Proc.\ of the Reasoning on Data Workshop (RoD'18), Companion of the The Web Conference 2018}, doi = {https://dx.doi.org/10.1145/3184558.3191618}, pages = {1603--1607}, publisher = {ACM}, title = {The Data Complexity of Answering Instance Queries in $\mathcal{FL}_0$}, year = {2018}, }

Franz Baader and Adrian Nuradiansyah:

Abstract BibTeX Entry PDF File

**Towards Privacy-Preserving Ontology Publishing**. In Magdalena Ortiz and Thomas Schneider, editors,*Proceedings of the 31st International Workshop on Description Logics, Tempe, Arizona, October 27-29, 2018*,*CEUR Workshop Proceedings*. CEUR-WS.org, 2018.Abstract BibTeX Entry PDF File

We make a first step towards adapting the approach of Cuenca Grau and Kostylev for privacy-preserving publishing of linked data to Description Logic ontologies. We consider the case where both the knowledge about individuals and the privacy policies are expressed using EL concepts. We introduce the notions of compliance of a concept with a policy and of safety of a concept for a policy, and show how optimal compliant (safe) generalizations of a given EL concept can be computed.

@inproceedings{ BaNu-DL2018, author = {Franz {Baader} and Adrian {Nuradiansyah}}, booktitle = {Proceedings of the 31st International Workshop on Description Logics, Tempe, Arizona, October 27-29, 2018}, editor = {Magdalena {Ortiz} and Thomas {Schneider}}, note = {}, publisher = {CEUR-WS.org}, series = {{CEUR} Workshop Proceedings}, title = {{Towards Privacy-Preserving Ontology Publishing}}, year = {2018}, }

Stefan Borgwardt, Ismail Ilkan Ceylan, and Thomas Lukasiewicz:

Abstract BibTeX Entry PDF File

**Recent Advances in Querying Probabilistic Knowledge Bases**. In Jérôme Lang, editor,*Proceedings of the 27th International Joint Conferences on Artificial Intelligence and the 23rd European Conference on Artificial Intelligence (IJCAI-ECAI'18)*, pages 5420–5426. Stockholm, Sweden, IJCAI, 2018. Survey paper.Abstract BibTeX Entry PDF File

We give a survey on recent advances at the forefront of research on probabilistic knowledge bases for representing and querying large-scale automatically extracted data. We concentrate especially on increasing the semantic expressivity of formalisms for representing and querying probabilistic knowledge (i) by giving up the closed-world assumption, (ii) by allowing for commonsense knowledge (and in parallel giving up the tuple-independence assumption), and (iii) by giving up the closed-domain assumption, while preserving some computational properties of query answering in such formalisms.

@inproceedings{ BoCL-IJCAI18, address = {Stockholm, Sweden}, author = {Stefan {Borgwardt} and Ismail Ilkan {Ceylan} and Thomas {Lukasiewicz}}, booktitle = {Proceedings of the 27th International Joint Conferences on Artificial Intelligence and the 23rd European Conference on Artificial Intelligence (IJCAI-ECAI'18)}, editor = {J{\'e}r{\^o}me {Lang}}, note = {Survey paper.}, pages = {5420--5426}, publisher = {IJCAI}, title = {Recent Advances in Querying Probabilistic Knowledge Bases}, year = {2018}, }

Patrick Koopmann:

Abstract BibTeX Entry PDF File PDF File (Extended Technical Report)

**Ontology-Mediated Query Answering for Probabilistic Temporal Data with**\(\mathcal{EL}\)**Ontologies**. In*Proceedings of the 7th Workshop on Dynamics of Knowledge and Belief (DKB-2018) and the 6th Workshop KI & Kognition (KIK-2018)*, volume 2194 of*CEUR-Workshop Proceedings*, pages 68–79. CEUR-WS.org, 2018.Abstract BibTeX Entry PDF File PDF File (Extended Technical Report)

Especially in the field of stream reasoning, there is an increased interest in reasoning about temporal data in order to detect situations of interest or complex events. Ontologies have been proved a useful way to infer missing information from incomplete data, or simply to allow for a higher order vocabulary to be used in the event descriptions. Motivated by this, ontology-based temporal query answering has been proposed as a means for the recognition of situations and complex events. But often, the data to be processed do not only contain temporal information, but also probabilistic information, for example because of uncertain sensor measurements. While there has been a plethora of research on ontology-based temporal query answering, only little is known so far about querying temporal probabilistic data using ontologies. This work addresses this problem by introducing a temporal query language that extends a well-investigated temporal query language with probability operators, and investigating the complexity of answering queries using this query language together with ontologies formulated in the description logic EL.

@inproceedings{ Ko-DKB-KIK-18, author = {Patrick {Koopmann}}, booktitle = {Proceedings of the 7th Workshop on Dynamics of Knowledge and Belief (DKB-2018) and the 6th Workshop KI \& Kognition (KIK-2018)}, pages = {68--79}, publisher = {CEUR-WS.org}, series = {CEUR-Workshop Proceedings}, title = {Ontology-Mediated Query Answering for Probabilistic Temporal Data with {$\mathcal{EL}$} Ontologies}, volume = {2194}, year = {2018}, }

Francesco Kriegel:

Abstract BibTeX Entry PDF File DOI ©Springer-Verlag Extended Technical Report

**Acquisition of Terminological Knowledge in Probabilistic Description Logic**. In Frank Trollmann and Anni-Yasmin Turhan, editors,*KI 2018: Advances in Artificial Intelligence - 41st German Conference on AI, Berlin, Germany, September 24-28, 2018, Proceedings*, volume 11117 of*Lecture Notes in Computer Science*, pages 46–53. Berlin, Germany, Springer, 2018.Abstract BibTeX Entry PDF File DOI ©Springer-Verlag Extended Technical Report

For a probabilistic extension of the description logic \(\mathcal{E\mkern-1.618mu L}^{\bot}\), we consider the task of automatic acquisition of terminological knowledge from a given probabilistic interpretation. Basically, such a probabilistic interpretation is a family of directed graphs the vertices and edges of which are labeled, and where a discrete probability measure on this graph family is present. The goal is to derive so-called concept inclusions which are expressible in the considered probabilistic description logic and which hold true in the given probabilistic interpretation. A procedure for an appropriate axiomatization of such graph families is proposed and its soundness and completeness is justified.

@inproceedings{ Kr-KI18, address = {Berlin, Germany}, author = {Francesco {Kriegel}}, booktitle = {{{KI} 2018: Advances in Artificial Intelligence - 41st German Conference on AI, Berlin, Germany, September 24-28, 2018, Proceedings}}, doi = {https://doi.org/10.1007/978-3-030-00111-7_5}, editor = {Frank {Trollmann} and Anni-Yasmin {Turhan}}, pages = {46--53}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {{Acquisition of Terminological Knowledge in Probabilistic Description Logic}}, volume = {11117}, year = {2018}, }

Francesco Kriegel:

Abstract BibTeX Entry PDF File PDF File (ceur-ws.org)

**The Distributive, Graded Lattice of**\(\mathcal{E\mkern-1.618mu L}\)**Concept Descriptions and its Neighborhood Relation**. In Dmitry I. Ignatov and Lhouari Nourine, editors,*Proceedings of the 14th International Conference on Concept Lattices and Their Applications (CLA 2018)*, volume 2123 of*CEUR Workshop Proceedings*, pages 267–278. Olomouc, Czech Republic, CEUR-WS.org, 2018.Abstract BibTeX Entry PDF File PDF File (ceur-ws.org)

For the description logic \(\mathcal{E\mkern-1.618mu L}\), we consider the neighborhood relation which is induced by the subsumption order, and we show that the corresponding lattice of \(\mathcal{E\mkern-1.618mu L}\) concept descriptions is distributive, modular, graded, and metric. In particular, this implies the existence of a rank function as well as the existence of a distance function.

@inproceedings{ Kr-CLA18, address = {Olomouc, Czech Republic}, author = {Francesco {Kriegel}}, booktitle = {{Proceedings of the 14th International Conference on Concept Lattices and Their Applications ({CLA 2018})}}, editor = {Dmitry I. {Ignatov} and Lhouari {Nourine}}, pages = {267--278}, publisher = {CEUR-WS.org}, series = {{CEUR} Workshop Proceedings}, title = {{The Distributive, Graded Lattice of $\mathcal{E\mkern-1.618mu L}$ Concept Descriptions and its Neighborhood Relation}}, volume = {2123}, year = {2018}, }

Rafael Peñaloza, Veronika Thost, and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File ©AAAI

**Query Answering for Rough**\(\mathcal{EL}\)**Ontologies**. In Michael Thielscher and Francesca Toni, editors,*Proceedings of 16. International Conference on Principles of Knowledge Representation and Reasoning (KR 2018)*,*AAAI*, pages 399–408, 2018.Abstract BibTeX Entry PDF File ©AAAI

Querying large datasets with incomplete and vague data is still a challenge. Ontology-based query answering extends standard database query answering by background knowledge from an ontology to augment incomplete data. We focus on ontologies written in rough description logics (DLs), which allow to represent vague knowledge by partitioning the domain of discourse into classes of indiscernible elements. In this paper, we extend the combined approach for ontology-based query answering to a variant of the DL ELH_{b}ot augmented with rough concept constructors. We show that this extension preserves the good computational properties of classical EL and can be implemented by standard database systems.

@inproceedings{ PeThTu-KR-18, author = {Rafael {Pe\~naloza} and Veronika {Thost} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of 16. International Conference on Principles of Knowledge Representation and Reasoning (KR 2018)}, editor = {Michael {Thielscher} and Francesca {Toni}}, pages = {399--408}, series = {AAAI}, title = {Query Answering for Rough $\mathcal{EL}$ Ontologies}, year = {2018}, }

Maximilian Pensel and Anni-Yasmin Turhan:

Abstract BibTeX Entry DOI

**Reasoning in the Defeasible Description Logic**\(\mathcal{EL}_{\bot}\)**—Computing Standard Inferences under Rational and Relevant Semantics**.*International Journal of Approximate Reasoning (IJAR)*, 103:28–70, 2018.Abstract BibTeX Entry DOI

Defeasible Description Logics (DDLs) extend Description Logics with defeasible concept inclusions. Reasoning in DDLs often employs rational closure according to the (propositional) KLM postulates. A well-known approach to lift this closure to DDLs is by so-called materialisation. Previously investigated algorithms for materialisation-based reasoning employ reductions to classical reasoning using all Boolean connectors. As a first result in this paper, we present a materialisation-based algorithm for the sub-Boolean DDL EL_{bot}, using a reduction to reasoning in classical EL_{bot}, rendering materialisation-based defeasible reasoning tractable. The main contribution of this article is a kind of canonical model construction, which can be used to decide defeasible subsumption and instance queries in EL_{bot}under rational and the stronger relevant entailment. Our so-called typicality models can reproduce the entailments obtained from materialisation-based rational and relevant closure and, more importantly, obtain stronger versions of rational and relevant entailment. These do not suffer from neglecting defeasible information for concepts appearing nested inside quantifications, which all materialisation-based approaches do. We also show the computational complexity of defeasible subsumption and instance checking in our stronger rational and relevant semantics.

@article{ PeTu-IJAR-18, author = {Maximilian {Pensel} and Anni-Yasmin {Turhan}}, doi = {https://doi.org/10.1016/j.ijar.2018.08.005}, journal = {International Journal of Approximate Reasoning ({IJAR})}, pages = {28--70}, title = {Reasoning in the Defeasible Description Logic $\mathcal{EL}_{\bot}$---Computing Standard Inferences under Rational and Relevant Semantics}, volume = {103}, year = {2018}, }

Sebastian Rudolph, Lukas Schweizer, and Satyadharma Tirtarasa:

Abstract BibTeX Entry PDF File (The final publication is available at link.springer.com) ©Springer Nature Switzerland

**Justifications for Description Logic Knowledge Bases Under the Fixed-Domain Semantics**. In Christoph Benzmüller, Francesco Ricca, Xavier Parent, and Dumitru Roman, editors,*Rules and Reasoning*, pages 185–200. Cham, Springer International Publishing, 2018.Abstract BibTeX Entry PDF File (The final publication is available at link.springer.com) ©Springer Nature Switzerland

The fixed-domain semantics for OWL and description logic has been introduced to open up the OWL modeling and reasoning tool landscape for use cases resembling constraint satisfaction problems. While standard reasoning under this new semantics is by now rather well-understood theoretically and supported practically, more elaborate tasks like computation of justifications have not been considered so far, although being highly important in the modeling phase. In this paper, we compare three approaches to this problem: one using standard OWL technology employing an axiomatization of the fixed-domain semantics, one using our dedicated fixed-domain reasoner Wolpertinger in combination with standard justification computation technology, and one where the problem is encoded entirely into answer-set programming.

@inproceedings{ RuScTi-RR-18, address = {Cham}, author = {Sebastian {Rudolph} and Lukas {Schweizer} and Satyadharma {Tirtarasa}}, booktitle = {Rules and Reasoning}, editor = {Christoph {Benzm{\"u}ller} and Francesco {Ricca} and Xavier {Parent} and Dumitru {Roman}}, pages = {185--200}, publisher = {Springer International Publishing}, title = {Justifications for Description Logic Knowledge Bases Under the Fixed-Domain Semantics}, year = {2018}, }

Benjamin Zarrieß:

Abstract BibTeX Entry PDF File ©AAAI

**Complexity of Projection with Stochastic Actions in a Probabilistic Description Logic**. In Frank Wolter, Michael Thielscher, and Francesca Toni, editors,*Principles of Knowledge Representation and Reasoning: Proceedings of the Sixteenth International Conference, KR 2018, Tempe, Arizona, 30 October - 2 November 2018*, pages 514–523. USA, AAAI Press, 2018.Abstract BibTeX Entry PDF File ©AAAI

We consider an action language extended with quantitative notions of uncertainty. In our setting, the initial beliefs of an agent are represented as a probabilistic knowledge base with axioms formulated in the Description Logic ALCO. Action descriptions describe the possibly context-sensitive and non-deterministic effects of actions and provide likelihood distributions over the different possible outcomes of actions. In this paper, we prove decidability of the projection problem which is the basic reasoning task needed for predicting the outcome of action sequences. Furthermore, we investigate how the non-determinism in the action model affects the complexity of the projection problem.

@inproceedings{ Za-KR2018, address = {USA}, author = {Benjamin {Zarrie{\ss}}}, booktitle = {Principles of Knowledge Representation and Reasoning: Proceedings of the Sixteenth International Conference, {KR} 2018, Tempe, Arizona, 30 October - 2 November 2018}, editor = {Frank {Wolter} and Michael {Thielscher} and Francesca {Toni}}, pages = {514--523}, publisher = {{AAAI} Press}, title = {{Complexity of Projection with Stochastic Actions in a Probabilistic Description Logic}}, year = {2018}, }

## 2017

Franz Baader:

Abstract BibTeX Entry PDF File

**A New Description Logic with Set Constraints and Cardinality Constraints on Role Successors**. In Clare Dixon and Marcelo Finger, editors,*Proceedings of the 11th International Symposium on Frontiers of Combining Systems (FroCoS'17)*, volume 10483 of*Lecture Notes in Computer Science*, pages 43–59. Brasília, Brazil, Springer-Verlag, 2017.Abstract BibTeX Entry PDF File

We introduce a new description logic that extends the well-known logic ALCQ by allowing the statement of constraints on role successors that are more general than the qualified number restrictions of ALCQ. To formulate these constraints, we use the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA), in which one can express Boolean combinations of set constraints and numerical constraints on the cardinalities of sets. Though our new logic is considerably more expressive than ALCQ, we are able to show that the complexity of reasoning in it is the same as in ALCQ, both without and with TBoxes.

@inproceedings{ Baader-FroCoS17, address = {Bras{\'i}lia, Brazil}, author = {Franz {Baader}}, booktitle = {Proceedings of the 11th International Symposium on Frontiers of Combining Systems (FroCoS'17)}, editor = {Clare {Dixon} and Marcelo {Finger}}, pages = {43--59}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {A New Description Logic with Set Constraints and Cardinality Constraints on Role Successors}, volume = {10483}, year = {2017}, }

Franz Baader, Daniel Borchmann, and Adrian Nuradiansyah:

Abstract BibTeX Entry PDF File

**Preliminary Results on the Identity Problem in Description Logic Ontologies**. In Alessandro Artale, Birte Glimm, and Roman Kontchakov, editors,*Proceedings of the 30th International Workshop on Description Logics, Montpellier, France, July 18-21, 2017.*, volume 1879 of*CEUR Workshop Proceedings*. CEUR-WS.org, 2017.Abstract BibTeX Entry PDF File

The work in this paper is motivated by a privacy scenario in which the identity of certain persons (represented as anonymous individ- uals) should be hidden. We assume that factual information about known individuals (i.e., individuals whose identity is known) and anonymous individuals is stored in an ABox and general background information is expressed in a TBox, where both the TBox and the ABox are publicly accessible. The identity problem then asks whether one can deduce from the TBox and the ABox that a given anonymous individual is equal to a known one. Since this would reveal the identity of the anonymous indi- vidual, such a situation needs to be avoided. We first observe that not all Description Logics (DLs) are able to derive any such equalities between individuals, and thus the identity problem is trivial in these DLs. We then consider DLs with nominals, number restrictions, or function de- pendencies, in which the identity problem is non-trivial. We show that in these DLs the identity problem has the same complexity as the instance problem. Finally, we consider an extended scenario in which users with different rôles can access different parts of the TBox and ABox, and we want to check whether, by a sequence of rôle changes and queries asked in each rôle, one can deduce the identity of an anonymous individual.

@inproceedings{ DBLP:conf/dlog/BaaderBN17, author = {Franz {Baader} and Daniel {Borchmann} and Adrian {Nuradiansyah}}, booktitle = {Proceedings of the 30th International Workshop on Description Logics, Montpellier, France, July 18-21, 2017.}, editor = {Alessandro {Artale} and Birte {Glimm} and Roman {Kontchakov}}, publisher = {CEUR-WS.org}, series = {{CEUR} Workshop Proceedings}, title = {Preliminary Results on the Identity Problem in Description Logic Ontologies}, volume = {1879}, year = {2017}, }

Franz Baader, Daniel Borchmann, and Adrian Nuradiansyah:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**The Identity Problem in Description Logic Ontologies and Its Application to View-Based Information Hiding**. In Zhe Wang, Anni-Yasmin Turhan, Kewen Wang, and Xiaowang Zhang, editors,*Semantic Technology - 7th Joint International Conference, JIST 2017, Gold Coast, QLD, Australia, November 10-12, 2017, Proceedings*, pages 102–117, 2017.Abstract BibTeX Entry PDF File ©Springer-Verlag

@inproceedings{ BaBoNu-JIST-2017, author = {Franz {Baader} and Daniel {Borchmann} and Adrian {Nuradiansyah}}, booktitle = {Semantic Technology - 7th Joint International Conference, {JIST} 2017, Gold Coast, QLD, Australia, November 10-12, 2017, Proceedings}, editor = {Zhe {Wang} and Anni-Yasmin {Turhan} and Kewen {Wang} and Xiaowang {Zhang}}, pages = {102--117}, title = {The Identity Problem in Description Logic Ontologies and Its Application to View-Based Information Hiding}, year = {2017}, }

Franz Baader, Stefan Borgwardt, Patrick Koopmann, Ana Ozaki, and Veronika Thost:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Metric Temporal Description Logics with Interval-Rigid Names**. In Clare Dixon and Marcelo Finger, editors,*Proceedings of the 11th International Symposium on Frontiers of Combining Systems (FroCoS'17)*, volume 10483 of*Lecture Notes in Computer Science*, pages 60–76, 2017.Abstract BibTeX Entry PDF File ©Springer-Verlag

In contrast to qualitative linear temporal logics, which can be used to state that some property will eventually be satisfied, metric temporal logics allow to formulate constraints on how long it may take until the property is satisfied. While most of the work on combining Description Logics (DLs) with temporal logics has concentrated on qualitative temporal logics, there has recently been a growing interest in extending this work to the quantitative case. In this paper, we complement existing results on the combination of DLs with metric temporal logics over the natural numbers by introducing interval-rigid names. This allows to state that elements in the extension of certain names stay in this extension for at least some specified amount of time.

@inproceedings{ BaBoKoOzTh-FroCoS17, address = {Bras{\'i}lia, Brazil}, author = {Franz {Baader} and Stefan {Borgwardt} and Patrick {Koopmann} and Ana {Ozaki} and Veronika {Thost}}, booktitle = {Proceedings of the 11th International Symposium on Frontiers of Combining Systems (FroCoS'17)}, editor = {Clare {Dixon} and Marcelo {Finger}}, pages = {60--76}, series = {Lecture Notes in Computer Science}, title = {Metric Temporal Description Logics with Interval-Rigid Names}, volume = {10483}, year = {2017}, }

Franz Baader, Stefan Borgwardt, Patrick Koopmann, Ana Ozaki, and Veronika Thost:

Abstract BibTeX Entry PDF File

**Metric Temporal Description Logics with Interval-Rigid Names (Extended Abstract)**. In Alessandro Artale, Birte Glimm, and Roman Kontchakov, editors,*Proceedings of the 30th International Workshop on Description Logics (DL'17)*, volume 1879 of*CEUR Workshop Proceedings*. Montpellier, France, CEUR-WS, 2017.Abstract BibTeX Entry PDF File

@inproceedings{ BBK+-DL17, address = {Montpellier, France}, author = {Franz {Baader} and Stefan {Borgwardt} and Patrick {Koopmann} and Ana {Ozaki} and Veronika {Thost}}, booktitle = {Proceedings of the 30th International Workshop on Description Logics (DL'17)}, editor = {Alessandro {Artale} and Birte {Glimm} and Roman {Kontchakov}}, publisher = {CEUR-WS}, series = {CEUR Workshop Proceedings}, title = {Metric Temporal Description Logics with Interval-Rigid Names (Extended Abstract)}, volume = {1879}, year = {2017}, }

Franz Baader, Stefan Borgwardt, and Marcel Lippmann:

Abstract BibTeX Entry PDF File ©IJCAI

**Query Rewriting for DL-Lite with**\(n\)**-ary Concrete Domains**. In Carles Sierra, editor,*Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI'17)*, pages 786–792, 2017.Abstract BibTeX Entry PDF File ©IJCAI

We investigate ontology-based query answering (OBQA) in a setting where both the ontology and the query can refer to concrete values such as numbers and strings. In contrast to previous work on this topic, the built-in predicates used to compare values are not restricted to being unary. We introduce restrictions on these predicates and on the ontology language that allow us to reduce OBQA to query answering in databases using the so-called combined rewriting approach. Though at first sight our restrictions are different from the ones used in previous work, we show that our results strictly subsume some of the existing first-order rewritability results for unary predicates.

@inproceedings{ BaBL-IJCAI17, address = {Melbourne, Australia}, author = {Franz {Baader} and Stefan {Borgwardt} and Marcel {Lippmann}}, booktitle = {Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI'17)}, editor = {Carles {Sierra}}, pages = {786--792}, title = {Query Rewriting for \textit{{DL-Lite}} with {$n$}-ary Concrete Domains}, year = {2017}, }

Franz Baader, Stefan Borgwardt, and Marcel Lippmann:

BibTeX Entry PDF File

**Query Rewriting for DL-Lite with**\(n\)**-ary Concrete Domains (Abstract)**. In Alessandro Artale, Birte Glimm, and Roman Kontchakov, editors,*Proceedings of the 30th International Workshop on Description Logics (DL'17)*, volume 1879 of*CEUR Workshop Proceedings*. Montpellier, France, CEUR-WS, 2017.BibTeX Entry PDF File

@inproceedings{ BaBL-DL17, address = {Montpellier, France}, author = {Franz {Baader} and Stefan {Borgwardt} and Marcel {Lippmann}}, booktitle = {Proceedings of the 30th International Workshop on Description Logics (DL'17)}, editor = {Alessandro {Artale} and Birte {Glimm} and Roman {Kontchakov}}, publisher = {CEUR-WS}, series = {CEUR Workshop Proceedings}, title = {Query Rewriting for \textit{{DL-Lite}} with {$n$}-ary Concrete Domains (Abstract)}, volume = {1879}, year = {2017}, }

Franz Baader, Stefan Borgwardt, and Rafael Peñaloza:

Abstract BibTeX Entry PDF File DOI

**Decidability and Complexity of Fuzzy Description Logics**.*Künstliche Intelligenz*, 31(1):85–90, 2017. Project report.Abstract BibTeX Entry PDF File DOI

Fuzzy description logics (FDLs) have been introduced to represent concepts for which membership cannot be determined in a precise way, i.e., where instead of providing a strict border between being a member and not being a member, it is more appropriate to model a gradual change from membership to non-membership. First approaches for reasoning in FDLs where based either on a reduction to reasoning in classical description logics (DLs) or on adaptations of reasoning approaches for DLs to the fuzzy case. However, it turned out that these approaches in general do not work if expressive terminological axioms, called general concept inclusions (GCIs), are available in the FDL. The goal of this project was a comprehensive study of the border between decidability and undecidability for FDLs with GCIs, as well as determining the exact complexity of the decidable logics. As a result, we have provided an almost complete classification of the decidability and complexity of FDLs with GCIs.

@article{ BaBP-KI17, author = {Franz {Baader} and Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}}, doi = {http://dx.doi.org/10.1007/s13218-016-0459-3}, journal = {K{\"u}nstliche Intelligenz}, note = {Project report.}, number = {1}, pages = {85--90}, title = {Decidability and Complexity of Fuzzy Description Logics}, volume = {31}, year = {2017}, }

Franz Baader and Andreas Ecke:

Abstract BibTeX Entry PDF File

**Extending the Description Logic ALC with More Expressive Cardinality Constraints on Concepts**. In*GCAI 2017. 3rd Global Conference on Artificial Intelligence*, volume 50 of*EPiC Series in Computing*, pages 6–19. EasyChair, 2017.Abstract BibTeX Entry PDF File

We extend the terminological formalism of the well-known description logic ALC from concept inclusions (CIs) to more general constraints formulated in the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA). In QFBAPA one can formulate Boolean combinations of inclusion constraints and numerical constraints on the cardinalities of sets. Our new formalism extends, on the one hand, so-called cardinality restrictions on concepts, which have been introduced two decades ago, and on the other hand the recently introduced statistical knowledge bases. Though considerably more expressive, our formalism has the same complexity (NExpTime) as cardinality restrictions on concepts. We will also introduce a restricted version of our formalism for which the complexity is ExpTime. This yields the until now unknown exact complexity of the consistency problem for statistical knowledge bases.

@inproceedings{ BaEc-GCAI17, author = {Franz {Baader} and Andreas {Ecke}}, booktitle = {{GCAI} 2017. 3rd Global Conference on Artificial Intelligence}, pages = {6--19}, publisher = {EasyChair}, series = {EPiC Series in Computing}, title = {Extending the Description Logic ALC with More Expressive Cardinality Constraints on Concepts}, volume = {50}, year = {2017}, }

Franz Baader and Oliver Fernández Gil:

Abstract BibTeX Entry PDF File

**Decidability and Complexity of Threshold Description Logics Induced by Concept Similarity Measures**. In*Proceedings of the 32nd Annual ACM Symposium on Applied Computing, Marrakech, Morocco, April 4-6, 2017*, pages 983–988. ACM, 2017.Abstract BibTeX Entry PDF File

In a recent research paper, we have proposed an extension of the light-weight Description Logic (DL) EL in which concepts can be defined in an approximate way. To this purpose, the notion of a graded membership function m, which instead of a Boolean membership value 0 or 1 yields a membership degree from the interval [0,1], was introduced. Threshold concepts can then, for example, require that an individual belongs to a concept C with degree at least 0.8. Reasoning in the threshold DL tel(m) obtained this way of course depends on the employed graded membership function m. The paper defines a specific such function, called deg, and determines the exact complexity of reasoning in tel(deg). In addition, it shows how concept similarity measures (CSMs) satisfying certain properties can be used to define graded membership functions m , but it does not investigate the complexity of reasoning in the induced threshold DLs tel(m ). In the present paper, we start filling this gap. In particular, we show that computability of implies decidability of tel(m ), and we introduce a class of CSMs for which reasoning in the induced threshold DLs has the same complexity as in tel(deg).

@inproceedings{ sacBaFe17, author = {Franz {Baader} and Oliver {Fern{\'a}ndez Gil}}, booktitle = {Proceedings of the 32nd Annual {ACM} Symposium on Applied Computing, Marrakech, Morocco, April 4-6, 2017}, pages = {983--988}, publisher = {{ACM}}, title = {Decidability and Complexity of Threshold Description Logics Induced by Concept Similarity Measures}, year = {2017}, }

Franz Baader, Oliver Fernández Gil, and Pavlos Marantidis:

Abstract BibTeX Entry PDF File DOI

**Approximation in Description Logics: How Weighted Tree Automata Can Help to Define the Required Concept Comparison Measures in**\(\mathcal{FL}_0\). In Frank Drewes, Carlos Martín-Vide, and Bianca Truthe, editors,*Proceedings of the 11th International Conference on Language and Automata Theory and Applications (LATA 2017)*, volume 10168 of*Lecture Notes in Computer Science*, pages 3–26. Springer, 2017.Abstract BibTeX Entry PDF File DOI

Recently introduced approaches for relaxed query answering, approximately defining concepts, and approximately solving unification problems in Description Logics have in common that they are based on the use of concept comparison measures together with a threshold construction. In this paper, we will briefly review these approaches, and then show how weighted automata working on infinite trees can be used to construct computable concept comparison measures for FL0 that are equivalence invariant w.r.t. general TBoxes. This is a first step towards employing such measures in the mentioned approximation approaches.

@inproceedings{ BaFM-LATA17, author = {Franz {Baader} and Oliver {Fern{\'a}ndez Gil} and Pavlos {Marantidis}}, booktitle = {Proceedings of the 11th International Conference on Language and Automata Theory and Applications ({LATA 2017})}, doi = {https://dx.doi.org/10.1007/978-3-319-53733-7_1}, editor = {Frank {Drewes} and Carlos {Mart{\'i}n{-}Vide} and Bianca {Truthe}}, pages = {3--26}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Approximation in Description Logics: How Weighted Tree Automata Can Help to Define the Required Concept Comparison Measures in $\mathcal{FL}_0$}, venue = {Ume{\aa}, Sweden}, volume = {10168}, year = {2017}, }

Franz Baader, Ian Horrocks, Carsten Lutz, and Ulrike Sattler:

Abstract BibTeX Entry

**An Introduction to Description Logic**. Cambridge University Press, 2017.Abstract BibTeX Entry

Description logics (DLs) have a long tradition in computer science and knowledge representation, being designed so that domain knowledge can be described and so that computers can reason about this knowledge. DLs have recently gained increased importance since they form the logical basis of widely used ontology languages, in particular the web ontology language OWL. Written by four renowned experts, this is the first textbook on description logics. It is suitable for self-study by graduates and as the basis for a university course. Starting from a basic DL, the book introduces the reader to their syntax, semantics, reasoning problems and model theory and discusses the computational complexity of these reasoning problems and algorithms to solve them. It then explores a variety of reasoning techniques, knowledge-based applications and tools and it describes the relationship between DLs and OWL.

@book{ DLbook-2017, author = {Franz {Baader} and Ian {Horrocks} and Carsten {Lutz} and Ulrike {Sattler}}, publisher = {Cambridge University Press}, title = {An Introduction to Description Logic}, year = {2017}, }

Franz Baader, Patrick Koopmann, and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File PDF File (Extended Technical Report) DOI (The final publication is available at link.springer.com) ©Spinger International Publishing

**Using Ontologies to Query Probabilistic Numerical Data**. In*Frontiers of Combining Systems: 11th International Symposium*, volume 10483 of*Lecture Notes in Computer Science*, pages 77–94. Springer International Publishing, 2017.Abstract BibTeX Entry PDF File PDF File (Extended Technical Report) DOI (The final publication is available at link.springer.com) ©Spinger International Publishing

We consider ontology-based query answering in a setting where some of the data are numerical and of a probabilistic nature, such as data obtained from uncertain sensor readings. The uncertainty for such numerical values can be more precisely represented by continu- ous probability distributions than by discrete probabilities for numerical facts concerning exact values. For this reason, we extend existing ap- proaches using discrete probability distributions over facts by continuous probability distributions over numerical values. We determine the exact (data and combined) complexity of query answering in extensions of the well-known description logics EL and ALC with numerical comparison operators in this probabilistic setting.

@inproceedings{ BaKoTu-FroCoS-17, author = {Franz {Baader} and Patrick {Koopmann} and Anni-Yasmin {Turhan}}, booktitle = {Frontiers of Combining Systems: 11th International Symposium}, doi = {https://dx.doi.org/10.1007/978-3-319-66167-4_5}, pages = {77--94}, publisher = {Springer International Publishing}, series = {Lecture Notes in Computer Science}, title = {Using Ontologies to Query Probabilistic Numerical Data}, volume = {10483}, year = {2017}, }

Franz Baader and Pavlos Marantidis:

Abstract BibTeX Entry PDF File

**Language equations for approximate matching in the Description Logic FL0**. In Adrià Gascón and Christopher Lynch, editors,*Proceedings of the 31st International Workshop on Unification (UNIF'17)*, 2017.Abstract BibTeX Entry PDF File

Both matching and unification in the Description Logic FL0 can be reduced to solving certain formal language equations. In previous work, we have extended unification in FL0 to approximate unification, and have shown that approximate unification can be reduced to approximately solving language equations. An approximate solution of a language equation need not make the languages on the left- and right-hand side of the equation equal, but close w.r.t. a given distance function. In the present paper, we consider approximate matching. We show that, for a large class of distance functions, approximate matching is in NP. We then consider a particular distance function d1(K,L) = 2^{−}n, where n is the length of the shortest word in the symmetric difference of the languages K, L, and show that w.r.t. this distance function approximate matching is polynomial.

@inproceedings{ BaMa-UNIF2017, address = {Oxford, UK}, author = {Franz {Baader} and Pavlos {Marantidis}}, booktitle = {Proceedings of the 31st International Workshop on Unification ({UNIF'17})}, editor = {Adri\`{a} {Gasc\'{o}n} and Christopher {Lynch}}, title = {Language equations for approximate matching in the Description Logic FL0}, year = {2017}, }

Stephan Böhme and Thomas Kühn:

Abstract BibTeX Entry PDF File DOI

**Reasoning on Context-Dependent Domain Models**. In Zhe Wang, Anni-Yasmin Turhan, Kewen Wang, and Xiaowang Zhang, editors,*7th Joint International Conference Semantic Technology, JIST 2017*, pages 69–85. Gold Coast, Australia, Springer International Publishing, 2017.Abstract BibTeX Entry PDF File DOI

Modelling context-dependent domains is hard, as capturing multiple context-dependent concepts and constraints easily leads to inconsistent models or unintended restrictions. However, current semantic technologies not yet support reasoning on context-dependent domains. To remedy this, we introduced ConDL, a set of novel description logics tailored to reason on contextual knowledge, as well as JConHT, a dedicated reasoner for ConDL ontologies. ConDL enables reasoning on the consistency and satisfiability of context-dependent domain models, e.g., Compartment Role Object Models (CROM). We evaluate the suitability and efficiency of our approach by reasoning on a modelled banking application and measuring the performance on randomly generated models.

@inproceedings{ BoKu-JIST2017, address = {Gold Coast, Australia}, author = {Stephan {B{\"o}hme} and Thomas {K{\"u}hn}}, booktitle = {7th Joint International Conference Semantic Technology, JIST 2017}, doi = {https://doi.org/10.1007/978-3-319-70682-5_5}, editor = {Zhe {Wang} and Anni-Yasmin {Turhan} and Kewen {Wang} and Xiaowang {Zhang}}, pages = {69--85}, publisher = {Springer International Publishing}, title = {Reasoning on Context-Dependent Domain Models}, year = {2017}, }

Stefan Borgwardt, Marco Cerami, and Rafael Peñaloza:

Abstract BibTeX Entry PDF File DOI

**The Complexity of Fuzzy**\(\mathcal{EL}\)**under the Lukasiewicz T-norm**.*International Journal of Approximate Reasoning*, 91:179–201, 2017.Abstract BibTeX Entry PDF File DOI

Fuzzy Description Logics (DLs) are are a family of knowledge representation formalisms designed to represent and reason about vague and imprecise knowledge that is inherent to many application domains. Previous work has shown that the complexity of reasoning in a fuzzy DL using finitely many truth degrees is usually not higher than that of the underlying classical DL. We show that this does not hold for fuzzy extensions of the light-weight DL EL, which is used in many biomedical ontologies, under the finitely valued Łukasiewicz semantics. More precisely, the complexity of reasoning increases from P to ExpTime, even if only one additional truth value is introduced. When adding complex role inclusions and inverse roles, the logic even becomes undecidable. Even more surprisingly, when considering the infinitely valued Łukasiewicz semantics, reasoning in fuzzy EL is undecidable.

@article{ BoCP-IJAR17, author = {Stefan {Borgwardt} and Marco {Cerami} and Rafael {Pe{\~n}aloza}}, doi = {http://dx.doi.org/10.1016/j.ijar.2017.09.005}, journal = {International Journal of Approximate Reasoning}, pages = {179--201}, title = {The Complexity of Fuzzy {$\mathcal{EL}$} under the {L}ukasiewicz T-norm}, volume = {91}, year = {2017}, }

Stefan Borgwardt, Marco Cerami, and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Lukasiewicz Fuzzy**\(\mathcal{EL}\)**is Undecidable**. In Alessandro Artale, Birte Glimm, and Roman Kontchakov, editors,*Proceedings of the 30th International Workshop on Description Logics (DL'17)*, volume 1879 of*CEUR Workshop Proceedings*. Montpellier, France, CEUR-WS, 2017.Abstract BibTeX Entry PDF File

Fuzzy Description Logics have been proposed as formalisms for representing and reasoning about imprecise knowledge by introducing intermediate truth degrees. Unfortunately, it has been shown that reasoning in these logics easily becomes undecidable, when infinitely many truth degrees are considered and conjunction is not idempotent. In this paper, we take those results to the extreme, and show that subsumption in fuzzy EL under Łukasiewicz semantics is undecidable.This provides the first instance of a Horn-style logic with polynomial-time reasoning whose fuzzy extension becomes undecidable.

@inproceedings{ BoCP-DL17, address = {Montpellier, France}, author = {Stefan {Borgwardt} and Marco {Cerami} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 30th International Workshop on Description Logics (DL'17)}, editor = {Alessandro {Artale} and Birte {Glimm} and Roman {Kontchakov}}, publisher = {CEUR-WS}, series = {CEUR Workshop Proceedings}, title = {{L}ukasiewicz Fuzzy {$\mathcal{EL}$} is Undecidable}, volume = {1879}, year = {2017}, }

Stefan Borgwardt, Ismail Ilkan Ceylan, and Thomas Lukasiewicz:

Abstract BibTeX Entry PDF File

**Ontology-Mediated Queries for Probabilistic Databases**. In Satinder Singh and Shaul Markovitch, editors,*Proceedings of the 31st AAAI Conf. on Artificial Intelligence (AAAI'17)*, pages 1063–1069. San Francisco, USA, AAAI Press, 2017.Abstract BibTeX Entry PDF File

Probabilistic databases (PDBs) are usually incomplete, e.g., contain only the facts that have been extracted from the Web with high confidence. However, missing facts are often treated as being false, which leads to unintuitive results when querying PDBs. Recently, open-world probabilistic databases (OPDBs) were proposed to address this issue by allowing probabilities of unknown facts to take any value from a fixed probability interval. In this paper, we extend OPDBs by Datalog+/- ontologies, under which both upper and lower probabilities of queries become even more informative, enabling us to distinguish queries that were indistinguishable before. We show that the dichotomy between P and PP in (Open)PDBs can be lifted to the case of first-order rewritable positive programs (without negative constraints); and that the problem can become NP^{P}P-complete, once negative constraints are allowed. We also propose an approximating semantics that circumvents the increase in complexity caused by negative constraints.

@inproceedings{ BoCL-AAAI17, address = {San Francisco, USA}, author = {Stefan {Borgwardt} and Ismail Ilkan {Ceylan} and Thomas {Lukasiewicz}}, booktitle = {Proceedings of the 31st AAAI Conf.\ on Artificial Intelligence (AAAI'17)}, editor = {Satinder {Singh} and Shaul {Markovitch}}, pages = {1063--1069}, publisher = {AAAI Press}, title = {Ontology-Mediated Queries for Probabilistic Databases}, year = {2017}, }

Stefan Borgwardt, Ismail Ilkan Ceylan, and Thomas Lukasiewicz:

BibTeX Entry PDF File

**Ontology-Mediated Queries for Probabilistic Databases (Extended Abstract)**. In Alessandro Artale, Birte Glimm, and Roman Kontchakov, editors,*Proceedings of the 30th International Workshop on Description Logics (DL'17)*, volume 1879 of*CEUR Workshop Proceedings*. Montpellier, France, CEUR-WS, 2017.BibTeX Entry PDF File

@inproceedings{ BoCL-DL17, address = {Montpellier, France}, author = {Stefan {Borgwardt} and Ismail Ilkan {Ceylan} and Thomas {Lukasiewicz}}, booktitle = {Proceedings of the 30th International Workshop on Description Logics (DL'17)}, editor = {Alessandro {Artale} and Birte {Glimm} and Roman {Kontchakov}}, publisher = {CEUR-WS}, series = {CEUR Workshop Proceedings}, title = {Ontology-Mediated Queries for Probabilistic Databases (Extended Abstract)}, volume = {1879}, year = {2017}, }

Stefan Borgwardt and Rafael Peñaloza:

Abstract BibTeX Entry PDF File DOI

**Algorithms for Reasoning in Very Expressive Description Logics under Infinitely Valued Gödel Semantics**.*International Journal of Approximate Reasoning*, 83:60–101, 2017.Abstract BibTeX Entry PDF File DOI

Fuzzy description logics (FDLs) are knowledge representation formalisms capable of dealing with imprecise knowledge by allowing intermediate membership degrees in the interpretation of concepts and roles. One option for dealing with these intermediate degrees is to use the so-called Gödel semantics, under which conjunction is interpreted by the minimum of the degrees of the conjuncts. Despite its apparent simplicity, developing reasoning techniques for expressive FDLs under this semantics is a hard task. In this paper, we introduce two new algorithms for reasoning in very expressive FDLs under Gödel semantics. They combine the ideas of a previous automata-based algorithm for Gödel FDLs with the known crispification and tableau approaches for FDL reasoning. The results are the two first practical algorithms capable of reasoning in infinitely valued FDLs supporting general concept inclusions.

@article{ BoPe-IJAR17, author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}}, doi = {http://dx.doi.org/10.1016/j.ijar.2016.12.014}, journal = {International Journal of Approximate Reasoning}, pages = {60--101}, title = {Algorithms for Reasoning in Very Expressive Description Logics under Infinitely Valued {G}{\"o}del Semantics}, volume = {83}, year = {2017}, }

Stefan Borgwardt and Rafael Peñaloza:

BibTeX Entry PDF File DOI

**Fuzzy Description Logics – A Survey**. In Serafín Moral, Olivier Pivert, Daniel Sánchez, and Nicolás Marín, editors,*Proceedings of the 11th International Conference on Scalable Uncertainty Management (SUM'17)*, volume 10564 of*Lecture Notes in Computer Science*, pages 31–45. Granada, Spain, Springer-Verlag, 2017.BibTeX Entry PDF File DOI

@inproceedings{ BoPe-SUM17, address = {Granada, Spain}, author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 11th International Conference on Scalable Uncertainty Management (SUM'17)}, doi = {http://dx.doi.org/10.1007/978-3-319-67582-4_3}, editor = {Seraf{\'i}n {Moral} and Olivier {Pivert} and Daniel {S{\'a}nchez} and Nicol{\'a}s {Mar{\'i}n}}, pages = {31--45}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Fuzzy Description Logics -- {A} Survey}, volume = {10564}, year = {2017}, }

Camille Bourgaux and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File

**Temporal Query Answering in DL-Lite over Inconsistent Data**. In Claudia d'Amato and Miriam Fernandez, editors,*Proceedings of the 16th International Semantic Web Conference (ISWC 2017)*,*LNCS*, 2017.Abstract BibTeX Entry PDF File

In ontology-based systems that process data stemming from different sources and that is received over time, as in context-aware systems, reasoning needs to cope with the temporal dimension and should be resilient against inconsistencies in the data. Motivated by such settings, this paper addresses the problem of handling inconsistent data in a temporal version of ontology-based query answering. We consider a recently proposed temporal query language that combines conjunctive queries with operators of propositional linear temporal logic and extend to this setting three inconsistency-tolerant semantics that have been introduced for querying inconsistent description logic knowledge bases. We investigate their complexity for DL-Lite_{R}temporal knowledge bases, and furthermore complete the picture for the consistent case.

@inproceedings{ BoTu-ISWC-17, author = {Camille {Bourgaux} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of the 16th International Semantic Web Conference (ISWC 2017)}, editor = {Claudia {d'Amato} and Miriam {Fernandez}}, series = {LNCS}, title = {Temporal Query Answering in DL-Lite over Inconsistent Data}, year = {2017}, }

Ismail Ilkan Ceylan, Stefan Borgwardt, and Thomas Lukasiewicz:

Abstract BibTeX Entry PDF File ©IJCAI

**Most Probable Explanations for Probabilistic Database Queries**. In Carles Sierra, editor,*Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI'17)*, pages 950–956, 2017.Abstract BibTeX Entry PDF File ©IJCAI

Forming the foundations of large-scale knowledge bases, probabilistic databases have been widely studied in the literature. In particular, probabilistic query evaluation has been investigated intensively as a central inference mechanism. However, despite its power, query evaluation alone cannot extract all the relevant information encompassed in large-scale knowledge bases. To exploit this potential, we study two inference tasks; namely finding the most probable database and the most probable hypothesis for a given query. As natural counterparts of most probable explanations (MPE) and maximum a posteriori hypotheses (MAP) in probabilistic graphical models, they can be used in a variety of applications that involve prediction or diagnosis tasks. We investigate these problems relative to a variety of query languages, ranging from conjunctive queries to ontology-mediated queries, and provide a detailed complexity analysis.

@inproceedings{ CeBL-IJCAI17, address = {Melbourne, Australia}, author = {Ismail Ilkan {Ceylan} and Stefan {Borgwardt} and Thomas {Lukasiewicz}}, booktitle = {Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI'17)}, editor = {Carles {Sierra}}, pages = {950--956}, title = {Most Probable Explanations for Probabilistic Database Queries}, year = {2017}, }

Ismail Ilkan Ceylan, Stefan Borgwardt, and Thomas Lukasiewicz:

BibTeX Entry PDF File

**Most Probable Explanations for Probabilistic Database Queries (Extended Abstract)**. In Alessandro Artale, Birte Glimm, and Roman Kontchakov, editors,*Proceedings of the 30th International Workshop on Description Logics (DL'17)*, volume 1879 of*CEUR Workshop Proceedings*. Montpellier, France, CEUR-WS, 2017.BibTeX Entry PDF File

@inproceedings{ CeBL-DL17, address = {Montpellier, France}, author = {Ismail Ilkan {Ceylan} and Stefan {Borgwardt} and Thomas {Lukasiewicz}}, booktitle = {Proceedings of the 30th International Workshop on Description Logics (DL'17)}, editor = {Alessandro {Artale} and Birte {Glimm} and Roman {Kontchakov}}, publisher = {CEUR-WS}, series = {CEUR Workshop Proceedings}, title = {Most Probable Explanations for Probabilistic Database Queries (Extended Abstract)}, volume = {1879}, year = {2017}, }

Ismail Ilkan Ceylan, Adnan Darwiche, and Guy Van Den Broeck:

Abstract BibTeX Entry PDF File

**Open-World Probabilistic Databases: An Abridged Report**. In Carles Sierra, editor,*Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI'17)*, 2017. Sister Conference Best Paper Track.Abstract BibTeX Entry PDF File

Large-scale probabilistic knowledge bases are be- coming increasingly important in academia and industry alike. They are constantly extended with new data, powered by modern information extraction tools that associate probabilities with database tuples. In this paper, we revisit the semantics under- lying such systems. In particular, the closed-world assumption of probabilistic databases, that facts not in the database have probability zero, clearly conflicts with their everyday use. To address this discrepancy, we propose an open-world probabilistic database semantics, which relaxes the probabilities of open facts to default intervals. For this open- world setting, we lift the existing data complexity dichotomy of probabilistic databases, and propose an efficient evaluation algorithm for unions of conjunctive queries. We also show that query evaluation can become harder for non-monotone queries.

@inproceedings{ CDV-IJCAI17, address = {Melbourne, Australia}, author = {Ismail Ilkan {Ceylan} and Adnan {Darwiche} and Guy Van Den {Broeck}}, booktitle = {Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI'17)}, editor = {Carles {Sierra}}, note = {Sister Conference Best Paper Track.}, title = {{Open-World Probabilistic Databases: An Abridged Report}}, year = {2017}, }

Ismail Ilkan Ceylan, Thomas Lukasiewicz, Rafael Peñaloza, and Oana Tifrea-Marciuska:

Abstract BibTeX Entry PDF File

**Query Answering in Ontologies under Preference Rankings**. In Carles Sierra, editor,*Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI'17)*, 2017.Abstract BibTeX Entry PDF File

We present an ontological framework, based on preference rankings, that allows users to express their preferences between the knowledge explicitly available in the ontology. Using this formalism, the answers for a given query to an ontology can be ranked by preference, allowing users to retrieve the most preferred answers only. We provide a host of complexity results for the main computational tasks in this framework, for the general case, and for EL and DL-Lite_{core}as underlying ontology languages.

@inproceedings{ CLPT-IJCAI17, address = {Melbourne, Australia}, author = {Ismail Ilkan {Ceylan} and Thomas {Lukasiewicz} and Rafael {Pe\~naloza} and Oana {Tifrea-Marciuska}}, booktitle = {Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI'17)}, editor = {Carles {Sierra}}, title = {Query Answering in Ontologies under Preference Rankings}, year = {2017}, }

Ismail Ilkan Ceylan and Rafael Peñaloza Nyssen:

Abstract BibTeX Entry PDF File DOI

**The Bayesian Ontology Language BEL**.*Journal of Automated Reasoning*, 58(1):67–95, 2017.Abstract BibTeX Entry PDF File DOI

We introduce the new probabilistic description logic (DL) BEL, which extends the light-weight DL EL with the possibility of expressing uncertainty about the validity of some knowledge. Contrary to other probabilistic DLs, BEL is designed to represent classical knowledge that depends on an uncertain context; that is, some of the knowledge may hold or not depending on the current situation. The probability distribution of these contexts is expressed by a Bayesian network (BN). We study different reasoning problems in BEL, providing tight complexity bounds for all of them. One particularly interesting property of our framework is that reasoning can be decoupled between the logical (i.e., EL), and the probabilistic (i.e., the BN) components. We later generalize all the notions presented to introduce Bayesian extensions of arbitrary ontology languages. Using the decoupling property, we are able to provide tight complexity bounds for reasoning in the Bayesian extensions of many other DLs. We provide a detailed analysis of our formalism w.r.t. the assumptions made and compare it with the existing approaches.

@article{ CePe-JAR, author = {Ismail Ilkan {Ceylan} and Rafael Pe{\~{n}}aloza {Nyssen}}, doi = {http://dx.doi.org/10.1007/s10817-016-9386-0}, journal = {Journal of Automated Reasoning}, number = {1}, pages = {67--95}, title = {The Bayesian Ontology Language {BEL}}, volume = {58}, year = {2017}, }

Patrick Koopmann and Jieying Chen:

Abstract BibTeX Entry PDF File

**Computing ALCH-Subsumption Modules Using Uniform Interpolation**. In Patrick Koopmann, Sebastian Rudolph, Renate Schmidt, and Christoph Wernhard, editors,*Proceedings of SOQE 2017*,*CEUR Workshop Proceedings*. CEUR-WS.org, 2017.Abstract BibTeX Entry PDF File

We investigate how minimal subsumption modules can be extracted using methods for uniform interpolation and forgetting. Given an ontology and a signature of concept and role names, a subsumption module is a subset of the ontology that preserves all logical entailments that can be expressed in the description logic of the ontology using only terms in the specified signature. As such, they are useful for ontology reuse and ontology analysis. While there exists a range of methods for computing or approximating minimal modules for a range of module types, we are not aware of a practical, implemented method for computing minimal subsumption modules in description logics beyond ELH. In this paper, we present a method that uses uniform interpolation/forgetting to compute subsumption modules in ALCH, and which under certain conditions guarantees minimality of the extracted modules. As a side product, our method computes a so-called LK subsumption module, which over-approximates the union of all minimal subsumption modules, and as such may already have applications of its own. We further present an initial evaluation of this method on a varied corpus of ontologies.

@inproceedings{ KoCH-SOQE-17, author = {Patrick {Koopmann} and Jieying {Chen}}, booktitle = {Proceedings of SOQE 2017}, editor = {Patrick {Koopmann} and Sebastian {Rudolph} and Renate {Schmidt} and Christoph {Wernhard}}, publisher = {CEUR-WS.org}, series = {CEUR Workshop Proceedings}, title = {Computing ALCH-Subsumption Modules Using Uniform Interpolation}, year = {2017}, }

Patrick Koopmann, Marcus Hähnel, and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File ©Springer-Verlag ©Springer International Publishing

**Energy-Efficiency of OWL Reasoners—Frequency Matters**. In*Proceedings of JIST 2017*. Springer International Publishing, 2017.Abstract BibTeX Entry PDF File ©Springer-Verlag ©Springer International Publishing

While running times of ontology reasoners have been studied extensively, studies on energy-consumption of reasoning are scarce, and the energy-efficiency of ontology reasoning is not fully understood yet. Earlier empirical studies on the energy-consumption of ontology reasoners focused on reasoning on smart phones and used measurement methods prone to noise and side-effects. This paper presents an evaluation of the energy-efficiency of five state-of-the-art OWL reasoners on an ARM single-board computer that has built-in sensors to measure the energy consumption of CPUs and memory precisely. Using such a machine gives full control over installed and running software, active clusters and CPU frequencies, allowing for a more precise and detailed picture of the energy consumption of ontology reasoning. Besides evaluating the energy consumption of reasoning, our study further explores the relationship between computation power of the CPU, reasoning time, and energy consumption.

@inproceedings{ KoHaTu-JIST-2017, author = {Patrick {Koopmann} and Marcus {H\"ahnel} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of JIST 2017}, publisher = {Springer International Publishing}, title = {Energy-Efficiency of {OWL} Reasoners---Frequency Matters}, year = {2017}, }

Francesco Kriegel:

Abstract BibTeX Entry PDF File DOI ©Springer-Verlag

**Acquisition of Terminological Knowledge from Social Networks in Description Logic**. In Rokia Missaoui, Sergei O. Kuznetsov, and Sergei Obiedkov, editors,*Formal Concept Analysis of Social Networks*,*Lecture Notes in Social Networks (LNSN)*, pages 97–142. Cham, Springer International Publishing, 2017.Abstract BibTeX Entry PDF File DOI ©Springer-Verlag

The Web Ontology Language (OWL) has gained serious attraction since its foundation in 2004, and it is heavily used in applications requiring representation of as well as reasoning with knowledge. It is the language of the Semantic Web, and it has a strong logical underpinning by means of so-called Description Logics (DLs). DLs are a family of conceptual languages suitable for knowledge representation and reasoning due to their strong logical foundation, and for which the decidability and complexity of common reasoning problems are widely explored. In particular, the reasoning tasks allow for the deduction of implicit knowledge from explicitly stated facts and axioms, and plenty of appropriate algorithms were developed, optimized, and implemented, e.g., tableaux algorithms and completion algorithms. In this document, we present a technique for the acquisition of terminological knowledge from social networks. More specifically, we show how OWL axioms, i.e., concept inclusions and role inclusions in DLs, can be obtained from social graphs in a sound and complete manner. A social graph is simply a directed graph, the vertices of which describe the entities, e.g., persons, events, messages, etc.; and the edges of which describe the relationships between the entities, e.g., friendship between persons, attendance of a person to an event, a person liking a message, etc. Furthermore, the vertices of social graphs are labeled, e.g., to describe properties of the entities, and also the edges are labeled to specify the concrete relationships. As an exemplary social network we consider Facebook, and show that it fits our use case.

@incollection{ Kr-FCAoSN17, address = {Cham}, author = {Francesco {Kriegel}}, booktitle = {Formal Concept Analysis of Social Networks}, doi = {https://dx.doi.org/10.1007/978-3-319-64167-6_5}, editor = {Rokia {Missaoui} and Sergei O. {Kuznetsov} and Sergei {Obiedkov}}, pages = {97--142}, publisher = {Springer International Publishing}, series = {Lecture Notes in Social Networks ({LNSN})}, title = {Acquisition of Terminological Knowledge from Social Networks in Description Logic}, year = {2017}, }

Francesco Kriegel:

Abstract BibTeX Entry PDF File DOI ©Springer-Verlag

**First Notes on Maximum Entropy Entailment for Quantified Implications**. In Karell Bertet, Daniel Borchmann, Peggy Cellier, and Sébastien Ferré, editors,*Proceedings of the 14th International Conference on Formal Concept Analysis (ICFCA 2017)*, volume 10308 of*Lecture Notes in Computer Science (LNCS)*, pages 155–167. Rennes, France, Springer Verlag, 2017.Abstract BibTeX Entry PDF File DOI ©Springer-Verlag

Entropy is a measure for the uninformativeness or randomness of a data set, i.e., the higher the entropy is, the lower is the amount of information. In the field of propositional logic it has proven to constitute a suitable measure to be maximized when dealing with models of probabilistic propositional theories. More specifically, it was shown that the model of a probabilistic propositional theory with maximal entropy allows for the deduction of other formulae which are somehow expected by humans, i.e., allows for some kind of common sense reasoning. In order to pull the technique of maximum entropy entailment to the field of Formal Concept Analysis, we define the notion of entropy of a formal context with respect to the frequency of its object intents, and then define maximum entropy entailment for quantified implication sets, i.e., for sets of partial implications where each implication has an assigned degree of confidence. Furthermore, then this entailment technique is utilized to define so-called maximum entropy implicational bases (ME-bases), and a first general example of such a ME-base is provided.

@inproceedings{ Kr-ICFCA17b, address = {Rennes, France}, author = {Francesco {Kriegel}}, booktitle = {Proceedings of the 14th International Conference on Formal Concept Analysis ({ICFCA} 2017)}, doi = {https://doi.org/10.1007/978-3-319-59271-8_10}, editor = {Karell {Bertet} and Daniel {Borchmann} and Peggy {Cellier} and S\'{e}bastien {Ferr\'{e}}}, pages = {155--167}, publisher = {Springer Verlag}, series = {Lecture Notes in Computer Science ({LNCS})}, title = {First Notes on Maximum Entropy Entailment for Quantified Implications}, volume = {10308}, year = {2017}, }

Francesco Kriegel:

Abstract BibTeX Entry PDF File DOI ©Springer-Verlag

**Implications over Probabilistic Attributes**. In Karell Bertet, Daniel Borchmann, Peggy Cellier, and Sébastien Ferré, editors,*Proceedings of the 14th International Conference on Formal Concept Analysis (ICFCA 2017)*, volume 10308 of*Lecture Notes in Computer Science (LNCS)*, pages 168–183. Rennes, France, Springer Verlag, 2017.Abstract BibTeX Entry PDF File DOI ©Springer-Verlag

We consider the task of acquisition of terminological knowledge from given assertional data. However, when evaluating data of real-world applications we often encounter situations where it is impractical to deduce only crisp knowledge, due to the presence of exceptions or errors. It is rather appropriate to allow for degrees of uncertainty within the derived knowledge. Consequently, suitable methods for knowledge acquisition in a probabilistic framework should be developed. In particular, we consider data which is given as a probabilistic formal context, i.e., as a triadic incidence relation between objects, attributes, and worlds, which is furthermore equipped with a probability measure on the set of worlds. We define the notion of a probabilistic attribute as a probabilistically quantified set of attributes, and define the notion of validity of implications over probabilistic attributes in a probabilistic formal context. Finally, a technique for the axiomatization of such implications from probabilistic formal contexts is developed. This is done is a sound and complete manner, i.e., all derived implications are valid, and all valid implications are deducible from the derived implications. In case of finiteness of the input data to be analyzed, the constructed axiomatization is finite, too, and can be computed in finite time.

@inproceedings{ Kr-ICFCA17a, address = {Rennes, France}, author = {Francesco {Kriegel}}, booktitle = {Proceedings of the 14th International Conference on Formal Concept Analysis ({ICFCA} 2017)}, doi = {https://doi.org/10.1007/978-3-319-59271-8_11}, editor = {Karell {Bertet} and Daniel {Borchmann} and Peggy {Cellier} and S\'{e}bastien {Ferr\'{e}}}, pages = {168--183}, publisher = {Springer Verlag}, series = {Lecture Notes in Computer Science ({LNCS})}, title = {Implications over Probabilistic Attributes}, volume = {10308}, year = {2017}, }

Francesco Kriegel:

Abstract BibTeX Entry PDF File DOI ©Taylor and Francis

**Probabilistic Implication Bases in FCA and Probabilistic Bases of GCIs in**\(\mathcal{E\mkern-1.618mu L}^{\bot}\).*International Journal of General Systems*, 46(5):511–546, 2017.Abstract BibTeX Entry PDF File DOI ©Taylor and Francis

A probabilistic formal context is a triadic context the third dimension of which is a set of worlds equipped with a probability measure. After a formal definition of this notion, this document introduces probability of implications with respect to probabilistic formal contexts, and provides a construction for a base of implications the probabilities of which exceed a given lower threshold. A comparison between confidence and probability of implications is drawn, which yields the fact that both measures do not coincide. Furthermore, the results are extended towards the lightweight description logic \(\mathcal{E\mkern-1.618mu L}^{\bot}\) with probabilistic interpretations, and a method for computing a base of general concept inclusions the probabilities of which are greater than a pre-defined lower bound is proposed. Additionally, we consider so-called probabilistic attributes over probabilistic formal contexts, and provide a method for the axiomatization of implications over probabilistic attributes.

@article{ Kr-IJGS17, author = {Francesco {Kriegel}}, doi = {https://doi.org/10.1080/03081079.2017.1349575}, journal = {International Journal of General Systems}, number = {5}, pages = {511--546}, title = {Probabilistic Implication Bases in {FCA} and Probabilistic Bases of GCIs in $\mathcal{E\mkern-1.618mu L}^{\bot}$}, volume = {46}, year = {2017}, }

Francesco Kriegel and Daniel Borchmann:

Abstract BibTeX Entry PDF File DOI ©Taylor and Francis

**NextClosures: Parallel Computation of the Canonical Base with Background Knowledge**.*International Journal of General Systems*, 46(5):490–510, 2017.Abstract BibTeX Entry PDF File DOI ©Taylor and Francis

The canonical base of a formal context plays a distinguished role in Formal Concept Analysis, as it is the only minimal implicational base known so far that can be described explicitly. Consequently, several algorithms for the computation of this base have been proposed. However, all those algorithms work sequentially by computing only one pseudo-intent at a time – a fact that heavily impairs the practicability in real-world applications. In this paper, we shall introduce an approach that remedies this deficit by allowing the canonical base to be computed in a parallel manner with respect to arbitrary implicational background knowledge. First experimental evaluations show that for sufficiently large data sets the speed-up is proportional to the number of available CPU cores.

@article{ KrBo-IJGS17, author = {Francesco {Kriegel} and Daniel {Borchmann}}, doi = {https://doi.org/10.1080/03081079.2017.1349570}, journal = {International Journal of General Systems}, number = {5}, pages = {490--510}, title = {NextClosures: Parallel Computation of the Canonical Base with Background Knowledge}, volume = {46}, year = {2017}, }

Markus Krötzsch, Maximilian Marx, Ana Ozaki, and Veronika Thost:

Abstract BibTeX Entry PDF File DOI ©Springer-Verlag

**Attributed Description Logics: Ontologies for Knowledge Graphs**. In Claudia d'Amato, Miriam Fernández, Valentina A. M. Tamma, Freddy Lécué, Philippe Cudré-Mauroux, Juan F. Sequeda, Christoph Lange, and Jeff Heflin, editors,*Proceedings of the 16th International Semantic Web Conference (ISWC'17)*, volume 10587 of*LNCS*, pages 418–435. Springer, October 2017.Abstract BibTeX Entry PDF File DOI ©Springer-Verlag

In modelling real-world knowledge, there often arises a need to represent and reason with meta-knowledge. To equip description logics (DLs) for dealing with such ontologies, we enrich DL concepts and roles with finite sets of attribute–value pairs, called annotations, and allow concept inclusions to express constraints on annotations. We show that this may lead to increased complexity or even undecidability, and we identify cases where this increased expressivity can be achieved without incurring increased complexity of reasoning. In particular, we describe a tractable fragment based on the lightweight description logic EL, and we cover SROIQ, the DL underlying OWL 2 DL.

@inproceedings{ KMOT2017, author = {Markus {Kr{\"{o}}tzsch} and Maximilian {Marx} and Ana {Ozaki} and Veronika {Thost}}, booktitle = {Proceedings of the 16th International Semantic Web Conference (ISWC'17)}, doi = {https://dx.doi.org/10.1007/978-3-319-68288-4_25}, editor = {Claudia {d'Amato} and Miriam {Fern{\'{a}}ndez} and Valentina A. M. {Tamma} and Freddy {L{\'{e}}cu{\'{e}}} and Philippe {Cudr{\'{e}}-Mauroux} and Juan F. {Sequeda} and Christoph {Lange} and Jeff {Heflin}}, month = {October}, pages = {418--435}, publisher = {Springer}, series = {LNCS}, title = {Attributed Description Logics: Ontologies for Knowledge Graphs}, volume = {10587}, year = {2017}, }

Markus Krötzsch, Maximilian Marx, Ana Ozaki, and Veronika Thost:

Abstract BibTeX Entry PDF File

**Reasoning with Attributed Description Logics**. In*Proceedings of the 30th International Workshop on Description Logics (DL 2017)*,*CEUR Workshop Proceedings*. CEUR-WS.org, July 2017.Abstract BibTeX Entry PDF File

In modelling real-world knowledge, there often arises a need to represent and reason with meta-knowledge. To equip description logics (DLs) for dealing with such ontologies, we enrich DL concepts and roles with finite sets of attribute–value pairs, called annotations, and allow concept inclusions to express constraints on annotations. We show that this may lead to increased complexity or even undecidability, and we identify cases where this increased expressivity can be achieved without incurring increased complexity of reasoning. In particular, we describe a tractable fragment based on the lightweight description logic EL.

@inproceedings{ KMOT-DL17, author = {Markus {Kr{\"{o}}tzsch} and Maximilian {Marx} and Ana {Ozaki} and Veronika {Thost}}, booktitle = {Proceedings of the 30th International Workshop on Description Logics (DL 2017)}, month = {July}, publisher = {CEUR-WS.org}, series = {CEUR Workshop Proceedings}, title = {Reasoning with Attributed Description Logics}, year = {2017}, }

Maximilian Marx, Markus Krötzsch, and Veronika Thost:

Abstract BibTeX Entry PDF File

**Logic on MARS: Ontologies for generalised property graphs**. In Carles Sierra, editor,*Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI'17)*, pages 1188–1194. International Joint Conferences on Artificial Intelligence, 2017.Abstract BibTeX Entry PDF File

Graph-structured data is used to represent large information collections, called knowledge graphs, in many applications. Their exact format may vary, but they often share the concept that edges can be annotated with additional information, such as validity time or provenance information. Property Graph is a popular graph database format that also provides this feature. We give a formalisation of a generalised notion of Property Graphs, called multi-attributed relational structures (MARS), and introduce a matching knowledge representation formalism, multi-attributed predicate logic (MAPL). We analyse the expressive power of MAPL and suggest a simpler, rule-based fragment of MAPL that can be used for ontological reasoning on Property Graphs. To the best of our knowledge, this is the first approach to making Property Graphs and related data structures accessible to symbolic AI.

@inproceedings{ MKT-IJCAI17, author = {Maximilian {Marx} and Markus {Kr{\"{o}}tzsch} and Veronika {Thost}}, booktitle = {Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI'17)}, editor = {Carles {Sierra}}, pages = {1188--1194}, publisher = {International Joint Conferences on Artificial Intelligence}, title = {Logic on {MARS:} Ontologies for generalised property graphs}, year = {2017}, }

Maximilian Pensel and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File DOI

**Including Quantification in Defeasible Reasoning for the Description Logic**\(\mathcal{EL}_{\bot}\). In Marcello Balduccini and Tomi Janhunen, editors,*Proceedings of the 14th International Conference on Logic Programming and Nonmonotonic Reasoning - LPNMR*, pages 78–84. Springer, 2017.Abstract BibTeX Entry PDF File DOI

Defeasible Description Logics (DDLs) extend classical Description Logics with defeasible concept inclusions and offer thereby a form of non-monotonicity. For reasoning in such settings often the rational closure according to the well-known KLM postulates (for propositional logic) was employed in earlier approaches. If in DDLs that use quantification a defeasible subsumption relationship holds between two concepts, such a relationship might also hold if these concepts appear nested in existential restrictions. Earlier reasoning algorithms for DDLs do not detect this kind of defeasible subsumption relationships. We devise a new form of canonical models that extend classical canonical models for EL_{b}ot by elements that satisfy increasing amounts of defeasible knowledge. We show that reasoning based on these models yields the missing entailments.

@inproceedings{ PeTu-LPNMR-17, author = {Maximilian {Pensel} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of the 14th International Conference on Logic Programming and Nonmonotonic Reasoning - {LPNMR}}, doi = {https://dx.doi.org/10.1007/978-3-319-61660-5_9}, editor = {Marcello {Balduccini} and Tomi {Janhunen}}, pages = {78--84}, publisher = {Springer}, title = {Including Quantification in Defeasible Reasoning for the Description Logic $\mathcal{EL}_{\bot}$}, year = {2017}, }

Maximilian Pensel and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File

**Making Quantification Relevant again—the Case of Defeasible**\(\mathcal{EL}_{\bot}\). In Richard Booth, Giovanni Casini, and Ivan Varzinczak, editors,*Proceedings of the 4th International Workshop on Defeasible and Ampliative Reasoning - DARe*. CEUR-WS.org, 2017.Abstract BibTeX Entry PDF File

Defeasible Description Logics (DDLs) extend Description Logics with defeasible concept inclusions. Reasoning in DDLs often employs rational or relevant closure according to the (propositional) KLM postulates. If in DDLs with quantification a defeasible subsumption relationship holds between concepts, this relationship might also hold if these concepts appear in existential restrictions. Such nested defeasible subsumption relationships were not detected by earlier reasoning algorithms—neither for rational nor relevant closure. Recently, we devised a new approach for EL_{b}ot that alleviates this problem for rational closure by the use of typicality models that extend classical canonical models by domain elements that individually satisfy any amount of consistent defeasible knowledge. In this paper we lift our approach to relevant closure and show that reasoning based on typicality models yields the missing entailments.

@inproceedings{ PeTu-DARE-17, author = {Maximilian {Pensel} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of the 4th International Workshop on Defeasible and Ampliative Reasoning - {DARe}}, editor = {Richard {Booth} and Giovanni {Casini} and Ivan {Varzinczak}}, publisher = {CEUR-WS.org}, title = {Making Quantification Relevant again---the Case of Defeasible $\mathcal{EL}_{\bot}$}, year = {2017}, }

Veronika Thost:

Abstract BibTeX Entry PDF File

**News on Temporal Conjunctive Queries**. In Daniele Dell'Aglio, Darko Anicic, Payam M. Barnaghi, Emanuele Della Valle, Deborah L. McGuinness, Loris Bozzato, Thomas Eiter, Martin Homola, and Daniele Porello, editors,*Joint Proceedings of the Web Stream Processing workshop (WSP 2017) and the 2nd International Workshop on Ontology Modularity, Contextuality, and Evolution (WOMoCoE 2017) co-located with 16th International Semantic Web Conference (ISWC 2017), Vienna, Austria, October 22nd, 2017*, volume 1936 of*CEUR Workshop Proceedings*, pages 1–16. CEUR-WS.org, October 2017.Abstract BibTeX Entry PDF File

Temporal query languages are important for stream processing, and ontologies for stream reasoning. Temporal conjunctive queries have therefore been investigated recently together with description logic ontologies, and the knowledge we have about the combined complexities is rather complete. However, often the size of the queries and the ontology is negligible, and what costs is the data. We present new results on the data complexity of ontology-based temporal query answering and close the gap between co-NP and ExpTime for many description logics.

@inproceedings{ Thost-WSP17, author = {Veronika {Thost}}, booktitle = {Joint Proceedings of the Web Stream Processing workshop (WSP 2017) and the 2nd International Workshop on Ontology Modularity, Contextuality, and Evolution (WOMoCoE 2017) co-located with 16th International Semantic Web Conference (ISWC 2017), Vienna, Austria, October 22nd, 2017}, editor = {Daniele {Dell'Aglio} and Darko {Anicic} and Payam M. {Barnaghi} and Emanuele Della {Valle} and Deborah L. {McGuinness} and Loris {Bozzato} and Thomas {Eiter} and Martin {Homola} and Daniele {Porello}}, month = {October}, pages = {1--16}, publisher = {CEUR-WS.org}, series = {CEUR Workshop Proceedings}, title = {News on Temporal Conjunctive Queries}, volume = {1936}, year = {2017}, }

Veronika Thost:

Abstract BibTeX Entry PDF File DOI

**Using Ontology-Based Data Access to Enable Context Recognition in the Presence of Incomplete Information (Extended Abstract)**.*KI*, 31(4):377–380, 2017.Abstract BibTeX Entry PDF File DOI

Ontologies may capture the terminology of an application domain and describe domain knowledge in a machine-processable way. Formal ontology languages, such as description logics, additionally provide semantics to these specifications. Systems for ontology-based data access (OBDA) may thus apply logical reasoning to answer queries over given data; they use the ontological knowledge to infer new information that is implicit in the data. The classical OBDA setting regards however only a single moment, which means that information about time is not used for reasoning and that the queries cannot express temporal aspects. We investigate temporal query languages that allow to access temporal data through classical ontologies. In particular, we study the computational complexity of temporal query answering regarding ontologies written in lightweight description logics, which are known to allow for efficient reasoning in the atemporal setting and are successfully applied in practice. Furthermore, we present a so-called rewritability result for ontology-based temporal query answering, which suggests ways for implementation. Our results may thus guide the choice of a query language for temporal OBDA in data-intensive applications that require fast processing.

@article{ Thost-KIJ2017, author = {Veronika {Thost}}, doi = {https://dx.doi.org/10.1007/s13218-017-0510-z}, journal = {{KI}}, number = {4}, pages = {377--380}, title = {Using Ontology-Based Data Access to Enable Context Recognition in the Presence of Incomplete Information (Extended Abstract)}, volume = {31}, year = {2017}, }

Marco Wilhelm, Gabriele Kern-Isberner, and Andreas Ecke:

Abstract BibTeX Entry PDF File

**Basic Independence Results for Maximum Entropy Reasoning Based on Relational Conditionals**. In*GCAI 2017. 3rd Global Conference on Artificial Intelligence*, volume 50 of*EPiC Series in Computing*, pages 36–50. EasyChair, 2017.Abstract BibTeX Entry PDF File

Maximum entropy reasoning (ME-reasoning) based on relational conditionals combines both the capability of ME-distributions to express uncertain knowledge in a way that excellently fits to commonsense, and the great expressivity of an underlying first-order logic. The drawbacks of this approach are its high complexity which is generally paired with a costly domain size dependency, and its non-transparency due to the non-existent a priori independence assumptions as against in Bayesian networks. In this paper we present some independence results for ME-reasoning based on the aggregating semantics for relational conditionals that help to disentangle the composition of ME-distributions, and therefore, lead to a problem reduction and provide structural insights into ME-reasoning.

@inproceedings{ WiKeEc-GCAI17, author = {Marco {Wilhelm} and Gabriele {Kern-Isberner} and Andreas {Ecke}}, booktitle = {{GCAI} 2017. 3rd Global Conference on Artificial Intelligence}, pages = {36--50}, publisher = {EasyChair}, series = {EPiC Series in Computing}, title = {Basic Independence Results for Maximum Entropy Reasoning Based on Relational Conditionals}, volume = {50}, year = {2017}, }

## 2016

F. Baader, M. Bienvenu, C. Lutz, and F. Wolter:

Abstract BibTeX Entry PDF File DOI

**Query and Predicate Emptiness in Ontology-Based Data Access**.*Journal of Artificial Intelligence Research (JAIR)*, 56:1–59, 2016.Abstract BibTeX Entry PDF File DOI

In ontology-based data access (OBDA), database querying is enriched with an ontology that provides domain knowledge and additional vocabulary for query formulation. We identify query emptiness and predicate emptiness as two central reasoning services in this context. Query emptiness asks whether a given query has an empty answer over all databases formulated in a given vocabulary. Predicate emptiness is defined analogously, but quantifies universally over all queries that contain a given predicate. In this paper, we determine the computational complexity of query emptiness and predicate emptiness in the EL, DL-Lite, and ALC-families of description logics, investigate the connection to ontology modules, and perform a practical case study to evaluate the new reasoning services.

@article{ BBLW-JAIR16, author = {F. {Baader} and M. {Bienvenu} and C. {Lutz} and F. {Wolter}}, doi = {http://dx.doi.org/10.1613/jair.4866}, journal = {Journal of Artificial Intelligence Research (JAIR)}, pages = {1--59}, title = {Query and Predicate Emptiness in Ontology-Based Data Access}, volume = {56}, year = {2016}, }

Franz Baader, Nguyen Thanh Binh, Stefan Borgwardt, and Barbara Morawska:

Abstract BibTeX Entry PDF File DOI

**Deciding Unifiability and Computing Local Unifiers in the Description Logic**\(\mathcal{EL}\)**without Top Constructor**.*Notre Dame Journal of Formal Logic*, 57(4):443–476, 2016.Abstract BibTeX Entry PDF File DOI

Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. The inexpressive description logic EL is of particular interest in this context since, on the one hand, several large biomedical ontologies are defined using EL. On the other hand, unification in EL has been shown to be NP-complete, and thus of considerably lower complexity than unification in other description logics of similarly restricted expressive power. However, EL allows the use of the top concept, which represents the whole interpretation domain, whereas the large medical ontology SNOMED CT makes no use of this feature. Surprisingly, removing the top concept from EL makes the unification problem considerably harder. More precisely, we will show that unification in EL without the top concept is PSpace-complete. In addition to the decision problem, we also consider the problem of actually computing unifiers in EL without top.

@article{ BBBM-NDJFL15, author = {Franz {Baader} and Nguyen Thanh {Binh} and Stefan {Borgwardt} and Barbara {Morawska}}, doi = {http://dx.doi.org/10.1215/00294527-3555507}, journal = {Notre Dame Journal of Formal Logic}, number = {4}, pages = {443--476}, title = {Deciding Unifiability and Computing Local Unifiers in the Description Logic {$\mathcal{EL}$} without Top Constructor}, volume = {57}, year = {2016}, }

Franz Baader, Stefan Borgwardt, and Barbara Morawska:

Abstract BibTeX Entry PDF File DOI

**Extending Unification in**\(\mathcal{EL}\)**to Disunification: The Case of Dismatching and Local Disunification**.*Logical Methods in Computer Science*, 12(4:1):1–28, 2016.Abstract BibTeX Entry PDF File DOI

Unification in Description Logics has been introduced as a means to detect redundancies in ontologies. We try to extend the known decidability results for unification in the Description Logic EL to disunification since negative constraints can be used to avoid unwanted unifiers. While decidability of the solvability of general EL-disunification problems remains an open problem, we obtain NP-completeness results for two interesting special cases: dismatching problems, where one side of each negative constraint must be ground, and local solvability of disunification problems, where we consider only solutions that are constructed from terms occurring in the input problem. More precisely, we first show that dismatching can be reduced to local disunification, and then provide two complementary NP-algorithms for finding local solutions of disunification problems.

@article{ BaBM-LMCS16, author = {Franz {Baader} and Stefan {Borgwardt} and Barbara {Morawska}}, doi = {http://dx.doi.org/10.2168/LMCS-12(4:1)2016}, journal = {Logical Methods in Computer Science}, number = {4:1}, pages = {1--28}, title = {Extending Unification in {$\mathcal{EL}$} to Disunification: {T}he Case of Dismatching and Local Disunification}, volume = {12}, year = {2016}, }

Franz Baader and Andreas Ecke:

Abstract BibTeX Entry PDF File

**Reasoning with Prototypes in the Description Logic ALC using Weighted Tree Automata**. In*Proceedings of the 10th International Conference on Language and Automata Theory and Applications (LATA 2016)*, volume 9618 of*Lecture Notes in Computer Science*, pages 63–75. Springer-Verlag, 2016.Abstract BibTeX Entry PDF File

We introduce an extension to Description Logics that allows us to use prototypes to define concepts. To accomplish this, we introduce the notion of a prototype distance functions (pdf), which assign to each element of an interpretation a distance value. Based on this, we define a new concept constructor of the form P n(d) for being a relation from ≤,<,≥,>, which is interpreted as the set of all elements with a distance n according to the pdf d. We show how weighted alternating parity tree automata (wapta) over the integers can be used to define pdfs, and how this allows us to use both concepts and pointed interpretations as prototypes. Finally, we investigate the complexity of reasoning in ALCP(wapta), which extends the Description Logic ALC with prototype constructors for pdfs defined using wapta.

@inproceedings{ BaEc-LATA16, author = {Franz {Baader} and Andreas {Ecke}}, booktitle = {Proceedings of the 10th International Conference on Language and Automata Theory and Applications (LATA 2016)}, pages = {63--75}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Reasoning with Prototypes in the Description Logic ALC using Weighted Tree Automata}, venue = {Prague, Czeck}, volume = {9618}, year = {2016}, }

Franz Baader and Oliver Fernández Gil:

Abstract BibTeX Entry PDF File

**Extending the Description Logic**\(\tau\mathcal{EL}(deg)\)**with Acyclic TBoxes**. In*ECAI 2016 - 22nd European Conference on Artificial Intelligence, 29 August-2 September 2016, The Hague, The Netherlands - Including Prestigious Applications of Artificial Intelligence (PAIS 2016)*, volume 285 of*Frontiers in Artificial Intelligence and Applications*, pages 1096–1104. IOS Press, 2016.Abstract BibTeX Entry PDF File

In a previous paper, we have introduced an extension of the lightweight Description Logic EL that allows us to define concepts in an approximate way. For this purpose, we have defined a graded membership function deg, which for each individual and concept yields a number in the interval [0,1] expressing the degree to which the individual belongs to the concept. Threshold concepts C t for in <, <=, >, >= then collect all the individuals that belong to C with degree t. We have then investigated the complexity of reasoning in the Description Logic tEL(deg), which is obtained from EL by adding such threshold concepts. In the present paper, we extend these results, which were obtained for reasoning without TBoxes, to the case of reasoning w.r.t. acyclic TBoxes. Surprisingly, this is not as easy as might have been expected. On the one hand, one must be quite careful to define acyclic TBoxes such that they still just introduce abbreviations for complex concepts, and thus can be unfolded. On the other hand, it turns out that, in contrast to the case of EL, adding acyclic TBoxes to tEL(deg) increases the complexity of reasoning by at least on level of the polynomial hierarchy.

@inproceedings{ DBLP:conf/ecai/BaaderG16, author = {Franz {Baader} and Oliver {Fern{\'a}ndez Gil}}, booktitle = {{ECAI} 2016 - 22nd European Conference on Artificial Intelligence, 29 August-2 September 2016, The Hague, The Netherlands - Including Prestigious Applications of Artificial Intelligence {(PAIS} 2016)}, pages = {1096--1104}, publisher = {{IOS} Press}, series = {Frontiers in Artificial Intelligence and Applications}, title = {Extending the Description Logic $\tau\mathcal{EL}(deg)$ with Acyclic TBoxes}, volume = {285}, year = {2016}, }

Franz Baader and Pierre Ludmann:

Abstract BibTeX Entry PDF File

**The Unification Type of**\({\mathsf{ACUI}}\)**w.r.t. the Unrestricted Instantiation Preorder is not Finitary**. In Silvio Ghilardi and Manfred Schmidt-Schauß, editors,*Proceedings of the 30th International Workshop on Unification (UNIF'16)*, pages 31–35, 2016.Abstract BibTeX Entry PDF File

The unification type of an equational theory is defined using a preorder on substitutions, called the instantiation preorder, whose scope is either restricted to the variables occurring in the unification problem, or unrestricted such that all variables are considered. It is known that the unification type of an equational theory may vary, depending on which instantiation preorder is used. More precisely, it was shown that the theory ACUI of an associative, commutative, and idempotent binary function symbol with a unit is unitary w.r.t. the restricted instantiation preorder, but not unitary w.r.t. the unrestricted one. Here, we improve on this result, by showing that, w.r.t. the unrestricted instantiation preorder, ACUI is not even finitary.

@inproceedings{ BaLu-UNIF2016, address = {Porto, Portugal}, author = {Franz {Baader} and Pierre {Ludmann}}, booktitle = {Proceedings of the 30th International Workshop on Unification ({UNIF'16})}, editor = {Silvio {Ghilardi} and Manfred {Schmidt-Schau{\ss}}}, pages = {31--35}, title = {The Unification Type of {${\mathsf{ACUI}}$} w.r.t.\ the Unrestricted Instantiation Preorder is not Finitary}, year = {2016}, }

Franz Baader, Pavlos Marantidis, and Alexander Okhotin:

Abstract BibTeX Entry

**Approximate Unification in the Description Logic**\(\mathcal{FL}_0\). In Loizos Michael and Antonis C. Kakas, editors,*Proc. of the 15th Eur. Conf. on Logics in Artificial Intelligence (JELIA 2016)*, volume 10021 of*Lecture Notes in Artificial Intelligence*, pages 49–63. Springer-Verlag, 2016.Abstract BibTeX Entry

Unification in Description logics (DLs) has been introduced as a novel inference service that can be used to detect redundancies in ontologies, by finding different concepts that may potentially stand for the same intuitive notion. It was first investigated in detail for the DL FL0, where unification can be reduced to solving certain language equations. In order to increase the recall of this method for finding redundancies, we introduce and investigate the notion of approximate unification, which basically finds pairs of concepts that "almost" unify. The meaning of "almost" is formalized using distance measures between concepts. We show that approximate unification in FL0 can be reduced to approximately solving language equations, and devise algorithms for solving the latter problem for two particular distance measures.

@inproceedings{ BaMaOk-JELIA16, author = {Franz {Baader} and Pavlos {Marantidis} and Alexander {Okhotin}}, booktitle = {Proc.\ of the 15th Eur.\ Conf.\ on Logics in Artificial Intelligence ({JELIA 2016})}, editor = {Loizos {Michael} and Antonis C. {Kakas}}, pages = {49--63}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Approximate Unification in the Description Logic {$\mathcal{FL}_0$}}, volume = {10021}, year = {2016}, }

Franz Baader, Pavlos Marantidis, and Alexander Okhotin:

Abstract BibTeX Entry PDF File

**Approximately Solving Set Equations**. In Silvio Ghilardi and Manfred Schmidt-Schauß, editors,*Proceedings of the 30th International Workshop on Unification (UNIF'16)*, pages 37–41, 2016.Abstract BibTeX Entry PDF File

Unification with constants modulo the theory ACUI of an associative (A), commutative (C) and idempotent (I) binary function symbol with a unit (U) corresponds to solving a very simple type of set equations. It is well-known that solvability of systems of such equations can be decided in polynomial time by reducing it to satisfiability of propositional Horn formulae. Here we introduce a modified version of this problem by no longer requiring all equations to be completely solved, but allowing for a certain number of violations of the equations. We introduce three different ways of counting the number of violations, and investigate the complexity of the respective decision problem, i.e., the problem of deciding whether there is an assignment that solves the system with at most l violations for a given threshold value l.

@inproceedings{ BaMaOk-UNIF2016, address = {Porto, Portugal}, author = {Franz {Baader} and Pavlos {Marantidis} and Alexander {Okhotin}}, booktitle = {Proceedings of the 30th International Workshop on Unification ({UNIF'16})}, editor = {Silvio {Ghilardi} and Manfred {Schmidt-Schau{\ss}}}, pages = {37--41}, title = {Approximately Solving Set Equations}, year = {2016}, }

Daniel Borchmann, Felix Distel, and Francesco Kriegel:

Abstract BibTeX Entry PDF File DOI ©Taylor and Francis

**Axiomatisation of General Concept Inclusions from Finite Interpretations**.*Journal of Applied Non-Classical Logics*, 26(1):1–46, 2016.Abstract BibTeX Entry PDF File DOI ©Taylor and Francis

Description logic knowledge bases can be used to represent knowledge about a particular domain in a formal and unambiguous manner. Their practical relevance has been shown in many research areas, especially in biology and the Semantic Web. However, the tasks of constructing knowledge bases itself, often performed by human experts, is difficult, time-consuming and expensive. In particular the synthesis of terminological knowledge is a challenge every expert has to face. Because human experts cannot be omitted completely from the construction of knowledge bases, it would therefore be desirable to at least get some support from machines during this process. To this end, we shall investigate in this work an approach which shall allow us to extract terminological knowledge in the form of general concept inclusions from factual data, where the data is given in the form of vertex and edge labeled graphs. As such graphs appear naturally within the scope of the Semantic Web in the form of sets of RDF triples, the presented approach opens up another possibility to extract terminological knowledge from the Linked Open Data Cloud.

@article{ BoDiKr-JANCL16, author = {Daniel {Borchmann} and Felix {Distel} and Francesco {Kriegel}}, doi = {https://dx.doi.org/10.1080/11663081.2016.1168230}, journal = {Journal of Applied Non-Classical Logics}, number = {1}, pages = {1--46}, title = {Axiomatisation of General Concept Inclusions from Finite Interpretations}, volume = {26}, year = {2016}, }

Daniel Borchmann and Tom Hanika:

Abstract BibTeX Entry PDF File

**Some Experimental Results on Randomly Generating Formal Contexts**. In Marianne Huchard and Sergei Kuznetsov, editors,*Proceedings of the Thirteenth International Conference on Concept Lattices and Their Applications*, volume 1624 of*CEUR Workshop Proceedings*, pages 57–69. CEUR-WS.org, July 2016.Abstract BibTeX Entry PDF File

We investigate different simple approaches to generate random formal contexts. To this end, we consider for each approach the empirical correlation between the number of intents and pseudo-intents. We compare the results of these experiments with corresponding observations on real-world use-cases. This comparison yields huge differences between artificially generated and real-world data sets, indicating that using randomly generated formal contexts for applications such as benchmarking may not necessarily be meaningful. In doing so, we additionally show that the previously observed phenomenon of the “Stegosaurus” does not express a real correlation between intents and pseudo-intents, but is an artifact of the way random contexts are generated.

@inproceedings{ conf/cla/BorchmannH16, author = {Daniel {Borchmann} and Tom {Hanika}}, booktitle = {Proceedings of the Thirteenth International Conference on Concept Lattices and Their Applications}, editor = {Marianne {Huchard} and Sergei {Kuznetsov}}, month = {July}, pages = {57--69}, publisher = {CEUR-WS.org}, series = {{CEUR} Workshop Proceedings}, title = {Some Experimental Results on Randomly Generating Formal Contexts}, venue = {Moscow, Russia}, volume = {1624}, year = {2016}, }

Stefan Borgwardt, Bettina Fazzinga, Thomas Lukasiewicz, Akanksha Shrivastava, and Oana Tifrea-Marciuska:

Abstract BibTeX Entry PDF File ©IJCAI

**Preferential Query Answering in the Semantic Web with Possibilistic Networks**. In Subbarao Kambhampati, editor,*Proceedings of the 25th International Joint Conference on Artificial Intelligence (IJCAI'16)*, pages 994–1000. New York City, USA, AAAI Press, 2016.Abstract BibTeX Entry PDF File ©IJCAI

In this paper, we explore how ontological knowledge expressed via existential rules can be combined with possibilistic networks (i) to represent qualitative preferences along with domain knowledge, and (ii) to realize preference-based answering of conjunctive queries (CQs). We call these combinations ontological possibilistic networks (OP-nets). We define skyline and k-rank answers to CQs under preferences and provide complexity (including data tractability) results for deciding consistency and CQ skyline membership for OP-nets. We show that our formalism has a lower complexity than a similar existing formalism.

@inproceedings{ BFLST-IJCAI16, address = {New York City, USA}, author = {Stefan {Borgwardt} and Bettina {Fazzinga} and Thomas {Lukasiewicz} and Akanksha {Shrivastava} and Oana {Tifrea-Marciuska}}, booktitle = {Proceedings of the 25th International Joint Conference on Artificial Intelligence (IJCAI'16)}, editor = {Subbarao {Kambhampati}}, pages = {994--1000}, publisher = {AAAI Press}, title = {Preferential Query Answering in the Semantic Web with Possibilistic Networks}, year = {2016}, }

Stefan Borgwardt, Bettina Fazzinga, Thomas Lukasiewicz, Akanksha Shrivastava, and Oana Tifrea-Marciuska:

Abstract BibTeX Entry PDF File DOI ©Springer-Verlag

**Preferential Query Answering in the Semantic Web with Possibilistic Networks**. In Gerhard Friedrich, Malte Helmert, and Franz Wotawa, editors,*Appendix to the 39th German Conference on Artificial Intelligence (KI'16)*, volume 9904 of*Lecture Notes in Artificial Intelligence*, pages 264–270. Klagenfurt, Austria, Springer-Verlag, 2016. Extended abstract.Abstract BibTeX Entry PDF File DOI ©Springer-Verlag

@inproceedings{ BFLST-KI16, address = {Klagenfurt, Austria}, author = {Stefan {Borgwardt} and Bettina {Fazzinga} and Thomas {Lukasiewicz} and Akanksha {Shrivastava} and Oana {Tifrea-Marciuska}}, booktitle = {Appendix to the 39th German Conference on Artificial Intelligence (KI'16)}, doi = {http://dx.doi.org/10.1007/978-3-319-46073-4}, editor = {Gerhard {Friedrich} and Malte {Helmert} and Franz {Wotawa}}, note = {Extended abstract.}, pages = {264--270}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Preferential Query Answering in the {Semantic Web} with Possibilistic Networks}, volume = {9904}, year = {2016}, }

Stefan Borgwardt, Theofilos Mailis, Rafael Peñaloza, and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File DOI

**Answering Fuzzy Conjunctive Queries over Finitely Valued Fuzzy Ontologies**.*Journal on Data Semantics*, 5(2):55–75, 2016.Abstract BibTeX Entry PDF File DOI

Fuzzy Description Logics (DLs) provide a means for representing vague knowledge about an application domain. In this paper, we study fuzzy extensions of conjunctive queries (CQs) over the DL SROIQ based on finite chains of degrees of truth. To answer such queries, we extend a well-known technique that reduces the fuzzy ontology to a classical one, and use classical DL reasoners as a black box. We improve the complexity of previous reduction techniques for finitely valued fuzzy DLs, which allows us to prove tight complexity results for answering certain kinds of fuzzy CQs. We conclude with an experimental evaluation of a prototype implementation, showing the feasibility of our approach.

@article{ BMPT-JoDS16, author = {Stefan {Borgwardt} and Theofilos {Mailis} and Rafael {Pe{\~n}aloza} and Anni-Yasmin {Turhan}}, doi = {http://dx.doi.org/10.1007/s13740-015-0055-y}, journal = {Journal on Data Semantics}, number = {2}, pages = {55--75}, title = {Answering Fuzzy Conjunctive Queries over Finitely Valued Fuzzy Ontologies}, volume = {5}, year = {2016}, }

Stefan Borgwardt and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Reasoning in Expressive Gödel Description Logics**. In Maurizio Lenzerini and Rafael Peñaloza, editors,*Proceedings of the 29th International Workshop on Description Logics (DL'16)*, volume 1577 of*CEUR Workshop Proceedings*, 2016.Abstract BibTeX Entry PDF File

Fuzzy description logics (FDLs) are knowledge representation formalisms capable of dealing with imprecise knowledge by allowing intermediate membership degrees in the interpretation of concepts and roles. One option for dealing with these intermediate degrees is to use the so-called Gödel semantics, under which conjunction is interpreted by the minimum of the degrees. Despite its apparent simplicity, developing reasoning techniques for expressive FDLs under this semantics is a hard task. In this paper, we illustrate two algorithms for deciding consistency in (sublogics of) SROIQ under Gödel semantics.

@inproceedings{ BoPe-DL16, address = {Cape Town, South Africa}, author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 29th International Workshop on Description Logics (DL'16)}, editor = {Maurizio {Lenzerini} and Rafael {Pe{\~n}aloza}}, series = {CEUR Workshop Proceedings}, title = {Reasoning in Expressive {G}{\"o}del Description Logics}, volume = {1577}, year = {2016}, }

Stefan Borgwardt and Rafael Peñaloza:

Abstract BibTeX Entry PDF File DOI

**Reasoning in fuzzy description logics using automata**.*Fuzzy Sets and Systems*, 298:22–43, 2016.Abstract BibTeX Entry PDF File DOI

Automata-based methods have been successfully employed to prove tight complexity bounds for reasoning in many classical logics, and in particular in Description Logics (DLs). Very recently, the ideas behind these automata-based approaches were adapted for reasoning also in fuzzy extensions of DLs, with semantics based either on finitely many truth degrees or the Gödel t-norm over the interval [0,1]. Clearly, due to the different semantics in these logics, the construction of the automata for fuzzy DLs is more involved than for the classical case. In this paper we provide an overview of the existing automata-based methods for reasoning in fuzzy DLs, with a special emphasis on explaining the ideas and the requirements behind them. The methods vary from deciding emptiness of automata on infinite trees to inclusions between automata on finite words. Overall, we provide a comprehensive perspective on the automata-based methods currently in use, and the many complexity results obtained through them.

@article{ BoPe-FSS15, author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}}, doi = {http://dx.doi.org/10.1016/j.fss.2015.07.013}, journal = {Fuzzy Sets and Systems}, pages = {22--43}, title = {Reasoning in fuzzy description logics using automata}, volume = {298}, year = {2016}, }

Claudia Carapelle and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File DOI

**Description Logics Reasoning w.r.t. general TBoxes is decidable for Concrete Domains with the EHD-property**. In Gal A. Kaminka, Maria Fox, Paolo Bouquet, Eyke Hüllermeier, Virginia Dignum, Frank Dignum, and Frank van Harmelen, editors,*Proceedings of the 22nd European Conference on Artificial Intelligence*, pages 1440–1448. Dresden, Germany, IOS Press, 2016.Abstract BibTeX Entry PDF File DOI

Reasoning for Description logics with concrete domains and w.r.t. general TBoxes easily becomes undecidable. However, with some restriction on the concrete domain, decidability can be regained. We introduce a novel way to integrate concrete domains D into the well-known description logic ALC, we call the resulting logic ALCP(D). We then identify sufficient conditions on D that guarantee decidability of the satisfiability problem, even in the presence of general TBoxes. In particular, we show decidability of ALCP(D) for several domains over the integers, for which decidabil- ity was open. More generally, this result holds for all negation-closed concrete domains with the EHD-property, which stands for ‘the exis- tence of a homomorphism is definable’. Such technique has recently been used to show decidability of CTL∗ with local constraints over the integers.

@inproceedings{ CaTu-ECAI-16, address = {Dresden, Germany}, author = {Claudia {Carapelle} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of the 22nd European Conference on Artificial Intelligence}, doi = {https://dx.doi.org/10.3233/978-1-61499-672-9-1440}, editor = {Gal A. {Kaminka} and Maria {Fox} and Paolo {Bouquet} and Eyke {H{\"{u}}llermeier} and Virginia {Dignum} and Frank {Dignum} and Frank van {Harmelen}}, pages = {1440--1448}, publisher = {{IOS} Press}, title = {Description Logics Reasoning w.r.t. general TBoxes is decidable for Concrete Domains with the EHD-property}, year = {2016}, }

Ismail Ilkan Ceylan, Adnan Darwiche, and Guy Van den Broeck:

Abstract BibTeX Entry PDF File

**Open-World Probabilistic Databases**. In Chitta Baral, James P. Delgrande, and Frank Wolter, editors,*Proceedings of 15. International Conference on Principles of Knowledge Representation and Reasoning (KR 2016)*, pages 339–348. AAAI Press, 2016. Marco Cadoli Best Student Paper PrizeAbstract BibTeX Entry PDF File

Large-scale probabilistic knowledge bases are becoming increasingly important in academia and industry alike. They are constantly extended with new data, powered by modern information extraction tools that associate probabilities with database tuples. In this paper, we revisit the semantics underlying such systems. In particular, the closed-world assumption of probabilistic databases, that facts not in the database have probability zero, clearly conflicts with their everyday use. To address this discrepancy, we propose an open-world probabilistic database semantics, which relaxes the probabilities of open facts to intervals. While still assuming a finite domain, this semantics can provide meaningful answers when some probabilities are not precisely known. For this open world setting, we propose an efficient evaluation algorithm for unions of conjunctive queries. Our open-world algorithm incurs no overhead compared to closed-world reasoning and runs in time linear in the size of the database for tractable queries. All other queries are #P-hard, implying a data complexity dichotomy between linear time and #P. For queries involving negation, however, open-world reasoning can become NP-, or even NP^{P}P-hard. Finally, we discuss additional knowledge-representation layers that can further strengthen open-world reasoning about big uncertain data.

@inproceedings{ CDB2016, author = {Ismail Ilkan {Ceylan} and Adnan {Darwiche} and Guy Van den {Broeck}}, booktitle = {Proceedings of 15. International Conference on Principles of Knowledge Representation and Reasoning (KR 2016)}, editor = {Chitta {Baral} and James P. {Delgrande} and Frank {Wolter}}, note = {Marco Cadoli Best Student Paper Prize}, pages = {339--348}, publisher = {AAAI Press}, title = {Open-World Probabilistic Databases}, year = {2016}, }

Ismail Ilkan Ceylan, Adnan Darwiche, and Guy Van den Broeck:

BibTeX Entry PDF File

**Open-World Probabilistic Databases (Extended Abstract)**. In Maurizio Lenzerini and Rafael Peñaloza, editors,*Proceedings of the 29th International Workshop on Description Logics (DL 2016)*. CEUR Workshop Proceedings, 2016.BibTeX Entry PDF File

@inproceedings{ CeDaVa-DL16, author = {Ismail Ilkan {Ceylan} and Adnan {Darwiche} and Guy Van den {Broeck}}, booktitle = {Proceedings of the 29th International Workshop on Description Logics (DL 2016)}, editor = {Maurizio {Lenzerini} and Rafael {Pe\~{n}aloza}}, publisher = {CEUR Workshop Proceedings}, title = {Open-World Probabilistic Databases (Extended Abstract)}, volume = {1577}, year = {2016}, }

Ismail Ilkan Ceylan, Thomas Lukasiewicz, and Rafael Peñaloza Nyssen:

Abstract BibTeX Entry PDF File

**Complexity Results for Probabilistic Datalog+/-**. In Maria S. Fox and Gal A. Kaminka, editors,*Proceedings of the 22nd European Conference on Artificial Intelligence (ECAI 2016)*, pages 1414–1422. IOS Press, 2016.Abstract BibTeX Entry PDF File

We study the query evaluation problem in probabilistic databases in the presence of probabilistic existential rules. Our focus is on Datalog+/- family of languages for which we define the probabilistic counterpart using a flexible and compact encoding of probabilities. This formalism can be viewed as a generalization of probabilistic databases as it allows to generate new facts from the given ones using the so-called tuple generating dependencies, or existential rules. We study the computational cost of this additional expressiveness under two different semantics. First, we use a conventional approach and assume that the probabilistic knowledge base is consistent and employ the standard possible world semantics. Afterwards, we introduce a probabilistic inconsistency-tolerant semantics, which we refer as inconsistency-tolerant possible world semantics. For both of these cases, we provide a through complexity analysis relative to different languages; drawing a complete picture of the complexity of probabilistic query answering in this family.

@inproceedings{ CeLuPe-ECAI16, author = {Ismail Ilkan {Ceylan} and Thomas {Lukasiewicz} and Rafael Pe\~{n}aloza {Nyssen}}, booktitle = {Proceedings of the 22nd European Conference on Artificial Intelligence (ECAI 2016)}, editor = {Maria S. {Fox} and Gal A. {Kaminka}}, pages = {1414--1422}, publisher = {IOS Press}, title = {Complexity Results for Probabilistic Datalog+/-}, volume = {285}, year = {2016}, }

Francesco Kriegel:

Abstract BibTeX Entry PDF File PDF File (ceur-ws.org)

**Axiomatization of General Concept Inclusions from Streams of Interpretations with Optional Error Tolerance**. In Sergei Kuznetsov, Amedeo Napoli, and Sebastian Rudolph, editors,*Proceedings of the 5th International Workshop "What can FCA do for Artificial Intelligence?" (FCA4AI 2016) co-located with the European Conference on Artificial Intelligence (ECAI 2016)*, volume 1703 of*CEUR Workshop Proceedings*, pages 9–16. The Hague, The Netherlands, CEUR-WS.org, 2016.Abstract BibTeX Entry PDF File PDF File (ceur-ws.org)

We propose applications that utilize the infimum and the supremum of closure operators that are induced by structures occuring in the field of Description Logics. More specifically, we consider the closure operators induced by interpretations as well as closure operators induced by TBoxes, and show how we can learn GCIs from streams of interpretations, and how an error-tolerant axiomatization of GCIs from an interpretation guided by a hand-crafted TBox can be achieved.

@inproceedings{ Kr-FCA4AI16, address = {The Hague, The Netherlands}, author = {Francesco {Kriegel}}, booktitle = {Proceedings of the 5th International Workshop "What can {FCA} do for Artificial Intelligence?" ({FCA4AI} 2016) co-located with the European Conference on Artificial Intelligence ({ECAI} 2016)}, editor = {Sergei {Kuznetsov} and Amedeo {Napoli} and Sebastian {Rudolph}}, pages = {9--16}, publisher = {CEUR-WS.org}, series = {{CEUR} Workshop Proceedings}, title = {Axiomatization of General Concept Inclusions from Streams of Interpretations with Optional Error Tolerance}, volume = {1703}, year = {2016}, }

Francesco Kriegel:

Abstract BibTeX Entry PDF File PDF File (ceur-ws.org)

**NextClosures with Constraints**. In Marianne Huchard and Sergei Kuznetsov, editors,*Proceedings of the 13th International Conference on Concept Lattices and Their Applications (CLA 2016)*, volume 1624 of*CEUR Workshop Proceedings*, pages 231–243. Moscow, Russia, CEUR-WS.org, 2016.Abstract BibTeX Entry PDF File PDF File (ceur-ws.org)

In a former paper, the algorithm NextClosures for computing the set of all formal concepts as well as the canonical base for a given formal context has been introduced. Here, this algorithm shall be generalized to a setting where the data-set is described by means of a closure operator in a complete lattice, and furthermore it shall be extended with the possibility to handle constraints that are given in form of a second closure operator. As a special case, constraints may be predefined as implicational background knowledge. Additionally, we show how the algorithm can be modified in order to do parallel Attribute Exploration for unconstrained closure operators, as well as give a reason for the impossibility of (parallel) Attribute Exploration for constrained closure operators if the constraint is not compatible with the data-set.

@inproceedings{ Kr-CLA16, address = {Moscow, Russia}, author = {Francesco {Kriegel}}, booktitle = {Proceedings of the 13th International Conference on Concept Lattices and Their Applications ({CLA 2016})}, editor = {Marianne {Huchard} and Sergei {Kuznetsov}}, pages = {231--243}, publisher = {CEUR-WS.org}, series = {{CEUR} Workshop Proceedings}, title = {NextClosures with Constraints}, volume = {1624}, year = {2016}, }

Francesco Kriegel:

Abstract BibTeX Entry PDF File DOI ©Springer-Verlag

**Parallel Attribute Exploration**. In Ollivier Haemmerlé, Gem Stapleton, and Catherine Faron-Zucker, editors,*Proceedings of the 22nd International Conference on Conceptual Structures (ICCS 2016)*, volume 9717 of*Lecture Notes in Computer Science*, pages 91–106. Annecy, France, Springer-Verlag, 2016.Abstract BibTeX Entry PDF File DOI ©Springer-Verlag

The canonical base of a formal context is a minimal set of implications that is sound and complete. A recent paper has provided a new algorithm for the parallel computation of canonical bases. An important extension is the integration of expert interaction for Attribute Exploration in order to explore implicational bases of inaccessible formal contexts. This paper presents and analyzes an algorithm that allows for Parallel Attribute Exploration.

@inproceedings{ Kr-ICCS16, address = {Annecy, France}, author = {Francesco {Kriegel}}, booktitle = {Proceedings of the 22nd International Conference on Conceptual Structures ({ICCS 2016})}, doi = {http://dx.doi.org/10.1007/978-3-319-40985-6_8}, editor = {Ollivier {Haemmerl{\'{e}}} and Gem {Stapleton} and Catherine {Faron{-}Zucker}}, pages = {91--106}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Parallel Attribute Exploration}, volume = {9717}, year = {2016}, }

Markus Krötzsch and Veronika Thost:

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**Ontologies for Knowledge Graphs: Breaking the Rules**. In Yolanda Gil, Elena Simperl, Paul Groth, Freddy Lecue, Markus Krötzsch, Alasdair Gray, Marta Sabou, Fabian Flöck, and Hideaki Takeda, editors,*Proceedings of the 15th International Semantic Web Conference (ISWC 2016)*,*LNCS*. Springer, 2016.Abstract BibTeX Entry PDF File

Large-scale knowledge graphs (KGs) are widely used in industry and academia, and provide excellent use-cases for ontologies. We find, however, that popular ontology languages, such as OWL and Datalog, cannot express even the most basic relationships on the normalised data format of KGs. Existential rules are more powerful, but may make reasoning undecidable. Normalising them to suit KGs often also destroys syntactic restrictions that ensure decidability and low complexity. We study this issue for several classes of existential rules and derive new syntactic criteria to recognise well-behaved rule-based ontologies over KGs.

@inproceedings{ KT-ISWC2016, author = {Markus {Kr{\"{o}}tzsch} and Veronika {Thost}}, booktitle = {Proceedings of the 15th International Semantic Web Conference (ISWC 2016)}, editor = {Yolanda {Gil} and Elena {Simperl} and Paul {Groth} and Freddy {Lecue} and Markus {Kr{\"{o}}tzsch} and Alasdair {Gray} and Marta {Sabou} and Fabian {Fl{\"{o}}ck} and Hideaki {Takeda}}, publisher = {Springer}, series = {LNCS}, title = {Ontologies for Knowledge Graphs: Breaking the Rules}, year = {2016}, }

Benjamin Zarrieß and Jens Claßen:

Abstract BibTeX Entry

**Decidable Verification of Golog Programs over Non-Local Effect Actions**. In Dale Schuurmans and Michael Wellman, editors,*Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence (AAAI-16)*. AAAI Press, February 2016.Abstract BibTeX Entry

The Golog action programming language is a powerful means to express high-level behaviours in terms of programs over actions defined in a Situation Calculus theory. In particular for physical systems, verifying that the program satisfies certain desired temporal properties is often crucial, but undecidable in general, the latter being due to the language's high expressiveness in terms of first-order quantification and program constructs. So far, approaches to achieve decidability involved restrictions where action effects either had to be context-free (i.e. not depend on the current state), local (i.e. only affect objects mentioned in the action's parameters), or at least bounded (i.e. only affect a finite number of objects). In this paper, we present a new, more general class of action theories (called acyclic) that allows for context-sensitive, non-local, unbounded effects, i.e. actions that may affect an unbounded number of possibly unnamed objects in a state-dependent fashion. We contribute to the further exploration of the boundary between decidability and undecidability for Golog, showing that for acyclic theories in the two-variable fragment of first-order logic, verification of CTL* properties of programs over ground actions is decidable.

@inproceedings{ ZC2016, author = {Benjamin {Zarrie{\ss}} and Jens {Cla{\ss}en}}, booktitle = {Proceedings of the Thirtieth {AAAI} Conference on Artificial Intelligence (AAAI-16)}, editor = {Dale {Schuurmans} and Michael {Wellman}}, month = {February}, publisher = {AAAI Press}, title = {Decidable Verification of Golog Programs over Non-Local Effect Actions}, year = {2016}, }

## 2015

Franz Baader, Stefan Borgwardt, and Marcel Lippmann:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Temporal Conjunctive Queries in Expressive Description Logics with Transitive Roles**. In Bernhard Pfahringer and Jochen Renz, editors,*Proceedings of the 28th Australasian Joint Conference on Artificial Intelligence (AI'15)*, volume 9457 of*Lecture Notes in Artificial Intelligence*, pages 21–33. Canberra, Australia, Springer-Verlag, 2015.Abstract BibTeX Entry PDF File ©Springer-Verlag

In Ontology-Based Data Access (OBDA), user queries are evaluated over a set of facts under the open world assumption, while taking into account background knowledge given in the form of a Description Logic (DL) ontology. In order to deal with dynamically changing data sources, temporal conjunctive queries (TCQs) have recently been proposed as a useful extension of OBDA to support the processing of temporal information. We extend the existing complexity analysis of TCQ entailment to very expressive DLs underlying the OWL 2 standard, and in contrast to previous work also allow for queries containing transitive roles.

@inproceedings{ BaBL-AI15, address = {Canberra, Australia}, author = {Franz {Baader} and Stefan {Borgwardt} and Marcel {Lippmann}}, booktitle = {Proceedings of the 28th Australasian Joint Conference on Artificial Intelligence (AI'15)}, editor = {Bernhard {Pfahringer} and Jochen {Renz}}, pages = {21--33}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Temporal Conjunctive Queries in Expressive Description Logics with Transitive Roles}, volume = {9457}, year = {2015}, }

Franz Baader, Stefan Borgwardt, and Marcel Lippmann:

Abstract BibTeX Entry PDF File DOI

**Temporal Query Entailment in the Description Logic**\(\mathcal{SHQ}\).*Journal of Web Semantics*, 33:71–93, 2015.Abstract BibTeX Entry PDF File DOI

Ontology-based data access (OBDA) generalizes query answering in databases towards deductive entailment since (i) the fact base is not assumed to contain complete knowledge (i.e., there is no closed world assumption), and (ii) the interpretation of the predicates occurring in the queries is constrained by axioms of an ontology. OBDA has been investigated in detail for the case where the ontology is expressed by an appropriate Description Logic (DL) and the queries are conjunctive queries. Motivated by situation awareness applications, we investigate an extension of OBDA to the temporal case. As the query language we consider an extension of the well-known propositional temporal logic LTL where conjunctive queries can occur in place of propositional variables, and as the ontology language we use the expressive DL SHQ. For the resulting instance of temporalized OBDA, we investigate both data complexity and combined complexity of the query entailment problem. In the course of this investigation, we also establish the complexity of consistency of Boolean knowledge bases in SHQ.

@article{ BaBL-JWS15, author = {Franz {Baader} and Stefan {Borgwardt} and Marcel {Lippmann}}, doi = {http://dx.doi.org/10.1016/j.websem.2014.11.008}, journal = {Journal of Web Semantics}, pages = {71--93}, title = {Temporal Query Entailment in the Description Logic {$\mathcal{SHQ}$}}, volume = {33}, year = {2015}, }

Franz Baader, Stefan Borgwardt, and Barbara Morawska:

Abstract BibTeX Entry PDF File

**Dismatching and Local Disunification in**\(\mathcal{EL}\). In Maribel Fernández, editor,*Proceedings of the 26th International Conference on Rewriting Techniques and Applications (RTA'15)*, volume 36 of*Leibniz International Proceedings in Informatics*, pages 40–56. Warsaw, Poland, Dagstuhl Publishing, 2015.Abstract BibTeX Entry PDF File

Unification in Description Logics has been introduced as a means to detect redundancies in ontologies. We try to extend the known decidability results for unification in the Description Logic EL to disunification since negative constraints on unifiers can be used to avoid unwanted unifiers. While decidability of the solvability of general EL-disunification problems remains an open problem, we obtain NP-completeness results for two interesting special cases: dismatching problems, where one side of each negative constraint must be ground, and local solvability of disunification problems, where we restrict the attention to solutions that are built from so-called atoms occurring in the input problem. More precisely, we first show that dismatching can be reduced to local disunification, and then provide two complementary NP-algorithms for finding local solutions of (general) disunification problems.

@inproceedings{ BaBM-RTA15, address = {Warsaw, Poland}, author = {Franz {Baader} and Stefan {Borgwardt} and Barbara {Morawska}}, booktitle = {Proceedings of the 26th International Conference on Rewriting Techniques and Applications (RTA'15)}, editor = {Maribel {Fern\'andez}}, pages = {40--56}, publisher = {Dagstuhl Publishing}, series = {Leibniz International Proceedings in Informatics}, title = {Dismatching and Local Disunification in {$\mathcal{EL}$}}, volume = {36}, year = {2015}, }

Franz Baader, Stefan Borgwardt, and Barbara Morawska:

BibTeX Entry PDF File

**Dismatching and Local Disunification in**\(\mathcal{EL}\)**(Extended Abstract)**. In Santiago Escobar and Mateu Villaret, editors,*Proceedings of the 29th International Workshop on Unification (UNIF'15)*, pages 13–18, 2015.BibTeX Entry PDF File

@inproceedings{ BaBM-UNIF15, address = {Warsaw, Poland}, author = {Franz {Baader} and Stefan {Borgwardt} and Barbara {Morawska}}, booktitle = {Proceedings of the 29th International Workshop on Unification (UNIF'15)}, editor = {Santiago {Escobar} and Mateu {Villaret}}, pages = {13--18}, title = {Dismatching and Local Disunification in {$\mathcal{EL}$} (Extended Abstract)}, year = {2015}, }

Franz Baader, Stefan Borgwardt, and Barbara Morawska:

Abstract BibTeX Entry PDF File

**Dismatching and Local Disunification in**\(\mathcal{EL}\)**(Extended Abstract)**. In Diego Calvanese and Boris Konev, editors,*Proceedings of the 28th International Workshop on Description Logics (DL'15)*, volume 1350 of*CEUR Workshop Proceedings*, pages 30–33, 2015.Abstract BibTeX Entry PDF File

@inproceedings{ BaBM-DL15, address = {Athens, Greece}, author = {Franz {Baader} and Stefan {Borgwardt} and Barbara {Morawska}}, booktitle = {Proceedings of the 28th International Workshop on Description Logics (DL'15)}, editor = {Diego {Calvanese} and Boris {Konev}}, pages = {30--33}, series = {CEUR Workshop Proceedings}, title = {Dismatching and Local Disunification in {$\mathcal{EL}$} (Extended Abstract)}, volume = {1350}, year = {2015}, }

Franz Baader, Stefan Borgwardt, and Rafael Peñaloza:

Abstract BibTeX Entry PDF File DOI

**On the Decidability Status of Fuzzy**\(\mathcal{ALC}\)**with General Concept Inclusions**.*Journal of Philosophical Logic*, 44(2):117–146, 2015.Abstract BibTeX Entry PDF File DOI

The combination of Fuzzy Logics and Description Logics (DLs) has been investigated for at least two decades because such fuzzy DLs can be used to formalize imprecise concepts. In particular, tableau algorithms for crisp Description Logics have been extended to reason also with their fuzzy counterparts. It has turned out, however, that in the presence of general concept inclusion axioms (GCIs) this extension is less straightforward than thought. In fact, a number of tableau algorithms claimed to deal correctly with fuzzy DLs with GCIs have recently been shown to be incorrect. In this paper, we concentrate on fuzzy ALC, the fuzzy extension of the well-known DL ALC. We present a terminating, sound, and complete tableau algorithm for fuzzy ALC with arbitrary continuous t-norms. Unfortunately, in the presence of GCIs, this algorithm does not yield a decision procedure for consistency of fuzzy ALC ontologies since it uses as a sub-procedure a solvability test for a finitely represented, but possibly infinite, system of inequations over the real interval [0,1], which are built using the t-norm. In general, it is not clear whether this solvability problem is decidable for such infinite systems of inequations. This may depend on the specific t-norm used. In fact, we also show in this paper that consistency of fuzzy ALC ontologies with GCIs is undecidable for the product t-norm. This implies, of course, that for the infinite systems of inequations produced by the tableau algorithm for fuzzy ALC with product t-norm, solvability is in general undecidable. We also give a brief overview of recently obtained (un)decidability results for fuzzy ALC w.r.t. other t-norms.

@article{ BaBP-JPL15, author = {Franz {Baader} and Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}}, doi = {http://dx.doi.org/10.1007/s10992-014-9329-3}, journal = {Journal of Philosophical Logic}, number = {2}, pages = {117--146}, title = {On the Decidability Status of Fuzzy {$\mathcal{ALC}$} with General Concept Inclusions}, volume = {44}, year = {2015}, }

Franz Baader, Gerhard Brewka, and Oliver Fernández Gil:

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**Adding Threshold Concepts to the Description Logic**\(\mathcal{EL}\). In Carsten Lutz and Silvio Ranise, editors,*Proceedings of the 10th International Symposium on Frontiers of Combining Systems (FroCoS'15)*, volume 9322 of*Lectures Notes in Artificial Intelligence*, pages 33–48. Wroclaw, Poland, Springer-Verlag, 2015.Abstract BibTeX Entry PDF File

We introduce an extension of the lightweight Description Logic EL that allows us to define concepts in an approximate way. For this purpose, we use a graded membership function, which for each individual and concept yields a number in the interval [0,1] expressing the degree to which the individual belongs to the concept. Threshold concepts C t for in <,<=,>,>= then collect all the individuals that belong to C with degree t. We generalize a well-known characterization of membership in EL concepts to construct a specific graded membership function deg , and investigate the complexity of reasoning in the Description Logic tauEL(deg), which extends EL by threshold concepts defined using deg . We also compare the instance problem for threshold concepts of the form C >t in tauEL(deg) with the relaxed instance queries of Ecke et al.

@inproceedings{ BBG-FROCOS-15, address = {Wroclaw, Poland}, author = {Franz {Baader} and Gerhard {Brewka} and Oliver {Fern\'andez Gil}}, booktitle = {Proceedings of the 10th International Symposium on Frontiers of Combining Systems (FroCoS'15)}, editor = {Carsten {Lutz} and Silvio {Ranise}}, pages = {33--48}, publisher = {Springer-Verlag}, series = {Lectures Notes in Artificial Intelligence}, title = {Adding Threshold Concepts to the Description Logic {$\mathcal{EL}$}}, volume = {9322}, year = {2015}, }

Franz Baader, Gerhard Brewka, and Oliver Fernández Gil:

Abstract BibTeX Entry PDF File

**Adding Threshold Concepts to the Description Logic EL (extended abstract)**. In Diego Calvanese and Boris Konev, editors,*Proceedings of the 28th International Workshop on Description Logics (DL-2015)*, volume 1350 of*CEUR Workshop Proceedings*. Athens, Greece, CEUR-WS.org, 2015.Abstract BibTeX Entry PDF File

We introduce an extension of the lightweight Description Logic EL that allows us to define concepts in an approximate way. For this purpose, we use a graded membership function which, for each individual and concept, yields a number in the interval [0,1] expressing the degree to which the individual belongs to the concept. Threshold concepts then collect all the individuals that belong to an EL concept C with degree less, less or equal, greater, respectively greater or equal r, for some r in [0,1] . We generalize a well-known characterization of membership in EL concepts to obtain an appropriate graded membership function deg, and investigate the complexity of reasoning in the Description Logic which extends EL by threshold concepts defined using deg.

@inproceedings{ BBGIL-DL-15, address = {Athens, Greece}, author = {Franz {Baader} and Gerhard {Brewka} and Oliver {Fern\'andez Gil}}, booktitle = {Proceedings of the 28th International Workshop on Description Logics (DL-2015)}, editor = {Diego {Calvanese} and Boris {Konev}}, publisher = {CEUR-WS.org}, series = {CEUR Workshop Proceedings}, title = {Adding Threshold Concepts to the Description Logic {EL} (extended abstract)}, volume = {1350}, year = {2015}, }

Franz Baader and Pierre Ludmann:

Abstract BibTeX Entry PDF File

**The Exact Unification Type of Commutative Theories**. In Santiago Escobar and Mateu Villaret, editors,*Proceedings of the 29th International Workshop on Unification (UNIF'15)*, pages 19–23, 2015.Abstract BibTeX Entry PDF File

The exact unification type of an equational theory is based on a new preorder on substitutions, called the exactness preorder, which is tailored towards transferring decidability results for unification to disunification. We show that two important results regarding the unification type of commutative theories hold not only for the usual instantiation preorder, but also for the exactness preorder: w.r.t. elementary unification, commutative theories are of type unary or nullary, and the theory ACUIh of Abelian idempotent monoids with a homomorphism is nullary.

@inproceedings{ BaLu-UNIF2015, address = {Warsaw, Poland}, author = {Franz {Baader} and Pierre {Ludmann}}, booktitle = {Proceedings of the 29th International Workshop on Unification ({UNIF'15})}, editor = {Santiago {Escobar} and Mateu {Villaret}}, pages = {19--23}, title = {The Exact Unification Type of Commutative Theories}, year = {2015}, }

Stephan Böhme and Marcel Lippmann:

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**Decidable Contextualized DLs with Rigid Roles**. In Diego Calvanese and Boris Konev, editors,*Proceedings of the 28th International Workshop on Description Logics (DL-2015)*, volume 1350 of*CEUR Workshop Proceedings*, pages 92–95. Athens, Greece, CEUR-WS.org, 2015.BibTeX Entry PDF File

@inproceedings{ BoLi-DL15, address = {Athens, Greece}, author = {Stephan {B{\"o}hme} and Marcel {Lippmann}}, booktitle = {Proceedings of the 28th International Workshop on Description Logics ({DL-2015})}, editor = {Diego {Calvanese} and Boris {Konev}}, pages = {92--95}, publisher = {CEUR-WS.org}, series = {CEUR Workshop Proceedings}, title = {Decidable Contextualized DLs with Rigid Roles}, volume = {1350}, year = {2015}, }

Stephan Böhme and Marcel Lippmann:

Abstract BibTeX Entry PDF File

**Decidable Description Logics of Context with Rigid Roles**. In Carsten Lutz and Silvio Ranise, editors,*Proceedings of the 10th International Symposium on Frontiers of Combining Systems (FroCoS'15)*, volume 9322 of*Lecture Notes in Artificial Intelligence*, pages 17–32. Wroclaw, Poland, Springer-Verlag, 2015.Abstract BibTeX Entry PDF File

To represent and reason about contextualized knowledge often two-dimensional Description Logics (DLs) are employed, where one DL is used to describe contexts (or possible worlds) and the other DL is used to describe the objects, i.e. the relational structure of the specific contexts. Previous approaches for DLs of context that combined pairs of DLs resulted in undecidability in those cases where so-called rigid roles are admitted, i.e. if parts of the relational structure are the same in all contexts. In this paper, we present a novel combination of pairs of DLs and show that reasoning stays decidable even in the presence of rigid roles. We give complexity results for various combinations of DLs including ALC, SHOQ, and EL.

@inproceedings{ BoLi-FroCoS15, address = {Wroclaw, Poland}, author = {Stephan {B{\"o}hme} and Marcel {Lippmann}}, booktitle = {Proceedings of the 10th International Symposium on Frontiers of Combining Systems (FroCoS'15)}, editor = {Carsten {Lutz} and Silvio {Ranise}}, pages = {17--32}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Decidable Description Logics of Context with Rigid Roles}, volume = {9322}, year = {2015}, }

Daniel Borchmann:

Abstract BibTeX Entry PDF File

**Exploring Faulty Data**. In Jaume Baixeries, Christian Sacarea, and Manuel Ojeda-Aciego, editors,*Proceedings of the 13th International Conference on Formal Concept Analysis (ICFCA'15)*, volume 9113 of*Lecture Notes in Computer Science*, pages 219–235. Springer-Verlag, 2015.Abstract BibTeX Entry PDF File

Within formal concept analysis, attribute exploration is a powerful tool to semi-automatically check data for completeness with respect to a given domain. However, the classical formulation of attribute exploration does not take into account possible errors which are present in the initial data. To remedy this, we present in this work a generalization of attribute exploration based on the notion of confidence, that will allow for the exploration of implications which are not necessarily valid in the initial data, but instead enjoy a minimal confidence therein.

@inproceedings{ Borc-ICFCA15, author = {Daniel {Borchmann}}, booktitle = {Proceedings of the 13th International Conference on Formal Concept Analysis {(ICFCA'15)}}, editor = {Jaume {Baixeries} and Christian {Sacarea} and Manuel {Ojeda{-}Aciego}}, pages = {219--235}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {{Exploring Faulty Data}}, volume = {9113}, year = {2015}, }

Stefan Borgwardt, Marco Cerami, and Rafael Peñaloza:

Abstract BibTeX Entry PDF File ©IJCAI

**The Complexity of Subsumption in Fuzzy**\(\mathcal{EL}\). In Qiang Yang and Michael Wooldridge, editors,*Proceedings of the 24th International Joint Conference on Artificial Intelligence (IJCAI'15)*, pages 2812–2818. Buenos Aires, Argentinia, AAAI Press, 2015.Abstract BibTeX Entry PDF File ©IJCAI

Fuzzy Description Logics (DLs) are used to represent and reason about vague and imprecise knowledge that is inherent to many application domains. It was recently shown that the complexity of reasoning in finitely-valued fuzzy DLs is often not higher than that of the underlying classical DL. We show that this does not hold for fuzzy extensions of the light-weight DL EL, which is used in many biomedical ontologies, under the Lukasiewicz semantics. The complexity of reasoning increases from PTime to ExpTime, even if only one additional truth value is introduced. The same lower bound holds also for infinitely-valued Lukasiewicz extensions of EL.

@inproceedings{ BoCP-IJCAI15, address = {Buenos Aires, Argentinia}, author = {Stefan {Borgwardt} and Marco {Cerami} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 24th International Joint Conference on Artificial Intelligence (IJCAI'15)}, editor = {Qiang {Yang} and Michael {Wooldridge}}, pages = {2812--2818}, publisher = {AAAI Press}, title = {The Complexity of Subsumption in Fuzzy {$\mathcal{EL}$}}, year = {2015}, }

Stefan Borgwardt, Felix Distel, and Rafael Peñaloza:

Abstract BibTeX Entry PDF File DOI

**The Limits of Decidability in Fuzzy Description Logics with General Concept Inclusions**.*Artificial Intelligence*, 218:23–55, 2015.Abstract BibTeX Entry PDF File DOI

Fuzzy Description Logics (DLs) can be used to represent and reason with vague knowledge. This family of logical formalisms is very diverse, each member being characterized by a specific choice of constructors, axioms, and triangular norms, which are used to specify the semantics. Unfortunately, it has recently been shown that the consistency problem in many fuzzy DLs with general concept inclusion axioms is undecidable. In this paper, we present a proof framework that allows us to extend these results to cover large classes of fuzzy DLs. On the other hand, we also provide matching decidability results for most of the remaining logics. As a result, we obtain a near-universal classification of fuzzy DLs according to the decidability of their consistency problem.

@article{ BoDP-AI15, author = {Stefan {Borgwardt} and Felix {Distel} and Rafael {Pe{\~n}aloza}}, doi = {http://dx.doi.org/10.1016/j.artint.2014.09.001}, journal = {Artificial Intelligence}, pages = {23--55}, title = {The Limits of Decidability in Fuzzy Description Logics with General Concept Inclusions}, volume = {218}, year = {2015}, }

Stefan Borgwardt, Marcel Lippmann, and Veronika Thost:

Abstract BibTeX Entry PDF File DOI

**Temporalizing Rewritable Query Languages over Knowledge Bases**.*Journal of Web Semantics*, 33:50–70, 2015.Abstract BibTeX Entry PDF File DOI

Ontology-based data access (OBDA) generalizes query answering in relational databases. It allows to query a database by using the language of an ontology, abstracting from the actual relations of the database. OBDA can sometimes be realized by compiling the information of the ontology into the query and the database. The resulting query is then answered using classical database techniques. In this paper, we consider a temporal version of OBDA. We propose a generic temporal query language that combines linear temporal logic with queries over ontologies. This language is well-suited for expressing temporal properties of dynamic systems and is useful in context-aware applications that need to detect specific situations. We show that, if atemporal queries are rewritable in the sense described above, then the corresponding temporal queries are also rewritable such that we can answer them over a temporal database. We present three approaches to answering the resulting queries.

@article{ BoLT-JWS15, author = {Stefan {Borgwardt} and Marcel {Lippmann} and Veronika {Thost}}, doi = {http://dx.doi.org/10.1016/j.websem.2014.11.007}, journal = {Journal of Web Semantics}, pages = {50--70}, title = {Temporalizing Rewritable Query Languages over Knowledge Bases}, volume = {33}, year = {2015}, }

Stefan Borgwardt, Theofilos Mailis, Rafael Peñaloza, and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File

**Conjunctive Query Answering with Finitely Many Truth Degrees**. In Diego Calvanese and Boris Konev, editors,*Proceedings of the 28th International Workshop on Description Logics (DL'15)*, volume 1350 of*CEUR Workshop Proceedings*, pages 364–367, 2015.Abstract BibTeX Entry PDF File

Fuzzy Description Logics (DLs) provide a means for representing vague knowledge about an application domain. In this paper, we study fuzzy extensions of conjunctive queries (CQs) over the DL SROIQ based on finite chains of degrees of truth. To answer such queries, we extend a well-known technique that reduces the fuzzy ontology to a classical one, and use classical DL reasoners as a black box. We improve the complexity of previous reduction techniques for finitely valued fuzzy DLs, which allows us to prove tight complexity results for answering certain kinds of fuzzy CQs.

@inproceedings{ BMPT-DL15, address = {Athens, Greece}, author = {Stefan {Borgwardt} and Theofilos {Mailis} and Rafael {Pe{\~n}aloza} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of the 28th International Workshop on Description Logics (DL'15)}, editor = {Diego {Calvanese} and Boris {Konev}}, pages = {364--367}, series = {CEUR Workshop Proceedings}, title = {Conjunctive Query Answering with Finitely Many Truth Degrees}, volume = {1350}, year = {2015}, }

Stefan Borgwardt and Rafael Peñaloza:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Reasoning in Expressive Description Logics under Infinitely Valued Gödel Semantics**. In Carsten Lutz and Silvio Ranise, editors,*Proceedings of the 10th International Symposium on Frontiers of Combining Systems (FroCoS'15)*, volume 9322 of*Lecture Notes in Artificial Intelligence*, pages 49–65. Wroclaw, Poland, Springer-Verlag, 2015.Abstract BibTeX Entry PDF File ©Springer-Verlag

Fuzzy Description Logics (FDLs) combine classical Description Logics with the semantics of Fuzzy Logics in order to represent and reason with vague knowledge. Most FDLs using truth values from the interval [0,1] have been shown to be undecidable in the presence of a negation constructor and general concept inclusions. One exception are those FDLs whose semantics is based on the infinitely valued Gödel t-norm (G). We extend previous decidability results for the FDL G-ALC to deal with complex role inclusions, nominals, inverse roles, and qualified number restrictions. Our novel approach is based on a combination of the known crispification technique for finitely valued FDLs and an automata-based procedure for reasoning in G-ALC.

@inproceedings{ BoPe-FroCoS15, address = {Wroclaw, Poland}, author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 10th International Symposium on Frontiers of Combining Systems (FroCoS'15)}, editor = {Carsten {Lutz} and Silvio {Ranise}}, pages = {49--65}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Reasoning in Expressive Description Logics under Infinitely Valued G{\"o}del Semantics}, volume = {9322}, year = {2015}, }

Stefan Borgwardt and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Reasoning in Infinitely Valued G-**\(\mathcal{IALCQ}\). In*Proceedings of the 3rd Workshop on Weighted Logics for AI (WL4AI'15)*, pages 2–8, 2015.Abstract BibTeX Entry PDF File

Fuzzy Description Logics (FDLs) are logic-based formalisms used to represent and reason with vague or imprecise knowledge. It has been recently shown that reasoning in most FDLs using truth values from the interval [0,1] becomes undecidable in the presence of a negation constructor and general concept inclusion axioms. One exception to this negative result are FDLs whose semantics is based on the infinitely valued Gödel t-norm (G). In this paper, we extend previous decidability results for G-IALC to deal also with qualified number restrictions. Our novel approach is based on a combination of the known crispification technique for finitely valued FDLs and the automata-based procedure originally developed for reasoning in G-IALC. The proposed approach combines the advantages of these two methods, while removing their respective drawbacks.

@inproceedings{ BoPe-WL4AI15, address = {Buenos Aires, Argentina}, author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 3rd Workshop on Weighted Logics for AI (WL4AI'15)}, pages = {2--8}, title = {Reasoning in Infinitely Valued {\textsf{G}-$\mathcal{IALCQ}$}}, year = {2015}, }

Stefan Borgwardt and Veronika Thost:

Abstract BibTeX Entry PDF File

**Temporal Query Answering in DL-Lite with Negation**. In Georg Gottlob, Geoff Sutcliffe, and Andrei Voronkov, editors,*Proceedings of the 1st Global Conference on Artificial Intelligence (GCAI'15)*, volume 36 of*EasyChair Proceedings in Computing*, pages 51–65. EasyChair, 2015.Abstract BibTeX Entry PDF File

Ontology-based query answering augments classical query answering in databases by adopting the open-world assumption and by including domain knowledge provided by an ontology. We investigate temporal query answering w.r.t. ontologies formulated in DLLite, a family of description logics that captures the conceptual features of relational databases and was tailored for efficient query answering. We consider a recently proposed temporal query language that combines conjunctive queries with the operators of propositional linear temporal logic (LTL). In particular, we consider negation in the ontology and query language, and study both data and combined complexity of query entailment.

@inproceedings{ BoTh-GCAI15, author = {Stefan {Borgwardt} and Veronika {Thost}}, booktitle = {Proceedings of the 1st Global Conference on Artificial Intelligence (GCAI'15)}, editor = {Georg {Gottlob} and Geoff {Sutcliffe} and Andrei {Voronkov}}, pages = {51--65}, publisher = {EasyChair}, series = {EasyChair Proceedings in Computing}, title = {Temporal Query Answering in \textit{{DL-Lite}} with Negation}, volume = {36}, year = {2015}, }

Stefan Borgwardt and Veronika Thost:

Abstract BibTeX Entry PDF File ©IJCAI

**Temporal Query Answering in the Description Logic**\(\mathcal{EL}\). In Qiang Yang and Michael Wooldridge, editors,*Proceedings of the 24th International Joint Conference on Artificial Intelligence (IJCAI'15)*, pages 2819–2825. Buenos Aires, Argentina, AAAI Press, 2015.Abstract BibTeX Entry PDF File ©IJCAI

Context-aware systems use data collected at runtime to recognize certain predefined situations and trigger adaptations. This can be implemented using ontology-based data access (OBDA), which augments classical query answering in databases by adopting the open-world assumption and including domain knowledge provided by an ontology. We investigate temporalized OBDA w.r.t. ontologies formulated in EL, a description logic that allows for efficient reasoning and is successfully used in practice. We consider a recently proposed temporalized query language that combines conjunctive queries with the operators of propositional linear temporal logic (LTL), and study both data and combined complexity of query entailment in this setting. We also analyze the satisfiability problem in the similar formalism EL-LTL.

@inproceedings{ BoTh-IJCAI15, address = {Buenos Aires, Argentina}, author = {Stefan {Borgwardt} and Veronika {Thost}}, booktitle = {Proceedings of the 24th International Joint Conference on Artificial Intelligence (IJCAI'15)}, editor = {Qiang {Yang} and Michael {Wooldridge}}, pages = {2819--2825}, publisher = {AAAI Press}, title = {Temporal Query Answering in the Description Logic {$\mathcal{EL}$}}, year = {2015}, }

Stefan Borgwardt and Veronika Thost:

Abstract BibTeX Entry PDF File

**Temporal Query Answering in the Description Logic**\(\mathcal{EL}\)**(extended abstract)**. In Diego Calvanese and Boris Konev, editors,*Proceedings of the 28th International Workshop on Description Logics (DL 2015)*, volume 1350 of*CEUR Workshop Proceedings*, pages 83–87, 2015.Abstract BibTeX Entry PDF File

@inproceedings{ BoTh-DL15, address = {Athens, Greece}, author = {Stefan {Borgwardt} and Veronika {Thost}}, booktitle = {Proceedings of the 28th International Workshop on Description Logics (DL 2015)}, editor = {Diego {Calvanese} and Boris {Konev}}, pages = {83--87}, series = {CEUR Workshop Proceedings}, title = {Temporal Query Answering in the Description Logic {$\mathcal{EL}$} (extended abstract)}, volume = {1350}, year = {2015}, }

Ismail Ilkan Ceylan:

Abstract BibTeX Entry PDF File

**Query Answering in Bayesian Description Logics**. In Diego Calvanese and Boris Konev, editors,*Proceedings of the 28th International Workshop on Description Logics (DL 2015)*, volume 1350 of*CEUR Workshop Proceedings*. CEUR-WS, 2015.Abstract BibTeX Entry PDF File

The Bayesian Description Logic (BDL) BEL is a probabilistic DL, which extends the lightweight DL EL by defining a joint probability distribution over EL axioms with the help of a Bayesian network (BN). In the recent work, extensions of standard logical reasoning tasks in BEL are shown to be reducible to inferences in BNs. This work concentrates on a more general reasoning task, namely on conjunctive query answering in BEL where every query is associated to a probability leading to different reasoning problems. In particular, we study the probabilistic query entailment, top-k answers, and top-k contexts as reasoning problems. Our complexity analysis suggests that all of these problems are tractable under certain assumptions.

@inproceedings{ Ce-DL15, author = {Ismail Ilkan {Ceylan}}, booktitle = {Proceedings of the 28th International Workshop on Description Logics (DL 2015)}, editor = {Diego {Calvanese} and Boris {Konev}}, publisher = {CEUR-WS}, series = {CEUR Workshop Proceedings}, title = {{Query Answering in Bayesian Description Logics}}, volume = {1350}, year = {2015}, }

Ismail Ilkan Ceylan and Rafael Peñaloza Julian Mendez:

Abstract BibTeX Entry PDF File

**The Bayesian Ontology reasoner is BORN!**. In Michel Dumontier, Birte Glimm, Rafael Gonçalves, Matthew Horridge, Ernesto Jiménez-Ruiz, Nicolas Matentzoglu, Bijan Parsia, Giorgos Stamou, and Giorgos Stoilos, editors,*Proceedings of the 4th International Workshop on OWL Reasoner Evaluation (ORE 2015)*, pages 8–14. CEUR Workshop Proceedings, 2015.Abstract BibTeX Entry PDF File

Bayesian ontology languages are a family of probabilistic ontology languages that allow to encode probabilistic information over the axioms of an ontology with the help of a Bayesian network. The Bayesian ontology language BEL is an extension of the lightweight Description Logic (DL) EL within the above-mentioned framework. We present the system BORN that implements the probabilistic subsumption problem for BEL.

@inproceedings{ CJ2015, author = {Ismail Ilkan {Ceylan} and Rafael Pe\~{n}aloza {Julian Mendez}}, booktitle = {Proceedings of the 4th International Workshop on {OWL} Reasoner Evaluation (ORE 2015)}, editor = {Michel {Dumontier} and Birte {Glimm} and Rafael {Gon\c{c}alves} and Matthew {Horridge} and Ernesto {Jim\'{e}nez-Ruiz} and Nicolas {Matentzoglu} and Bijan {Parsia} and Giorgos {Stamou} and Giorgos {Stoilos}}, pages = {8--14}, publisher = {CEUR Workshop Proceedings}, title = {The Bayesian Ontology reasoner is {BORN!}}, volume = {1387}, year = {2015}, }

Ismail Ilkan Ceylan, Thomas Lukasiewicz, and Rafael Peñaloza:

BibTeX Entry PDF File

**Answering EL Queries in the Presence of Preferences**. In Diego Calvanese and Boris Konev, editors,*Proceedings of the 28th International Workshop on Description Logics (DL 2015)*, volume 1350 of*CEUR Workshop Proceedings*. CEUR-WS, 2015.BibTeX Entry PDF File

@inproceedings{ CeThPe-DL15, author = {Ismail Ilkan {Ceylan} and Thomas {Lukasiewicz} and Rafael {Pe{\~{n}}aloza}}, booktitle = {Proceedings of the 28th International Workshop on Description Logics (DL 2015)}, editor = {Diego {Calvanese} and Boris {Konev}}, publisher = {CEUR-WS}, series = {CEUR Workshop Proceedings}, title = {{Answering {EL} Queries in the Presence of Preferences}}, volume = {1350}, year = {2015}, }

Ismail Ilkan Ceylan and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Probabilistic Query Answering in the Bayesian Description Logic BEL**. In Christoph Beierle and Alex Dekhtyar, editors,*Proceedings of 9th International Conference on Scalable Uncertainty Management (SUM 2015)*, volume 9310 of*LNAI*, pages 1–15. Springer, 2015.Abstract BibTeX Entry PDF File

BEL is a probabilistic description logic (DL) that extends the light-weight DL EL with a joint probability distribution over the axioms, expressed with the help of a Bayesian network (BN). In recent work it has been shown that the complexity of standard logical reasoning in BEL is the same as performing probabilistic inferences over the BN. In this paper we consider conjunctive query answering in BEL. We study the complexity of the three main problems associated to this setting: computing the probability of a query entailment, computing the most probable answers to a query, and computing the most probable context in which a query is entailed. In particular, we show that all these problems are tractable w.r.t. data and ontology complexity.

@inproceedings{ CePe-SUM15, author = {Ismail Ilkan {Ceylan} and Rafael {Pe\~{n}aloza}}, booktitle = {Proceedings of 9th International Conference on Scalable Uncertainty Management (SUM 2015)}, editor = {Christoph {Beierle} and Alex {Dekhtyar}}, pages = {1--15}, publisher = {Springer}, series = {LNAI}, title = {Probabilistic Query Answering in the Bayesian Description Logic {BEL}}, volume = {9310}, year = {2015}, }

Ismail Ilkan Ceylan and Rafael Peñaloza:

BibTeX Entry PDF File

**Dynamic Bayesian Description Logics**. In Diego Calvanese and Boris Konev, editors,*Proceedings of the 28th International Workshop on Description Logics (DL 2015)*, volume 1350 of*CEUR Workshop Proceedings*. CEUR-WS, 2015.BibTeX Entry PDF File

@inproceedings{ CePe-DL15, author = {Ismail Ilkan {Ceylan} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 28th International Workshop on Description Logics (DL 2015)}, editor = {Diego {Calvanese} and Boris {Konev}}, publisher = {CEUR-WS}, series = {CEUR Workshop Proceedings}, title = {{Dynamic Bayesian Description Logics}}, volume = {1350}, year = {2015}, }

Jieying Chen, Michel Ludwig, Yue Ma, and Dirk Walther:

Abstract BibTeX Entry PDF File DOI

**Towards Extracting Ontology Excerpts**. In Songmao Zhang, Martin Wirsing, and Zili Zhang, editors,*Proceedings of the 8th International Conference on Knowledge Science, Engineering and Management (KSEM 2015)*, volume 9403 of*Lecture Notes in Computer Science*, pages 78–89. Springer, 2015.Abstract BibTeX Entry PDF File DOI

In the presence of an ever growing amount of information, organizations and human users need to be able to focus on certain key pieces of information and to intentionally ignore all other possibly relevant parts. Knowledge about complex systems that is represented in ontologies yields collections of axioms that are too large for human users to browse, let alone to comprehend or reason about it. We introduce the notion of an ontology excerpt as being a fixed-size subset of an ontology, consisting of the most relevant axioms for a given set of terms. These axioms preserve as much as possible the knowledge about the considered terms described in the ontology. We consider different extraction techniques for ontology excerpts based on methods from the area of information retrieval. To evaluate these techniques, we propose to measure the degree of incompleteness of the resulting excerpts using the notion of logical difference.

@inproceedings{ ChLuMaWa-KSEM-2015, author = {Jieying {Chen} and Michel {Ludwig} and Yue {Ma} and Dirk {Walther}}, booktitle = {Proceedings of the 8th International Conference on Knowledge Science, Engineering and Management (KSEM 2015)}, doi = {https://dx.doi.org/10.1007/978-3-319-25159-2_7}, editor = {Songmao {Zhang} and Martin {Wirsing} and Zili {Zhang}}, pages = {78--89}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Towards Extracting Ontology Excerpts}, volume = {9403}, year = {2015}, }

Andreas Ecke, Rafael Peñaloza, and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File DOI

**Similarity-based Relaxed Instance Queries**.*Journal of Applied Logic*, 13(4, Part 1):480–508, 2015. Special Issue for the Workshop on Weighted Logics for AI 2013Abstract BibTeX Entry PDF File DOI

In Description Logics (DL) knowledge bases (KBs), information is typically captured by clear-cut concepts. For many practical applications querying the KB by crisp concepts is too restrictive; a user might be willing to lose some precision in the query, in exchange of a larger selection of answers. Similarity measures can offer a controlled way of gradually relaxing a query concept within a user-specified limit. In this paper we formalize the task of instance query answering for DL KBs using concepts relaxed by concept similarity measures (CSMs). We investigate computation algorithms for this task in the DL EL, their complexity and properties for the CSMs employed regarding whether unfoldable or general TBoxes are used. For the case of general TBoxes we define a family of CSMs that take the full TBox information into account, when assessing the similarity of concepts.

@article{ EcPeTu-JAL15, author = {Andreas {Ecke} and Rafael {Pe\~naloza} and Anni-Yasmin {Turhan}}, doi = {http://dx.doi.org/10.1016/j.jal.2015.01.002}, journal = {Journal of Applied Logic}, note = {Special Issue for the Workshop on Weighted Logics for {AI} 2013}, number = {4, Part 1}, pages = {480--508}, title = {Similarity-based Relaxed Instance Queries}, volume = {13}, year = {2015}, }

Andreas Ecke, Maximilian Pensel, and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File

**ELASTIQ: Answering Similarity-threshold Instance Queries in**\(\mathcal{EL}\). In Diego Calvanese and Boris Konev, editors,*Proceedings of the 28th International Workshop on Description Logics (DL-2015)*, volume 1350 of*CEUR Workshop Proceedings*. CEUR-WS.org, June 2015.Abstract BibTeX Entry PDF File

Recently an approach has been devised how to employ concept similarity measures (CSMs) for relaxing instance queries over EL ontologies in a controlled way. The approach relies on similarity measures between pointed interpretations to yield CSMs with certain properties. We report in this paper on ELASTIQ, which is a first implementation of this approach and propose initial optimizations for this novel inference. We also provide a first evaluation of ELASTIQ on the Gene Ontology.

@inproceedings{ EcPeTu-DL15, author = {Andreas {Ecke} and Maximilian {Pensel} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of the 28th International Workshop on Description Logics ({DL-2015})}, editor = {Diego {Calvanese} and Boris {Konev}}, month = {June}, publisher = {CEUR-WS.org}, series = {{CEUR} Workshop Proceedings}, title = {ELASTIQ: Answering Similarity-threshold Instance Queries in {$\mathcal{EL}$}}, venue = {Athens, Greece}, volume = {1350}, year = {2015}, }

Shasha Feng, Michel Ludwig, and Dirk Walther:

Abstract BibTeX Entry PDF File DOI

**Deciding Subsumers of Least Fixpoint Concepts w.r.t. general EL -TBoxes**. In Steffen Hölldobler, Markus Krötzsch, Rafael Peñaloza, and Sebastian Rudolph, editors,*Proceedings of the 38th Annual German Conference on AI (KI 2015)*, volume 9324 of*Lecture Notes in Computer Science*, pages 59–71, 2015.Abstract BibTeX Entry PDF File DOI

In this paper we provide a procedure for deciding subsumptions of the form \(\Tmc \models \Cmc \sqsubseteq E\), where \(\Cmc\) is an \(\ELU_\mu\)-concept, \(E\) an \(\ELU\)-concept and \(\Tmc\) a general \(\EL\)-TBox. Deciding such subsumptions can be used for computing the logical difference between general \(\EL\)-TBoxes. Our procedure is based on checking for the existence of a certain simulation between hypergraph representations of the set of subsumees of \(\Cmc\) and of \(E\) \(\Tmc\), respectively. With the aim of keeping the procedure implementable, we provide a detailed construction of such hypergraphs deliberately avoiding the use of intricate automata-theoretic techniques.

@inproceedings{ FeLuWa-KI-2015, author = {Shasha {Feng} and Michel {Ludwig} and Dirk {Walther}}, booktitle = {Proceedings of the 38th Annual German Conference on AI (KI 2015)}, doi = {https://dx.doi.org/10.1007/978-3-319-24489-1_5}, editor = {Steffen {H{\"{o}}lldobler} and Markus {Kr{\"{o}}tzsch} and Rafael {Pe{\~{n}}aloza} and Sebastian {Rudolph}}, pages = {59--71}, series = {Lecture Notes in Computer Science}, title = {Deciding Subsumers of Least Fixpoint Concepts w.r.t. general \emph{EL} -TBoxes}, volume = {9324}, year = {2015}, }

Shasha Feng, Michel Ludwig, and Dirk Walther:

Abstract BibTeX Entry PDF File

**Foundations for the Logical Difference of EL-TBoxes**. In Georg Gottlob, Geoff Sutcliffe, and Andrei Voronkov, editors,*GCAI 2015. Global Conference on Artificial Intelligence*, volume 36 of*EPiC Series in Computing*, pages 93–112. EasyChair, 2015.Abstract BibTeX Entry PDF File

We investigate the logical difference problem between general EL-TBoxes. The logical difference is the set of concept subsumptions that are logically entailed by a first TBox but not by a second one. We show how the logical difference between two EL-TBoxes can be reduced to fixpoint reasoning wrt. EL-TBoxes. Entailments of the first TBox can be represented by subsumptions of least fixpoint concepts by greatest fixpoint concepts, which can then be checked wrt. the second TBox. We present the foundations for a dedicated procedure based on a hypergraph representation of the fixpoint concepts without the use of automata-theoretic techniques, avoiding possible complexity issues of a reduction to modal mu-calculus reasoning. The subsumption checks are based on checking for the existence of simulations between the hypergraph representations of the fixpoint concepts and the TBoxes.

@inproceedings{ FeLuWa-GCAI-2015, author = {Shasha {Feng} and Michel {Ludwig} and Dirk {Walther}}, booktitle = {GCAI 2015. Global Conference on Artificial Intelligence}, editor = {Georg {Gottlob} and Geoff {Sutcliffe} and Andrei {Voronkov}}, pages = {93--112}, publisher = {EasyChair}, series = {EPiC Series in Computing}, title = {Foundations for the Logical Difference of EL-TBoxes}, volume = {36}, year = {2015}, }

Shasha Feng, Michel Ludwig, and Dirk Walther:

Abstract BibTeX Entry

**The Logical Difference for EL: from Terminologies towards TBoxes**. In*Proceedings of the 1st International Workshop on Semantic Technologies (IWOST)*,*CEUR workshop proceedings*, 2015.Abstract BibTeX Entry

In this paper we are concerned with the logical difference problem between ontologies. The logical difference is the set of subsumption queries that follow from a first ontology but not from a second one. We revisit our solution to logical difference problem for EL-terminologies based on finding simulations between hypergraph representations of the terminologies, and we investigate a possible extension of the method to general EL-TBoxes.

@inproceedings{ FeLuWa-IWOST-15, author = {Shasha {Feng} and Michel {Ludwig} and Dirk {Walther}}, booktitle = {Proceedings of the 1st International Workshop on Semantic Technologies (IWOST)}, series = {CEUR workshop proceedings}, title = {The Logical Difference for EL: from Terminologies towards TBoxes}, year = {2015}, }

Francesco Kriegel:

Abstract BibTeX Entry PDF File DOI ©Springer-Verlag

**Axiomatization of General Concept Inclusions in Probabilistic Description Logics**. In Steffen Hölldobler, Sebastian Rudolph, and Markus Krötzsch, editors,*Proceedings of the 38th German Conference on Artificial Intelligence (KI 2015)*, volume 9324 of*Lecture Notes in Artificial Intelligence (LNAI)*, pages 124–136. Dresden, Germany, Springer Verlag, 2015.Abstract BibTeX Entry PDF File DOI ©Springer-Verlag

Probabilistic interpretations consist of a set of interpretations with a shared domain and a measure assigning a probability to each interpretation. Such structures can be obtained as results of repeated experiments, e.g., in biology, psychology, medicine, etc. A translation between probabilistic and crisp description logics is introduced, and then utilized to reduce the construction of a base of general concept inclusions of a probabilistic interpretation to the crisp case for which a method for the axiomatization of a base of GCIs is well-known.

@inproceedings{ Kr-KI15, address = {Dresden, Germany}, author = {Francesco {Kriegel}}, booktitle = {Proceedings of the 38th German Conference on Artificial Intelligence ({KI 2015})}, doi = {http://dx.doi.org/10.1007/978-3-319-24489-1_10}, editor = {Steffen {H{\"o}lldobler} and Sebastian {Rudolph} and Markus {Kr{\"o}tzsch}}, pages = {124--136}, publisher = {Springer Verlag}, series = {Lecture Notes in Artificial Intelligence ({LNAI})}, title = {Axiomatization of General Concept Inclusions in Probabilistic Description Logics}, volume = {9324}, year = {2015}, }

Francesco Kriegel:

Abstract BibTeX Entry PDF File PDF File (ceur-ws.org)

**Extracting**\(\mathcal{A\mkern-1.618mu L\mkern-1.618mu E\mkern-1.618mu Q\mkern-1.618mu R}(\mathsf{Self})\)**-Knowledge Bases from Graphs**. In Sergei O. Kuznetsov, Rokia Missaoui, and Sergei A. Obiedkov, editors,*Proceedings of the International Workshop on Social Network Analysis using Formal Concept Analysis (SNAFCA 2015) in conjunction with the 13th International Conference on Formal Concept Analysis (ICFCA 2015)*, volume 1534 of*CEUR Workshop Proceedings*. Nerja, Spain, CEUR-WS.org, 2015.Abstract BibTeX Entry PDF File PDF File (ceur-ws.org)

A description graph is a directed graph that has labeled vertices and edges. This document proposes a method for extracting a knowledge base from a description graph. The technique is presented for the description logic \(\mathcal{A\mkern-1.618mu L\mkern-1.618mu E\mkern-1.618mu Q\mkern-1.618mu R}(\mathsf{Self})\) which allows for conjunctions, primitive negation, existential restrictions, value restrictions, qualified number restrictions, existential self restrictions, and complex role inclusion axioms, but also sublogics may be chosen to express the axioms in the knowledge base. The extracted knowledge base entails all statements that can be expressed in the chosen description logic and are encoded in the input graph.

@inproceedings{ Kr-SNAFCA15, address = {Nerja, Spain}, author = {Francesco {Kriegel}}, booktitle = {Proceedings of the International Workshop on Social Network Analysis using Formal Concept Analysis ({SNAFCA 2015}) in conjunction with the 13th International Conference on Formal Concept Analysis ({ICFCA} 2015)}, editor = {Sergei O. {Kuznetsov} and Rokia {Missaoui} and Sergei A. {Obiedkov}}, publisher = {CEUR-WS.org}, series = {CEUR Workshop Proceedings}, title = {Extracting $\mathcal{A\mkern-1.618mu L\mkern-1.618mu E\mkern-1.618mu Q\mkern-1.618mu R}(\mathsf{Self})$-Knowledge Bases from Graphs}, volume = {1534}, year = {2015}, }

Francesco Kriegel:

Abstract BibTeX Entry PDF File PDF File (ceur-ws.org)

**Incremental Learning of TBoxes from Interpretation Sequences with Methods of Formal Concept Analysis**. In Diego Calvanese and Boris Konev, editors,*Proceedings of the 28th International Workshop on Description Logics (DL 2015)*, volume 1350 of*CEUR Workshop Proceedings*, pages 452–464. Athens, Greece, CEUR-WS.org, 2015.Abstract BibTeX Entry PDF File PDF File (ceur-ws.org)

Formal Concept Analysis and its methods for computing minimal implicational bases have been successfully applied to axiomatise minimal \(\mathcal{E\mkern-1.618mu L}\)-TBoxes from models, so called bases of GCIs. However, no technique for an adjustment of an existing \(\mathcal{E\mkern-1.618mu L}\)-TBox w.r.t. a new model is available, i.e., on a model change the complete TBox has to be recomputed. This document proposes a method for the computation of a minimal extension of a TBox w.r.t. a new model. The method is then utilised to formulate an incremental learning algorithm that requires a stream of interpretations, and an expert to guide the learning process, respectively, as input.

@inproceedings{ Kr-DL15, address = {Athens, Greece}, author = {Francesco {Kriegel}}, booktitle = {Proceedings of the 28th International Workshop on Description Logics ({DL 2015})}, editor = {Diego {Calvanese} and Boris {Konev}}, pages = {452--464}, publisher = {CEUR-WS.org}, series = {CEUR Workshop Proceedings}, title = {Incremental Learning of TBoxes from Interpretation Sequences with Methods of Formal Concept Analysis}, volume = {1350}, year = {2015}, }

Francesco Kriegel:

Abstract BibTeX Entry PDF File PDF File (ceur-ws.org)

**Probabilistic Implicational Bases in FCA and Probabilistic Bases of GCIs in**\(\mathcal{E\mkern-1.618mu L}^{\bot}\). In Sadok Ben Yahia and Jan Konecny, editors,*Proceedings of the 12th International Conference on Concept Lattices and their Applications (CLA 2015)*, volume 1466 of*CEUR Workshop Proceedings*, pages 193–204. Clermont-Ferrand, France, CEUR-WS.org, 2015.Abstract BibTeX Entry PDF File PDF File (ceur-ws.org)

A probabilistic formal context is a triadic context whose third dimension is a set of worlds equipped with a probability measure. After a formal definition of this notion, this document introduces probability of implications, and provides a construction for a base of implications whose probability satisfy a given lower threshold. A comparison between confidence and probability of implications is drawn, which yields the fact that both measures do not coincide, and cannot be compared. Furthermore, the results are extended towards the light-weight description logic \(\mathcal{E\mkern-1.618mu L}^{\bot}\) with probabilistic interpretations, and a method for computing a base of general concept inclusions whose probability fulfill a certain lower bound is proposed.

@inproceedings{ Kr-CLA15, address = {Clermont-Ferrand, France}, author = {Francesco {Kriegel}}, booktitle = {Proceedings of the 12th International Conference on Concept Lattices and their Applications ({CLA 2015})}, editor = {Sadok {Ben Yahia} and Jan {Konecny}}, pages = {193--204}, publisher = {CEUR-WS.org}, series = {CEUR Workshop Proceedings}, title = {Probabilistic Implicational Bases in FCA and Probabilistic Bases of GCIs in $\mathcal{E\mkern-1.618mu L}^{\bot}$}, volume = {1466}, year = {2015}, }

Francesco Kriegel and Daniel Borchmann:

Abstract BibTeX Entry PDF File PDF File (ceur-ws.org)

**NextClosures: Parallel Computation of the Canonical Base**. In Sadok Ben Yahia and Jan Konecny, editors,*Proceedings of the 12th International Conference on Concept Lattices and their Applications (CLA 2015)*, volume 1466 of*CEUR Workshop Proceedings*, pages 182–192. Clermont-Ferrand, France, CEUR-WS.org, 2015. Best Paper Award.Abstract BibTeX Entry PDF File PDF File (ceur-ws.org)

The canonical base of a formal context plays a distinguished role in formal concept analysis. This is because it is the only minimal base so far that can be described explicitly. For the computation of this base several algorithms have been proposed. However, all those algorithms work sequentially, by computing only one pseudo-intent at a time - a fact which heavily impairs the practicability of using the canonical base in real-world applications. In this paper we shall introduce an approach that remedies this deficit by allowing the canonical base to be computed in a parallel manner. First experimental evaluations show that for sufficiently large data-sets the speedup is proportional to the number of available CPUs.

@inproceedings{ KrBo-CLA15, address = {Clermont-Ferrand, France}, author = {Francesco {Kriegel} and Daniel {Borchmann}}, booktitle = {Proceedings of the 12th International Conference on Concept Lattices and their Applications ({CLA 2015})}, editor = {Sadok {Ben Yahia} and Jan {Konecny}}, note = {Best Paper Award.}, pages = {182--192}, publisher = {CEUR-WS.org}, series = {CEUR Workshop Proceedings}, title = {NextClosures: Parallel Computation of the Canonical Base}, volume = {1466}, year = {2015}, }

Theofilos Malis, Anni-Yasmin Turhan, and Erik Zenker:

Abstract BibTeX Entry PDF File

**A Pragmatic Approach to Answering CQs over Fuzzy DL-Lite-ontologies - introducing FLite**. In*Proceedings of the 28th International Workshop on Description Logics (DL-2015)*, June 2015.Abstract BibTeX Entry PDF File

Fuzzy Description Logics (FDLs) generalize crisp ones by providing membership degree semantics. To offer efficient query answering for FDLs it is desirable to extend the rewriting-based approach for DL-Lite to its fuzzy variants. For answering conjunctive queries over fuzzy DL-LiteR ontologies we present an approach, that employs the crisp rewriting as a black-box procedure and treats the degrees in a second rewriting step. This pragmatic approach yields a sound procedure for the Goedel based fuzzy semantics, which we have implemented in the FLite reasoner that employs the Ontop system. A first evaluation of FLite suggests that one pays only a linear overhead for fuzzy queries.

@inproceedings{ MaTuZe-DL15, author = {Theofilos {Malis} and Anni-Yasmin {Turhan} and Erik {Zenker}}, booktitle = {Proceedings of the 28th International Workshop on Description Logics ({DL-2015})}, month = {June}, title = {A Pragmatic Approach to Answering CQs over Fuzzy \textit{DL-Lite}-ontologies - introducing FLite}, venue = {Athens, Greece}, year = {2015}, }

Alina Petrova, Yue Ma, George Tsatsaronis, Maria Kissa, Felix Distel, Franz Baader, and Michael Schroeder:

Abstract BibTeX Entry DOI

**Formalizing Biomedical Concepts from Textual Definitions**.*Journal of Biomedical Semantics*, 6(22), 2015.Abstract BibTeX Entry DOI

Background: Ontologies play a major role in life sciences, enabling a number of applications, from new data integration to knowledge verification. SNOMED CT is a large medical ontology that is formally defined so that it ensures global consistency and support of complex reasoning tasks. Most biomedical ontologies and taxonomies on the other hand define concepts only textually, without the use of logic. Here, we investigate how to automatically generate formal concept definitions from textual ones. We develop a method that uses machine learning in combination with several types of lexical and semantic features and outputs formal definitions that follow the structure of SNOMED CT concept definitions. Results: We evaluate our method on three benchmarks and test both the underlying relation extraction component as well as the overall quality of output concept definitions. In addition, we provide an analysis on the following aspects: (1) How do definitions mined from the Web and literature differ from the ones mined from manually created definitions, e.g., MESH? (2) How do different feature representations, e.g., the restrictions of relations' domain and range, impact on the generated definition quality?, (3) How do different machine learning algorithms compare to each other for the task of formal definition generation?, and, (4) What is the influence of the learning data size to the task? We discuss all of these settings in detail and show that the suggested approach can achieve success rates of over 90%. In addition, the results show that the choice of corpora, lexical features, learning algorithm and data size do not impact the performance as strongly as semantic types do. Semantic types limit the domain and range of a predicted relation, and as long as relations' domain and range pairs do not overlap, this information is most valuable in formalizing textual definitions. Conclusions: The analysis presented in this manuscript implies that automated methods can provide a valuable contribution to the formalization of biomedical knowledge, thus paving the way for future applications that go beyond retrieval and into complex reasoning. The method is implemented and accessible to the public from: https://github.com/alifahsyamsiyah/learningDL .

@article{ Petrovaetal-BioSem, author = {Alina {Petrova} and Yue {Ma} and George {Tsatsaronis} and Maria {Kissa} and Felix {Distel} and Franz {Baader} and Michael {Schroeder}}, doi = {https://dx.doi.org/10.1186/s13326-015-0015-3}, journal = {Journal of Biomedical Semantics}, number = {22}, title = {Formalizing Biomedical Concepts from Textual Definitions}, volume = {6}, year = {2015}, }

Veronika Thost, Jan Holste, and Özgür Özçep:

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**On Implementing Temporal Query Answering in DL-Lite (extended abstract)**. In*Proceedings of the 28th International Workshop on Description Logics (DL-2015)*. Athens, Greece, CEUR Workshop Proceedings, 2015.Abstract BibTeX Entry PDF File

Ontology-based data access augments classical query answering over fact bases by adopting the open-world assumption and by including domain know-ledge provided by an ontology. We implemented temporal query answering w.r.t. ontologies formulated in the Description Logic DL-Lite. Focusing on temporal conjunctive queries (TCQs), which combine conjunctive queries via the operators of propositional linear temporal logic, we regard three approaches for answering them: an iterative algorithm that considers all data available; a window-based algorithm; and a rewriting approach, which translates the TCQs to be answered into SQL queries. Since the relevant ontological knowledge is already encoded into the latter queries, they can be answered by a standard database system. Our evaluation especially shows that implementations of both the iterative and the window-based algorithm answer TCQs within a few milliseconds, and that the former achieves a constant performance, even if data is growing over time.

@inproceedings{ THOe-DL15, address = {Athens, Greece}, author = {Veronika {Thost} and Jan {Holste} and \"Ozg\"ur {\"Oz\c{c}ep}}, booktitle = {Proceedings of the 28th International Workshop on Description Logics (DL-2015)}, publisher = {CEUR Workshop Proceedings}, title = {On Implementing Temporal Query Answering in {\textit{DL-Lite}} (extended abstract)}, year = {2015}, }

Anni-Yasmin Turhan and Erik Zenker:

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**Towards Temporal Fuzzy Query Answering on Stream-based Data**. In Daniela Nicklas and Özgür Lütfü Özçep, editors,*Proceedings of the 1st Workshop on High-Level Declarative Stream Processing (HiDest'15)*, volume 1447 of*CEUR Workshop Proceedings*, pages 56–69. CEUR-WS.org, 2015.Abstract BibTeX Entry PDF File

For reasoning over streams of data ontology-based data access is a common approach. The method for answering conjunctive queries (CQs) over DL-Lite ontologies in this setting is by rewritings of the query and evaluation of the resulting query by a data base engine. For stream-based applications the classical expressivity of DL-Lite lacks means to handle fuzzy and temporal information. In this paper we report on a combination of a recently proposed pragmatic approach for answering CQs over fuzzy DL-Lite ontologies with answering of CQs over sequences of ABoxes, resulting in a system that supplies rewritings for query answering over temporal fuzzy DL-Lite-ontologies.

@inproceedings{ TuZe-HiDest-15, author = {Anni{-}Yasmin {Turhan} and Erik {Zenker}}, booktitle = {Proceedings of the 1st Workshop on High-Level Declarative Stream Processing (HiDest'15)}, editor = {Daniela {Nicklas} and {\"{O}}zg{\"{u}}r L{\"{u}}tf{\"{u}} {{\"{O}}z{\c{c}}ep}}, pages = {56--69}, publisher = {CEUR-WS.org}, series = {{CEUR} Workshop Proceedings}, title = {Towards Temporal Fuzzy Query Answering on Stream-based Data}, volume = {1447}, year = {2015}, }

Benjamin Zarrieß and Jens Claßen:

Abstract BibTeX Entry

**Verification of Knowledge-Based Programs over Description Logic Actions**. In Qiang Yang and Michael Wooldridge, editors,*Proceedings of the 24th International Joint Conference on Artificial Intelligence (IJCAI'15)*, pages 3278–3284. AAAI Press, 2015.Abstract BibTeX Entry

A knowledge-based program defines the behavior of an agent by combining primitive actions, programming constructs and test conditions that make explicit reference to the agent's knowledge. In this paper we consider a setting where an agent is equipped with a Description Logic (DL) knowledge base providing general domain knowledge and an incomplete description of the initial situation. We introduce a corresponding new DL-based action language that allows for representing both physical and sensing actions, that we then use to build knowledge-based programs with test conditions expressed in an epistemic DL. After proving undecidability for the general case, we then discuss a restricted fragment where verification becomes decidable. The provided proof is constructive and comes with an upper bound on the procedure's complexity.

@inproceedings{ ZC2015, author = {Benjamin {Zarrie{\ss}} and Jens {Cla{\ss}en}}, booktitle = {Proceedings of the 24th International Joint Conference on Artificial Intelligence (IJCAI'15)}, editor = {Qiang {Yang} and Michael {Wooldridge}}, pages = {3278--3284}, publisher = {AAAI Press}, title = {Verification of Knowledge-Based Programs over Description Logic Actions}, year = {2015}, }

## 2014

Josefine Asmus, Daniel Borchmann, Ivo F. Sbalzarini, and Dirk Walther:

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**Towards an FCA-based Recommender System for Black-Box Optimization**. In Sergei O. Kuznetsov, Amedeo Napoli, and Sebastian Rudolph, editors,*Proceedings of the 3rd International Workshop on "What can FCA do for Artificial Intelligence?" (FCA4AI'14)*, volume 1257 of*CEUR Workshop Proceedings*, pages 35–42, 2014.Abstract BibTeX Entry PDF File

Black-box optimization problems are of practical importance throughout science and engineering. Hundreds of algorithms and heuristics have been developed to solve them. However, none of them outperforms any other on all problems. The success of a particular heuristic is always relative to a class of problems. So far, these problem classes are elusive and it is not known what algorithm to use on a given problem. Here we describe the use of Formal Concept Analysis (FCA) to extract implications about problem classes and algorithm performance from databases of empirical benchmarks. We explain the idea in a small example and show that FCA produces meaningful implications. We further outline the use of attribute exploration to identify problem features that predict algorithm performance.

@inproceedings{ AsBoSbWa-FCA4AI-14, author = {Josefine {Asmus} and Daniel {Borchmann} and Ivo F. {Sbalzarini} and Dirk {Walther}}, booktitle = {Proceedings of the 3rd International Workshop on "What can FCA do for Artificial Intelligence?" ({FCA4AI'14})}, editor = {Sergei O. {Kuznetsov} and Amedeo {Napoli} and Sebastian {Rudolph}}, pages = {35--42}, series = {CEUR Workshop Proceedings}, title = {Towards an FCA-based Recommender System for Black-Box Optimization}, volume = {1257}, year = {2014}, }

Franz Baader:

Abstract BibTeX Entry PDF File

**Ontology-Based Monitoring of Dynamic Systems**. In Chitta Baral, Giuseppe De Giacomo, and Thomas Eiter, editors,*Proceedings of the 14th International Conference on Principles of Knowledge Representation and Reasoning (KR'14)*, pages 678–681. Vienna, Austria, AAAI Press, 2014. Invited contribution.Abstract BibTeX Entry PDF File

Our understanding of the notion "dynamic system" is a rather broad one: such a system has states, which can change over time. Ontologies are used to describe the states of the system, possibly in an incomplete way. Monitoring is then concerned with deciding whether some run of the system or all of its runs satisfy a certain property, which can be expressed by a formula of an appropriate temporal logic. We consider different instances of this broad framework, which can roughly be classified into two cases. In one instance, the system is assumed to be a black box, whose inner working is not known, but whose states can be (partially) observed during a run of the system. In the second instance, one has (partial) knowledge about the inner working of the system, which provides information on which runs of the system are possible. In this paper, we will review some of our recent work that can be seen as instances of this general framework of ontology-based monitoring of dynamic systems. We will also mention possible extensions towards probabilistic reasoning and the integration of mathematical modeling of dynamical systems.

@inproceedings{ Ba-KR-2014, address = {Vienna, Austria}, author = {Franz {Baader}}, booktitle = {Proceedings of the 14th International Conference on Principles of Knowledge Representation and Reasoning (KR'14)}, editor = {Chitta {Baral} and Giuseppe {De Giacomo} and Thomas {Eiter}}, note = {Invited contribution.}, pages = {678--681}, publisher = {AAAI Press}, title = {Ontology-Based Monitoring of Dynamic Systems}, year = {2014}, }

Franz Baader and Marcel Lippmann:

Abstract BibTeX Entry DOI

**Runtime Verification Using the Temporal Description Logic**\(\mathcal{ALC}\)**-LTL Revisited**.*Journal of Applied Logic*, 12(4):584–613, 2014.Abstract BibTeX Entry DOI

Formulae of linear temporal logic (LTL) can be used to specify (wanted or unwanted) properties of a dynamical system. In model checking, the system's behaviour is described by a transition system, and one needs to check whether all possible traces of this transition system satisfy the formula. In runtime verification, one observes the actual system behaviour, which at any point in time yields a finite prefix of a trace. The task is then to check whether all continuations of this prefix to a trace satisfy (violate) the formula. More precisely, one wants to construct a monitor, i.e., a finite automaton that receives the finite prefix as input and then gives the right answer based on the state currently reached. In this paper, we extend the known approaches to LTL runtime verification in two directions. First, instead of propositional LTL we use the more expressive temporal logic ALC-LTL, which can use axioms of the Description Logic (DL) ALC instead of propositional variables to describe properties of single states of the system. Second, instead of assuming that the observed system behaviour provides us with complete information about the states of the system, we assume that states are described in an incomplete way by ALC-knowledge bases. We show that also in this setting monitors can effectively be constructed. The (double-exponential) size of the constructed monitors is in fact optimal, and not higher than in the propositional case. As an auxiliary result, we show how to construct Büchi automata for ALC-LTL-formulae, which yields alternative proofs for the known upper bounds of deciding satisfiability in ALC-LTL.

@article{ BaLi-JAL14, author = {Franz {Baader} and Marcel {Lippmann}}, doi = {http://dx.doi.org/10.1016/j.jal.2014.09.001}, journal = {Journal of Applied Logic}, number = {4}, pages = {584--613}, title = {Runtime Verification Using the Temporal Description Logic $\mathcal{ALC}$-LTL Revisited}, volume = {12}, year = {2014}, }

Franz Baader and Barbara Morawska:

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**Matching with respect to general concept inclusions in the Description Logic**\(\mathcal{EL}\). In Temur Kutsia and Christophe Ringeissen, editors,*Proceedings of the 28th International Workshop on Unification (UNIF'14)*,*RISC-Linz Report Series No. 14-06*, pages 22–26, 2014.Abstract BibTeX Entry PDF File

Matching concept descriptions against concept patterns was introduced as a new inference task in Description Logics (DLs) almost 20 years ago, motivated by applications in the Classic system. For the DL EL, it was shown in 2000 that the matching problem is NP-complete. It then took almost 10 years before this NP-completeness result could be extended from matching to unification in EL. The next big challenge was then to further extend these results from matching and unification without a TBox to matching and unification w.r.t. a general TBox, i.e., a finite set of general concept inclusions. For unification, we could show some partial results for general TBoxes that satisfy a certain restriction on cyclic dependencies between concepts, but the general case is still open. For matching, we were able to solve the general case: we can show that matching in EL w.r.t. general TBoxes is NP-complete. We also determine some tractable variants of the matching problem.

@inproceedings{ BaMo-UNIF14, address = {Vienna, Austria}, author = {Franz {Baader} and Barbara {Morawska}}, booktitle = {Proceedings of the 28th International Workshop on Unification ({UNIF'14})}, editor = {Temur {Kutsia} and Christophe {Ringeissen}}, pages = {22--26}, series = {RISC-Linz Report Series No. 14-06}, title = {Matching with respect to general concept inclusions in the Description Logic $\mathcal{EL}$}, year = {2014}, }

Franz Baader and Barbara Morawska:

Abstract BibTeX Entry PDF File

**Matching with respect to general concept inclusions in the Description Logic**\(\mathcal{EL}\). In Carsten Lutz and Michael Thielscher, editors,*Proceedings of the 37th German Conference on Artificial Intelligence (KI'14)*, volume 8736 of*Lecture Notes in Artificial Intelligence*, pages 135–146. Springer-Verlag, 2014.Abstract BibTeX Entry PDF File

Matching concept descriptions against concept patterns was introduced as a new inference task in Description Logics (DLs) almost 20 years ago, motivated by applications in the Classic system. For the DL EL, it was shown in 2000 that matching without a TBox is NP-complete. In this paper we show that matching in EL w.r.t. general TBoxes (i.e., finite sets of general concept inclusions, GCIs) is in NP by introducing a goal-oriented matching algorithm that uses non-deterministic rules to transform a given matching problem into a solved form by a polynomial number of rule applications. We also investigate some tractable variants of the matching problem w.r.t. general TBoxes.

@inproceedings{ BaMo-KI2014, author = {Franz {Baader} and Barbara {Morawska}}, booktitle = {Proceedings of the 37th German Conference on Artificial Intelligence (KI'14)}, editor = {Carsten {Lutz} and Michael {Thielscher}}, pages = {135--146}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Matching with respect to general concept inclusions in the Description Logic $\mathcal{EL}$}, volume = {8736}, year = {2014}, }

Franz Baader and Barbara Morawska:

Abstract BibTeX Entry PDF File

**Matching with respect to general concept inclusions in the Description Logic**\(\mathcal{EL}\). In Meghyn Bienvenu, Magdalena Ortiz, Riccardo Rosati, and Mantas Simkus, editors,*Proceedings of the 27th International Workshop on Description Logics (DL'14)*, volume 1193 of*CEUR Workshop Proceedings*, pages 33–44, 2014.Abstract BibTeX Entry PDF File

Matching concept descriptions against concept patterns was introduced as a new inference task in Description Logics (DLs) almost 20 years ago, motivated by applications in the Classic system. For the DL EL, it was shown in 2000 that the matching problem is NP-complete. It then took almost 10 years before this NP-completeness result could be extended from matching to unification in EL. The next big challenge was then to further extend these results from matching and unification without a TBox to matching and unification w.r.t. a general TBox, i.e., a finite set of general concept inclusions. For unification, we could show some partial results for general TBoxes that satisfy a certain restriction on cyclic dependencies between concepts, but the general case is still open. For matching, we solve the general case in this paper: we show that matching in EL w.r.t. general TBoxes is NP-complete by introducing a goal-oriented matching algorithm that uses non-deterministic rules to transform a given matching problem into a solved form by a polynomial number of rule applications. We also investigate some tractable variants of the matching problem.

@inproceedings{ BaMo-DL14, address = {Vienna, Austria}, author = {Franz {Baader} and Barbara {Morawska}}, booktitle = {Proceedings of the 27th International Workshop on Description Logics ({DL'14})}, editor = {Meghyn {Bienvenu} and Magdalena {Ortiz} and Riccardo {Rosati} and Mantas {Simkus}}, pages = {33--44}, series = {CEUR Workshop Proceedings}, title = {Matching with respect to general concept inclusions in the Description Logic $\mathcal{EL}$}, volume = {1193}, year = {2014}, }

Daniel Borchmann, Rafael Peñaloza, and Wenqian Wang:

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**Classifying Software Bug Reports Using Methods from Formal Concept Analysis**.*Studia Universitatis Babeş-Bolyai Informatica*, 59:10–27, 2014. Suplemental proceedings of the 12th International Conference on Formal Concept Analysis (ICFCA'14)Abstract BibTeX Entry PDF File

We provide experience in applying methods from formal concept analysis to the problem of classifying software bug reports characterized by distinguished features. More specifically, we investigate the situation where we are given a set of already processed bug reports together with the components of the program that contained the corresponding error. The task is the following: given a new bug report with specific features, provide a list of components of the program based on the bug reports already processed that are likely to contain the error. To this end, we investigate several approaches that employ the idea of implications between features and program components. We describe these approaches in detail, and apply them to real-world data for evaluation. The best of our approaches is capable of identifying in just a fraction of a second the component causing a bug with an accuracy of over 70 percent.

@article{ BoPW-ICFCA14, author = {Daniel {Borchmann} and Rafael {Pe{\~n}aloza} and Wenqian {Wang}}, journal = {Studia Universitatis Babe{\c{s}}-Bolyai Informatica}, month = {June}, note = {Suplemental proceedings of the 12th International Conference on Formal Concept Analysis (ICFCA'14)}, pages = {10--27}, title = {Classifying Software Bug Reports Using Methods from Formal Concept Analysis}, volume = {59}, year = {2014}, }

Stefan Borgwardt:

Abstract BibTeX Entry PDF File

**Fuzzy DLs over Finite Lattices with Nominals**. In Meghyn Bienvenu, Magdalena Ortiz, Riccardo Rosati, and Mantas Simkus, editors,*Proceedings of the 27th International Workshop on Description Logics (DL'14)*, volume 1193 of*CEUR Workshop Proceedings*, pages 58–70, 2014.Abstract BibTeX Entry PDF File

The complexity of reasoning in fuzzy description logics (DLs) over a finite lattice L usually does not exceed that of the underlying classical DLs. This has recently been shown for the logics between L-IALC and L-ISCHI using a combination of automata- and tableau-based techniques. In this paper, this approach is modified to deal with nominals and constants in L-ISCHOI. Reasoning w.r.t. general TBoxes is ExpTime-complete, and PSpace-completeness is shown under the restriction to acyclic terminologies in two sublogics. The latter implies two previously unknown complexity results for the classical DLs ALCHO and SO.

@inproceedings{ Borg-DL14, author = {Stefan {Borgwardt}}, booktitle = {Proceedings of the 27th International Workshop on Description Logics ({DL'14})}, editor = {Meghyn {Bienvenu} and Magdalena {Ortiz} and Riccardo {Rosati} and Mantas {Simkus}}, pages = {58--70}, series = {CEUR Workshop Proceedings}, title = {Fuzzy DLs over Finite Lattices with Nominals}, volume = {1193}, year = {2014}, }

Stefan Borgwardt, Marco Cerami, and Rafael Peñaloza:

BibTeX Entry PDF File

**Many-Valued Horn Logic is Hard**. In Thomas Lukasiewicz, Rafael Peñaloza, and Anni-Yasmin Turhan, editors,*Proceedings of the 1st International Workshop on Logics for Reasoning about Preferences, Uncertainty, and Vagueness (PRUV'14)*, volume 1205 of*CEUR Workshop Proceedings*, pages 52–58, 2014.BibTeX Entry PDF File

@inproceedings{ BoCP-PRUV14, address = {Vienna, Austria}, author = {Stefan {Borgwardt} and Marco {Cerami} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 1st International Workshop on Logics for Reasoning about Preferences, Uncertainty, and Vagueness ({PRUV'14})}, editor = {Thomas {Lukasiewicz} and Rafael {Pe{\~n}aloza} and Anni-Yasmin {Turhan}}, pages = {52--58}, series = {CEUR Workshop Proceedings}, title = {Many-Valued Horn Logic is Hard}, volume = {1205}, year = {2014}, }

Stefan Borgwardt, Felix Distel, and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Decidable Gödel description logics without the finitely-valued model property**. In Chitta Baral, Giuseppe De Giacomo, and Thomas Eiter, editors,*Proceedings of the 14th International Conference on Principles of Knowledge Representation and Reasoning (KR'14)*, pages 228–237. AAAI Press, 2014.Abstract BibTeX Entry PDF File

In the last few years, there has been a large effort for analyzing the computational properties of reasoning in fuzzy description logics. This has led to a number of papers studying the complexity of these logics, depending on the chosen semantics. Surprisingly, despite being arguably the simplest form of fuzzy semantics, not much is known about the complexity of reasoning in fuzzy description logics w.r.t. witnessed models over the Gödel t-norm. We show that in the logic G-IALC, reasoning cannot be restricted to finitely-valued models in general. Despite this negative result, we also show that all the standard reasoning problems can be solved in exponential time, matching the complexity of reasoning in classical ALC.

@inproceedings{ BoDP-KR14, author = {Stefan {Borgwardt} and Felix {Distel} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 14th International Conference on Principles of Knowledge Representation and Reasoning (KR'14)}, editor = {Chitta {Baral} and Giuseppe {De Giacomo} and Thomas {Eiter}}, pages = {228--237}, publisher = {AAAI Press}, title = {Decidable {G}{\"o}del description logics without the finitely-valued model property}, year = {2014}, }

Stefan Borgwardt, Felix Distel, and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Gödel Description Logics with General Models**. In Meghyn Bienvenu, Magdalena Ortiz, Riccardo Rosati, and Mantas Simkus, editors,*Proceedings of the 27th International Workshop on Description Logics (DL'14)*, volume 1193 of*CEUR Workshop Proceedings*, pages 391–403, 2014.Abstract BibTeX Entry PDF File

In the last few years, the complexity of reasoning in fuzzy description logics has been studied in depth. Surprisingly, despite being arguably the simplest form of fuzzy semantics, not much is known about the complexity of reasoning in fuzzy description logics using the Gödel t-norm. It was recently shown that in the logic G-IALC under witnessed model semantics, all standard reasoning problems can be solved in exponential time, matching the complexity of reasoning in classical ALC. We show that this also holds under general model semantics.

@inproceedings{ BoDP-DL14, address = {Vienna, Austria}, author = {Stefan {Borgwardt} and Felix {Distel} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 27th International Workshop on Description Logics ({DL'14})}, editor = {Meghyn {Bienvenu} and Magdalena {Ortiz} and Riccardo {Rosati} and Mantas {Simkus}}, pages = {391--403}, series = {CEUR Workshop Proceedings}, title = {G\"odel Description Logics with General Models}, volume = {1193}, year = {2014}, }

Stefan Borgwardt, José A. Leyva Galano, and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Gödel**\(\mathcal{FL}_0\)**with Greatest Fixed-Point Semantics**. In Meghyn Bienvenu, Magdalena Ortiz, Riccardo Rosati, and Mantas Simkus, editors,*Proceedings of the 27th International Workshop on Description Logics (DL'14)*, volume 1193 of*CEUR Workshop Proceedings*, pages 71–82, 2014.Abstract BibTeX Entry PDF File

We study the fuzzy extension of FL_{0}with semantics based on the Gödel t-norm. We show that gfp-subsumption w.r.t. a finite set of primitive definitions can be characterized by a relation on weighted automata, and use this result to provide tight complexity bounds for reasoning in this logic.

@inproceedings{ BoLP-DL14, address = {Vienna, Austria}, author = {Stefan {Borgwardt} and Jos{\'e} A. {Leyva Galano} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 27th International Workshop on Description Logics ({DL'14})}, editor = {Meghyn {Bienvenu} and Magdalena {Ortiz} and Riccardo {Rosati} and Mantas {Simkus}}, pages = {71--82}, series = {CEUR Workshop Proceedings}, title = {G{\"o}del {$\mathcal{FL}_0$} with Greatest Fixed-Point Semantics}, volume = {1193}, year = {2014}, }

Stefan Borgwardt, José A. Leyva Galano, and Rafael Peñaloza:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**The Fuzzy Description Logic G-**\(\mathcal{FL}_0\)**with Greatest Fixed-Point Semantics**. In Eduardo Fermé and João Leite, editors,*Proceedings of the 14th European Conference on Logics in Artificial Intelligence (JELIA'14)*, volume 8761 of*Lecture Notes in Artificial Intelligence*, pages 62–76. Funchal, Portugal, Springer-Verlag, 2014.Abstract BibTeX Entry PDF File ©Springer-Verlag

We study the fuzzy extension of the Description Logic FL_{0}with semantics based on the Gödel t-norm. We show that subsumption w.r.t. a finite set of primitive definitions, using greatest fixed-point semantics, can be characterized by a relation on weighted automata. We use this result to provide tight complexity bounds for reasoning in this logic, showing that it is PSpace-complete. If the definitions do not contain cycles, subsumption becomes co-NP-complete.

@inproceedings{ BoLP-JELIA14, address = {Funchal, Portugal}, author = {Stefan {Borgwardt} and Jos{\'e} A. {Leyva Galano} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 14th European Conference on Logics in Artificial Intelligence (JELIA'14)}, editor = {Eduardo {Ferm{\'e}} and Jo{\~a}o {Leite}}, pages = {62--76}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {The Fuzzy Description Logic {\textsf{G}-$\mathcal{FL}_0$} with Greatest Fixed-Point Semantics}, volume = {8761}, year = {2014}, }

Stefan Borgwardt and Rafael Peñaloza:

Abstract BibTeX Entry PDF File DOI

**Consistency Reasoning in Lattice-Based Fuzzy Description Logics**.*International Journal of Approximate Reasoning*, 55(9):1917–1938, 2014.Abstract BibTeX Entry PDF File DOI

Fuzzy Description Logics have been widely studied as a formalism for representing and reasoning with vague knowledge. One of the most basic reasoning tasks in (fuzzy) Description Logics is to decide whether an ontology representing a knowledge domain is consistent. Surprisingly, not much is known about the complexity of this problem for semantics based on complete De Morgan lattices. To cover this gap, in this paper we study the consistency problem for the fuzzy Description Logic L-SHI and its sublogics in detail. The contribution of the paper is twofold. On the one hand, we provide a tableaux-based algorithm for deciding consistency when the underlying lattice is finite. The algorithm generalizes the one developed for classical SHI. On the other hand, we identify decidable and undecidable classes of fuzzy Description Logics over infinite lattices. For all the decidable classes, we also provide tight complexity bounds.

@article{ BoPe-IJAR14, author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}}, doi = {http://dx.doi.org/10.1016/j.ijar.2013.07.006}, journal = {International Journal of Approximate Reasoning}, number = {9}, pages = {1917--1938}, title = {Consistency Reasoning in Lattice-Based Fuzzy Description Logics}, volume = {55}, year = {2014}, }

Stefan Borgwardt and Rafael Peñaloza:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Finite Lattices Do Not Make Reasoning in ALCOI Harder**. In F. Bobillo, R.N. Carvalho, P.C.G. da Costa, C. d'Amato, N. Fanizzi, K.B. Laskey, K.J. Laskey, Th. Lukasiewicz, M. Nickles, and M. Pool, editors,*Uncertainty Reasoning for the Semantic Web III*, volume 8816 of*LNCS*, pages 122–141. Springer-Verlag, 2014. Revised Selected Papers from the ISWC International Workshops URSW 2011 - 2013Abstract BibTeX Entry PDF File ©Springer-Verlag

We consider the fuzzy description logic ALCOI with semantics based on a finite residuated De Morgan lattice. We show that reasoning in this logic is ExpTime-complete w.r.t. general TBoxes. In the sublogics ALCI and ALCO, it is PSpace-complete w.r.t. acyclic TBoxes. This matches the known complexity bounds for reasoning in classical description logics between ALC and ALCOI.

@inproceedings{ BoPe-URSW3, author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}}, booktitle = {Uncertainty Reasoning for the Semantic Web III}, editor = {F. {Bobillo} and R.N. {Carvalho} and P.C.G. {da Costa} and C. {d'Amato} and N. {Fanizzi} and K.B. {Laskey} and K.J. {Laskey} and Th. {Lukasiewicz} and M. {Nickles} and M. {Pool}}, note = {Revised Selected Papers from the ISWC International Workshops URSW 2011 - 2013}, pages = {122--141}, publisher = {Springer-Verlag}, series = {LNCS}, title = {Finite Lattices Do Not Make Reasoning in ALCOI Harder}, volume = {8816}, year = {2014}, }

Diego Calvanese, Ismail Ilkan Ceylan, Marco Montali, and Ario Santoso:

Abstract BibTeX Entry PDF File

**Verification of Context-Sensitive Knowledge and Action Bases**. In*Proceedings of the 14th European Conference on Logics in Artificial Intelligence (JELIA 2014)*, volume 8761 of*LNCS*, pages 514–528. Springer Verlag, 2014.Abstract BibTeX Entry PDF File

Knowledge and Action Bases (KABs) have been recently proposed as a formal framework to capture the dynamics of systems which manipulate Description Logic (DL) Knowledge Bases (KBs) through action execution. In this work, we enrich the KAB setting with contextual information, making use of different context dimensions. On the one hand, context is determined by the environment using context-changing actions that make use of the current state of the KB and the current context. On the other hand, it affects the set of TBox assertions that are relevant at each time point, and that have to be considered when processing queries posed over the KAB. Here we extend to our enriched setting the results on verification of rich temporal properties expressed in μ-calculus, which had been established for standard KABs. Specifically, we show that under a run-boundedness condition, verification stays decidable and does not incur in any additional cost in terms of worst-case complexity. We also show how to adapt syntactic conditions ensuring run-boundedness so as to account for contextual information, taking into account context-dependent activation of TBox assertions.

@inproceedings{ CaCeMoSa-JELIA14, author = {Diego {Calvanese} and Ismail Ilkan {Ceylan} and Marco {Montali} and Ario {Santoso}}, booktitle = {Proceedings of the 14th European Conference on Logics in Artificial Intelligence (JELIA 2014)}, pages = {514--528}, publisher = {Springer Verlag}, series = {LNCS}, title = {Verification of Context-Sensitive Knowledge and Action Bases}, volume = {8761}, year = {2014}, }

Diego Calvanese, Ismail Ilkan Ceylan, Marco Montali, and Ario Santoso:

Abstract BibTeX Entry PDF File

**Adding Context to Knowledge and Action Bases**. In*Proceedings of Acquisition, Representation and Reasoning About Context with Logic (ARCOE 2014)*. CoRR Technical Report, 2014.Abstract BibTeX Entry PDF File

Knowledge and Action Bases (KABs) have been recently proposed as a formal framework to capture the dynamics of systems which manipulate Description Logic (DL) Knowledge Bases (KBs) through action execution. In this work, we enrich the KAB setting with contextual information, making use of different context dimensions. On the one hand, context is determined by the environment using context-changing actions that make use of the current state of the KB and the current context. On the other hand, it affects the set of TBox assertions that are relevant at each time point, and that have to be considered when processing queries posed over the KAB. Here we extend to our enriched setting the results on verification of rich temporal properties expressed in mu-calculus, which had been established for standard KABs. Specifically, we show that under a run-boundedness condition, verification stays decidable.

@inproceedings{ Calvanese2014, author = {Diego {Calvanese} and Ismail Ilkan {Ceylan} and Marco {Montali} and Ario {Santoso}}, booktitle = {Proceedings of Acquisition, Representation and Reasoning About Context with Logic (ARCOE 2014)}, publisher = {CoRR Technical Report}, title = {{Adding Context to Knowledge and Action Bases}}, year = {2014}, }

Ismail Ilkan Ceylan and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Reasoning in the Description Logic BEL using Bayesian Networks**. In*Proceedings of 4th International Workshop on Statistical Relational AI (StarAI 2014)*, volume WS-14-13 of*AAAI Workshops*. AAAI Press, 2014.Abstract BibTeX Entry PDF File

We study the problem of reasoning in the probabilistic Description Logic BEL. Using a novel structure, we show that probabilistic reasoning in this logic can be reduced in polynomial time to standard inferences over a Bayesian network. This reduction provides tight complexity bounds for probabilistic reasoning in BEL.

@inproceedings{ CePe-starAI14, author = {Ismail Ilkan {Ceylan} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of 4th International Workshop on Statistical Relational AI (StarAI 2014)}, publisher = {AAAI Press}, series = {AAAI Workshops}, title = {Reasoning in the Description Logic BEL using Bayesian Networks}, volume = {WS-14-13}, year = {2014}, }

Ismail Ilkan Ceylan and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**The Bayesian Description Logic BEL**. In*Proceedings of 7th International Joint Conference on Automated Reasoning (IJCAR 2014)*, volume 8562 of*LNCS*, pages 480–494. Springer, 2014.Abstract BibTeX Entry PDF File

We introduce the probabilistic Description Logic BEL. In BEL, axioms are required to hold only in an associated context. The probabilistic component of the logic is given by a Bayesian network that describes the joint probability distribution of the contexts. We study the main reasoning problems in this logic; in particular, we (i) prove that deciding positive and almost-sure entailments is not harder for BEL than for the BN, and (ii) show how to compute the probability, and the most likely context for a consequence.

@inproceedings{ CePe-IJCAR14, author = {Ismail Ilkan {Ceylan} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of 7th International Joint Conference on Automated Reasoning (IJCAR 2014)}, pages = {480--494}, publisher = {Springer}, series = {LNCS}, title = {The Bayesian Description Logic BEL}, volume = {8562}, year = {2014}, }

Ismail Ilkan Ceylan and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Tight Complexity Bounds for Reasoning in the Description Logic**\(\mathcal{BEL}\). In*Proceedings of the 14th European Conference on Logics in Artificial Intelligence (JELIA 2014)*, volume 8761 of*LNCS*, pages 77–91. Springer, 2014.Abstract BibTeX Entry PDF File

Recently, Bayesian extensions of Description Logics, and in particular the logic BEL, were introduced as a means of representing certain knowledge that depends on an uncertain context. In this paper we introduce a novel structure, called proof structure, that encodes the contextual information required to deduce subsumption relations from a BEL knowledge base. Using this structure, we show that probabilistic reasoning in BEL can be reduced in polynomial time to standard Bayesian network inferences, thus obtaining tight complexity bounds for reasoning in BEL.

@inproceedings{ CePe-JELIA14, author = {Ismail Ilkan {Ceylan} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 14th European Conference on Logics in Artificial Intelligence (JELIA 2014)}, pages = {77--91}, publisher = {Springer}, series = {LNCS}, title = {Tight Complexity Bounds for Reasoning in the Description Logic {$\mathcal{BEL}$}}, volume = {8761}, year = {2014}, }

Ismail Ilkan Ceylan and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Bayesian Description Logics**. In Meghyn Bienvenu, Magdalena Ortiz, Riccardo Rosati, and Mantas Simkus, editors,*Proceedings of the 27th International Workshop on Description Logics (DL'14)*, volume 1193 of*CEUR Workshop Proceedings*. CEUR-WS, 2014.Abstract BibTeX Entry PDF File

We present Bayesian Description Logics (BDLs): an extension of Description Logics (DLs) with contextual probabilities encoded in a Bayesian network (BN). Classical DL reasoning tasks are extended to consider also the contextual and probabilistic information in BDLs. A complexity analysis of these problems shows that, for propositionally closed DLs, this extension comes without cost, while for tractable DLs the complexity is affected by the cost of reasoning in the BN.

@inproceedings{ CePe-DL14, author = {Ismail Ilkan {Ceylan} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 27th International Workshop on Description Logics (DL'14)}, editor = {Meghyn {Bienvenu} and Magdalena {Ortiz} and Riccardo {Rosati} and Mantas {Simkus}}, publisher = {CEUR-WS}, series = {CEUR Workshop Proceedings}, title = {{Bayesian Description Logics}}, volume = {1193}, year = {2014}, }

Jieying Chen, Michel Ludwig, Yue Ma, and Dirk Walther:

Abstract BibTeX Entry PDF File

**Evaluation of Extraction Techniques for Ontology Excerpts**. In Meghyn Bienvenu, Magdalena Ortiz, Riccardo Rosati, and Mantas Simkus, editors,*Proceedings of the 27th International Workshop on Description Logics (DL'14)*, volume 1193 of*CEUR Workshop Proceedings*, pages 471–482, 2014.Abstract BibTeX Entry PDF File

We introduce the notion of an ontology excerpt as being a fixed-size subset of an ontology that preserves as much knowledge as possible about the terms in a given vocabulary as described in the ontology. We consider different extraction techniques for ontology excerpts based on methods from Information Retrieval. To evaluate these techniques, we measure the degree of incompleteness of the resulting excerpts using the notion of logical difference. We provide an experimental evaluation of the extraction techniques by applying them on the biomedical ontology SNOMED CT.

@inproceedings{ ChLuMaWa-DL14, author = {Jieying {Chen} and Michel {Ludwig} and Yue {Ma} and Dirk {Walther}}, booktitle = {Proceedings of the 27th International Workshop on Description Logics ({DL'14})}, editor = {Meghyn {Bienvenu} and Magdalena {Ortiz} and Riccardo {Rosati} and Mantas {Simkus}}, pages = {471--482}, series = {CEUR Workshop Proceedings}, title = {Evaluation of Extraction Techniques for Ontology Excerpts}, volume = {1193}, year = {2014}, }

Jens Claßen, Martin Liebenberg, Gerhard Lakemeyer, and Benjamin Zarrieß:

Abstract BibTeX Entry PDF File

**Exploring the Boundaries of Decidable Verification of Non-Terminating Golog Programs**. In*Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence (AAAI 2014)*, pages 1012–1019. Quebec City, Quebec, Canada, AAAI Press, 2014.Abstract BibTeX Entry PDF File

The action programming language Golog has been found useful for the control of autonomous agents such as mobile robots. In scenarios like these, tasks are often open-ended so that the respective control programs are non-terminating. Before deploying such programs on a robot, it is often desirable to verify that they meet certain requirements. For this purpose, Claßen and Lakemeyer recently introduced algorithms for the verification of temporal properties of Golog programs. However, given the expressiveness of Golog, their verification procedures are not guaranteed to terminate. In this paper, we show how decidability can be obtained by suitably restricting the underlying base logic, the effect axioms for primitive actions, and the use of actions within Golog programs. Moreover, we show that dropping any of these restrictions immediately leads to undecidability of the verification problem.

@inproceedings{ ClaLLZ-AAAI14, address = {Quebec City, Quebec, Canada}, author = {Jens {Cla{\ss}en} and Martin {Liebenberg} and Gerhard {Lakemeyer} and Benjamin {Zarrie{\ss}}}, booktitle = {Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence (AAAI 2014)}, pages = {1012--1019}, publisher = {AAAI Press}, title = {Exploring the Boundaries of Decidable Verification of Non-Terminating Golog Programs}, type = {inproceedings}, year = {2014}, }

Chiara Del Vescovo and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**DeaLing with Ontologies using CODs**. In Meghyn Bienvenu, Magdalena Ortiz, Riccardo Rosati, and Mantas Simkus, editors,*Proceedings of the 27th International Workshop on Description Logics (DL'14)*, volume 1193 of*CEUR Workshop Proceedings*, pages 157–168, 2014.Abstract BibTeX Entry PDF File

A major challenge in knowledge representation is to manage the access to knowledge: users should not be presented with knowledge that is irrelevant to their topic of interest, or have no right to access. Two general strategies exist for providing access restrictions: (1) the ontology engineers describe the conditions that allow access to specific fragments of the ontology, or (2) fragments are automatically identified through their logical properties. The former is prone to miss logical connections between axioms, while the latter can fail to capture relevant knowledge that has no logical connection with the topic of interest. We define the Context-Oriented Decomposition (COD) of an ontology as a technique that combines the benefits of both approaches: it allows authors to identify relevant fragments, while guaranteeing the strong semantic properties of the logic-based Atomic Decomposition.

@inproceedings{ DVPe-DL14, address = {Vienna, Austria}, author = {Chiara {Del Vescovo} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 27th International Workshop on Description Logics ({DL'14})}, editor = {Meghyn {Bienvenu} and Magdalena {Ortiz} and Riccardo {Rosati} and Mantas {Simkus}}, pages = {157--168}, series = {CEUR Workshop Proceedings}, title = {DeaLing with Ontologies using CODs}, volume = {1193}, year = {2014}, }

Stathis Delivorias, Haralampos Hatzikirou, Rafael Penaloza, and Dirk Walther:

Abstract BibTeX Entry PDF File

**Detecting Emergent Phenomena in Cellular Automata Using Temporal Description Logics**. In*Proceedings of the 11th edition of Cellular Automata for Research and Industry (ACRI 2014)*,*Lecture Notes in Computer Science*. Springer-Verlag, 2014.Abstract BibTeX Entry PDF File

Cellular automata are discrete mathematical models that have been proven useful as representations of a wide variety of systems exhibiting emergent behavior. Detection of emergent behavior is typically computationally expensive as it relies on computer simulations. We pro- pose to specify cellular automata using a suitable Temporal Description Logic and we show that we can formulate queries about the evolution of a cellular automaton as reasoning tasks in this logic.

@inproceedings{ DeHaPeWa-ACRI14, author = {Stathis {Delivorias} and Haralampos {Hatzikirou} and Rafael {Penaloza} and Dirk {Walther}}, booktitle = {Proceedings of the 11th edition of Cellular Automata for Research and Industry (ACRI 2014)}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Detecting Emergent Phenomena in Cellular Automata Using Temporal Description Logics}, year = {2014}, }

Felix Distel, Jamal Atif, and Isabelle Bloch:

Abstract BibTeX Entry PDF File

**Concept Dissimilarity with Triangle Inequality**. In*Proceedings of the Fourteenth International Conference on Principles of Knowledge Representation and Reasoning (KR'14)*. Vienna, Austria, AAAI Press, 2014. Short Paper. To appear.Abstract BibTeX Entry PDF File

Several researchers have developed properties that ensure compatibility of a concept similarity or dissimilarity measure with the formal semantics of Description Logics. While these authors have highlighted the relevance of the triangle inequality, none of their proposed dissimilarity measures satisfy it. In this work we present a theoretical framework for dissimilarity measures with this property. Our approach is based on concept relaxations, operators that perform stepwise generalizations on concepts. We prove that from any relaxation we can derive a dissimilarity measure that satisfies a number or properties that are important when comparing concepts.

@inproceedings{ DiAtBl-KR14, address = {Vienna, Austria}, author = {Felix {Distel} and Jamal {Atif} and Isabelle {Bloch}}, booktitle = {Proceedings of the Fourteenth International Conference on Principles of Knowledge Representation and Reasoning ({KR'14})}, note = {Short Paper. To appear.}, publisher = {AAAI Press}, title = {Concept Dissimilarity with Triangle Inequality}, year = {2014}, }

Felix Distel, Jamal, Atif, and Isabelle Bloch:

Abstract BibTeX Entry PDF File

**Concept Dissimilarity Based on Tree Edit Distances and Morphological Dilations**. In Torsten Schaub, editor,*Proceedings of the 21st International Conference on Artificial Intelligence (ECAI'14)*, 2014.Abstract BibTeX Entry PDF File

A number of similarity measures for comparing description logic concepts have been proposed. Criteria have been developed to evaluate a measure's fitness for an application. These criteria include on the one hand those that ensure compatibility with the semantics, such as equivalence soundness, and on the other hand the properties of a metric, such as the triangle inequality. In this work we present two classes of dissimilarity measures that are at the same time equivalence sound and satisfy the triangle inequality: a simple dissimilarity measure, based on description trees for the lightweight description logic ; and an instantiation of a general framework, presented in our previous work, using dilation operators from mathematical morphology, and which exploits the link between Hausdorff distance and dilations using balls of the ground distance as structuring elements.

@inproceedings{ DiAtBl-ECAI14, address = {Prague, Czech Republic}, author = {Felix {Distel} and Jamal, {Atif} and Isabelle {Bloch}}, booktitle = {Proceedings of the 21st International Conference on Artificial Intelligence (ECAI'14)}, editor = {Torsten {Schaub}}, title = {Concept Dissimilarity Based on Tree Edit Distances and Morphological Dilations}, year = {2014}, }

Andreas Ecke:

Abstract BibTeX Entry PDF File

**Similarity-based Relaxed Instance Queries in**\(\mathcal{EL}^{++}\). In Thomas Lukasiewicz, Rafael Peñaloza, and Anni-Yasmin Turhan, editors,*Proceedings of the First Workshop on Logics for Reasoning about Preferences, Uncertainty, and Vagueness*, volume 1205 of*CEUR Workshop Proceedings*, pages 101–113. CEUR-WS.org, 2014.Abstract BibTeX Entry PDF File

Description Logic (DL) knowledge bases (KBs) allow to express knowledge about concepts and individuals in a formal way. This knowledge is typically crisp, i.e., an individual either is an instance of a given concept or it is not. However, in practice this is often too restrictive: when querying for instances, one may often also want to find suitable alternatives, i.e., individuals that are not instances of query concept, but could still be considered `good enough'. Relaxed instance queries have been introduced to gradually relax this inference in a controlled way via the use of concept similarity measures (CSMs). So far, those algorithms only work for the DL EL, which has limited expressive power. In this paper, we introduce a suitable CSM for EL++-concepts. EL++ adds nominals, role inclusion axioms, and concrete domains to EL. We extend the algorithm to compute relaxed instance queries w.r.t. this new CSM, and thus to work for general EL++ KBs.

@inproceedings{ Ecke-PRUV-14, author = {Andreas {Ecke}}, booktitle = {Proceedings of the First Workshop on Logics for Reasoning about Preferences, Uncertainty, and Vagueness}, editor = {Thomas {Lukasiewicz} and Rafael {Pe{\~n}aloza} and Anni-Yasmin {Turhan}}, pages = {101--113}, publisher = {CEUR-WS.org}, series = {{CEUR} Workshop Proceedings}, title = {Similarity-based Relaxed Instance Queries in $\mathcal{EL}^{++}$}, volume = {1205}, year = {2014}, }

Andreas Ecke, Rafael Peñaloza, and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File

**Answering Instance Queries Relaxed by Concept Similarity**. In Chitta Baral, Giuseppe De Giacomo, and Thomas Eiter, editors,*Proceedings of the Fourteenth International Conference on Principles of Knowledge Representation and Reasoning (KR'14)*, pages 248–257. Vienna, Austria, AAAI Press, 2014.Abstract BibTeX Entry PDF File

In Description Logics (DL) knowledge bases (KBs) information is typically captured by crisp concepts. For many applications querying the KB by crisp query concepts is too restrictive. A controlled way of gradually relaxing a query concept can be achieved by the use of concept similarity. In this paper we formalize the task of instance query answering for crisp DL KBs using concepts relaxed by concept similarity measures (CSM). For the DL \(\mathcal{EL}\) we investigate computation algorithms for this task, their complexity and properties for the employed CSM in case unfoldabel Tboxes or general TBoxes aer used.

@inproceedings{ EcPeTu-KR14, address = {Vienna, Austria}, author = {Andreas {Ecke} and Rafael {Pe{\~n}aloza} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of the Fourteenth International Conference on Principles of Knowledge Representation and Reasoning ({KR'14})}, editor = {Chitta {Baral} and Giuseppe {De Giacomo} and Thomas {Eiter}}, pages = {248--257}, publisher = {AAAI Press}, title = {Answering Instance Queries Relaxed by Concept Similarity}, year = {2014}, }

Andreas Ecke, Rafael Peñaloza, and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File DOI

**Completion-based Generalization Inferences for the Description Logic**\(\mathcal{ELOR}\)**with Subjective Probabilities**.*International Journal of Approximate Reasoning*, 55(9):1939–1970, 2014.Abstract BibTeX Entry PDF File DOI

Description Logics (DLs) are a well-established family of knowledge representation formalisms. One of its members, the DL \(\mathcal{ELOR}\) has been successfully used for representing knowledge from the bio-medical sciences, and is the basis for the OWL 2 EL profile of the standard ontology language for the Semantic Web. Reasoning in this DL can be performed in polynomial time through a completion-based algorithm. In this paper we study the logic Prob-\(\mathcal{ELOR}\), that extends \(\mathcal{ELOR}\) with subjective probabilities, and present a completion-based algorithm for polynomial time reasoning in a restricted version, Prob-\(\mathcal{ELOR}^c_{01}\), of Prob-\(\mathcal{ELOR}\). We extend this algorithm to computation algorithms for approximations of (i) the most specific concept, which generalizes a given individual into a concept description, and (ii) the least common subsumer, which generalizes several concept descriptions into one. Thus, we also obtain methods for these inferences for the OWL 2 EL profile. These two generalization inferences are fundamental for building ontologies automatically from examples. The feasibility of our approach is demonstrated empirically by our prototype system GEL.

@article{ EcPeTu-IJAR-14, author = {Andreas {Ecke} and Rafael {Pe{\~n}aloza} and Anni-Yasmin {Turhan}}, doi = {http://dx.doi.org/10.1016/j.ijar.2014.03.001}, journal = {International Journal of Approximate Reasoning}, number = {9}, pages = {1939--1970}, publisher = {Elsevier}, title = {Completion-based Generalization Inferences for the Description Logic $\mathcal{ELOR}$ with Subjective Probabilities}, volume = {55}, year = {2014}, }

Andreas Ecke, Rafael Peñaloza, and Anni-Yasmin Turhan:

BibTeX Entry PDF File

**Mary, What's Like All Cats?**. In Meghyn Bienvenu, Magdalena Ortiz, Riccardo Rosati, and Mantas Simkus, editors,*Proceedings of the 27th International Workshop on Description Logics (DL'14)*, volume 1193 of*CEUR Workshop Proceedings*, pages 526–529, 2014.BibTeX Entry PDF File

@inproceedings{ EcPT-DL14, address = {Vienna, Austria}, author = {Andreas {Ecke} and Rafael {Pe{\~n}aloza} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of the 27th International Workshop on Description Logics ({DL'14})}, editor = {Meghyn {Bienvenu} and Magdalena {Ortiz} and Riccardo {Rosati} and Mantas {Simkus}}, pages = {526--529}, series = {CEUR Workshop Proceedings}, title = {Mary, What's Like All Cats?}, volume = {1193}, year = {2014}, }

Marcus Hähnel, Julian Mendez, Veronika Thost, and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File

**Bridging the Application Knowledge Gap**. In*Workshop on Adaptive and Reflective Middleware'14*, December 2014.Abstract BibTeX Entry PDF File

Regarding energy efficiency, resource management in complex hard- and software systems that is based on the information typically available to the OS alone does not yield best results. Nevertheless, general-purpose resource management should stay independent of application-specific information. To resolve this dilemma, we propose a generic, ontology-based approach to resource scheduling that is context-aware and takes information of running applications into account. The central task here is to recognize situations that might necessitate an adaptation of resource scheduling. This task is performed by logical reasoning over OWL ontologies. Our initial study shows that current OWL 2 EL reasoner systems can perform recognition of exemplary situations relevant to resource management within 4 seconds.

@inproceedings{ HaMeTT-ARM-14, address = {Bordeaux, France}, author = {Marcus {H\"ahnel} and Julian {Mendez} and Veronika {Thost} and Anni-Yasmin {Turhan}}, booktitle = {Workshop on Adaptive and Reflective Middleware'14}, month = {December}, title = {Bridging the Application Knowledge Gap}, year = {2014}, }

Francesco Kriegel:

Abstract BibTeX Entry PDF File PDF File (ubbcluj.ro)

**Incremental Computation of Concept Diagrams**.*Studia Universitatis Babeş-Bolyai Informatica*, 59:45–61, 2014. Supplemental proceedings of the 12th International Conference on Formal Concept Analysis (ICFCA 2014), Cluj-Napoca, RomaniaAbstract BibTeX Entry PDF File PDF File (ubbcluj.ro)

Suppose a formal context \(\mathbb{K}=(G,M,I)\) is given, whose concept lattice \(\mathfrak{B}(\mathbb{K})\) with an attribute-additive concept diagram is already known, and an attribute column \(\mathbb{C}=(G,\{n\},J)\) shall be inserted to or removed from it. This paper introduces and proves an incremental update algorithm for both tasks.

@article{ Kr-ICFCA14, address = {Cluj-Napoca, Romania}, author = {Francesco {Kriegel}}, journal = {Studia Universitatis Babe{\c{s}}-Bolyai Informatica}, note = {Supplemental proceedings of the 12th International Conference on Formal Concept Analysis (ICFCA 2014), Cluj-Napoca, Romania}, pages = {45--61}, title = {Incremental Computation of Concept Diagrams}, volume = {59}, year = {2014}, }

Karsten Lehmann and Rafael Peñaloza:

Abstract BibTeX Entry PDF File DOI

**The Complexity of Computing the Behaviour of Lattice Automata on Infinite Trees**.*Theoretical Computer Science*, 534:53–68, 2014.Abstract BibTeX Entry PDF File DOI

Several logic-based decision problems have been shown to be reducible to the emptiness problem of automata. In a similar way, non-standard reasoning problems can be reduced to the computation of the behaviour of weighted automata. In this paper, we consider a variant of weighted Büchi automata working on (unlabeled) infinite trees, where the weights belong to a lattice. We analyse the complexity of computing the behaviour of this kind of automata if the underlying lattice is not distributive. We show that the decision version of this problem is in ExpTime and PSpace-hard in general, assuming that the lattice operations are polynomial-time computable. If the lattice is what we call "linear-space-computable-encoded", then the upper bound can be reduced to PSpace, but the lower bound also decreases to NP-hard and co-NP-hard. We conjecture that the upper bounds provided are in fact tight.

@article{ LePe-TCS14, author = {Karsten {Lehmann} and Rafael {Pe{\~n}aloza}}, doi = {http://dx.doi.org/10.1016/j.tcs.2014.02.036}, journal = {Theoretical Computer Science}, month = {May}, pages = {53--68}, publisher = {Elsevier}, title = {The Complexity of Computing the Behaviour of Lattice Automata on Infinite Trees}, volume = {534}, year = {2014}, }

Michel Ludwig:

Abstract BibTeX Entry PDF File

**Just: a Tool for Computing Justifications w.r.t. EL Ontologies**. In Samantha Bail, Birte Glimm, Ernesto Jiménez-Ruiz, Nicolas Matentzoglu, Bijan Parsia, and Andreas Steigmiller, editors,*Proceedings of the 3rd International Workshop on OWL Reasoner Evaluation (ORE 2014)*, pages 1–7. CEUR Workshop Proceedings, 2014.Abstract BibTeX Entry PDF File

We introduce the tool JUST for computing justifications for general concept inclusions w.r.t. ontologies formulated in the description logic EL extended with role inclusions. The computation of justifications in JUST is based on saturating the input axioms under all possible inferences w.r.t. a consequence-based calculus. We give an overview of the implemented techniques and we conclude with an experimental evaluation of the performance of JUST when applied on several practical ontologies.

@inproceedings{ Lu-ORE-2014, author = {Michel {Ludwig}}, booktitle = {Proceedings of the 3rd International Workshop on OWL Reasoner Evaluation (ORE 2014)}, editor = {Samantha {Bail} and Birte {Glimm} and Ernesto {Jim\'{e}nez-Ruiz} and Nicolas {Matentzoglu} and Bijan {Parsia} and Andreas {Steigmiller}}, pages = {1--7}, publisher = {CEUR Workshop Proceedings}, title = {Just: a Tool for Computing Justifications w.r.t.\ EL Ontologies}, volume = {1207}, year = {2014}, }

Michel Ludwig and Boris Konev:

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**Practical Uniform Interpolation and Forgetting for ALC TBoxes with Applications to Logical Difference**. In Chitta Baral, Giuseppe De Giacomo, and Thomas Eiter, editors,*Proceedings of the 14th International Conference on Principles of Knowledge Representation and Reasoning (KR'14)*. AAAI Press, 2014.Abstract BibTeX Entry PDF File

We develop a clausal resolution-based approach for computing uniform interpolants of TBoxes formulated in the description logic when such uniform interpolants exist. We also present an experimental evaluation of our approach and of its application to the logical difference problem for real-life ALC ontologies. Our results indicate that in many practical cases uniform interpolants exist and that they can be computed with the presented algorithm.

@inproceedings{ LuKo-KR-2014, author = {Michel {Ludwig} and Boris {Konev}}, booktitle = {Proceedings of the 14th International Conference on Principles of Knowledge Representation and Reasoning (KR'14)}, editor = {Chitta {Baral} and Giuseppe De {Giacomo} and Thomas {Eiter}}, publisher = {AAAI Press}, title = {Practical Uniform Interpolation and Forgetting for ALC TBoxes with Applications to Logical Difference}, year = {2014}, }

Michel Ludwig and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Brave and Cautious Reasoning in EL**. In Meghyn Bienvenu, Magdalena Ortiz, Riccardo Rosati, and Mantas Simkus, editors,*Proceedings of the 27th International Workshop on Description Logics (DL'14)*, volume 1193 of*CEUR Workshop Proceedings*, pages 274–286, 2014.Abstract BibTeX Entry PDF File

Developing and maintaining ontologies is an expensive and error-prone task. After an error is detected, users may have to wait for a long time before a corrected version of the ontology is available. In the meantime, one might still want to derive meaningful knowledge from the ontology, while avoiding the known errors. We introduce brave and cautious reasoning and show that it is hard for EL. We then propose methods for improving the reasoning times by precompiling information about the known errors and using proof-theoretic techniques for computing justifications. A prototypical implementation shows that our approach is feasible for large ontologies used in practice.

@inproceedings{ LuPe-DL14, address = {Vienna, Austria}, author = {Michel {Ludwig} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 27th International Workshop on Description Logics ({DL'14})}, editor = {Meghyn {Bienvenu} and Magdalena {Ortiz} and Riccardo {Rosati} and Mantas {Simkus}}, pages = {274--286}, series = {CEUR Workshop Proceedings}, title = {Brave and Cautious Reasoning in EL}, volume = {1193}, year = {2014}, }

Michel Ludwig and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Error-Tolerant Reasoning in the Description Logic EL**. In Eduardo Fermé and João Leite, editors,*Proceedings of the 14th European Conference on Logics in Artificial Intelligence (JELIA'14)*, volume 8761 of*Lecture Notes in Artificial Intelligence*, pages 107–121. Madeira, Portugal, Springer-Verlag, 2014.Abstract BibTeX Entry PDF File

Developing and maintaining ontologies is an expensive and error-prone task. After an error is detected, users may have to wait for a long time before a corrected version of the ontology is available. In the meantime, one might still want to derive meaningful knowledge from the ontology, while avoiding the known errors. We study error-tolerant reasoning tasks in the description logic . While these problems are intractable, we propose methods for improving the reasoning times by precompiling information about the known errors and using proof-theoretic techniques for computing justifications. A prototypical implementation shows that our approach is feasible for large ontologies used in practice.

@inproceedings{ LuPe-JELIA14, address = {Madeira, Portugal}, author = {Michel {Ludwig} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 14th European Conference on Logics in Artificial Intelligence {(JELIA'14)}}, editor = {Eduardo {Ferm{\'e}} and Jo{\~a}o {Leite}}, pages = {107--121}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Error-Tolerant Reasoning in the Description Logic EL}, volume = {8761}, year = {2014}, }

Michel Ludwig and Dirk Walther:

Abstract BibTeX Entry PDF File

**Detecting Conjunctive Query Differences between ELHr-Terminologies using Hypergraphs**. In Meghyn Bienvenu, Magdalena Ortiz, Riccardo Rosati, and Mantas Simkus, editors,*Proceedings of the 27th International Workshop on Description Logics (DL'14)*, volume 1193 of*CEUR Workshop Proceedings*, pages 287–298, 2014.Abstract BibTeX Entry PDF File

We present a new method for detecting logical differences between EL-terminologies extended with role inclusions, domain and range restrictions of roles using a hypergraph representation of ontologies. In this paper we consider differences given by pairs consisting of a conjunctive query and of an ABox formulated over a vocabulary of interest. We define a simulation notion between such hypergraph representations and we show that the existence of simulations coincides with the absence of a logical difference. To demonstrate the practical applicability of our approach, we evaluate a prototype implementation on large ontologies.

@inproceedings{ LuWa-DL14, author = {Michel {Ludwig} and Dirk {Walther}}, booktitle = {Proceedings of the 27th International Workshop on Description Logics ({DL'14})}, editor = {Meghyn {Bienvenu} and Magdalena {Ortiz} and Riccardo {Rosati} and Mantas {Simkus}}, pages = {287--298}, series = {CEUR Workshop Proceedings}, title = {Detecting Conjunctive Query Differences between ELHr-Terminologies using Hypergraphs}, volume = {1193}, year = {2014}, }

Michel Ludwig and Dirk Walther:

Abstract BibTeX Entry DOI

**The Logical Difference for ELHr-Terminologies using Hypergraphs**. In Torsten Schaub, Gerhard Friedrich, and Barry O'Sullivan, editors,*Proceedings of the 21st European Conference on Artifical Intelligence (ECAI 2014)*, volume 263 of*Frontiers in Artificial Intelligence and Applications*, pages 555–560. IOS Press, 2014.Abstract BibTeX Entry DOI

We propose a novel approach for detecting semantic diffferences between ontologies. In this paper we investigate the logical difference for EL-terminologies extended with role inclusions, domain and range restrictions of roles. Three types of queries are covered: concept subsumption, instance and conjunctive queries. Using a hypergraph representation of such ontologies, we show that logical differences can be detected by checking for the existence of simulations between the corresponding hypergraphs. A minor adaptation of the simulation notions allows us to capture different types of queries. We also evaluate our hypergraph approach by applying a prototype implementation on large ontologies.

@inproceedings{ LuWa-ECAI-2014, author = {Michel {Ludwig} and Dirk {Walther}}, booktitle = {Proceedings of the 21st European Conference on Artifical Intelligence (ECAI 2014)}, doi = {http://dx.doi.org/10.3233/978-1-61499-419-0-555}, editor = {Torsten {Schaub} and Gerhard {Friedrich} and Barry {O'Sullivan}}, pages = {555--560}, publisher = {IOS Press}, series = {Frontiers in Artificial Intelligence and Applications}, title = {The Logical Difference for ELHr-Terminologies using Hypergraphs}, volume = {263}, year = {2014}, }

Yue Ma and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Towards Parallel Repair: An Ontology Decomposition-based Approach**. In Meghyn Bienvenu, Magdalena Ortiz, Riccardo Rosati, and Mantas Simkus, editors,*Proceedings of the 27th International Workshop on Description Logics (DL'14)*, volume 1193 of*CEUR Workshop Proceedings*, pages 633–645, 2014.Abstract BibTeX Entry PDF File

Ontology repair remains one of the main bottlenecks for the development of ontologies for practical use. Many automated methods have been developed for suggesting potential repairs, but ultimately human intervention is required for selecting the adequate one, and the human expert might be overwhelmed by the amount of information delivered to her. We propose a decomposition of ontologies into smaller components that can be repaired in parallel. We show the utility of our approach for ontology repair, provide algorithms for computing this decomposition through standard reasoning, and study the complexity of several associated problems.

@inproceedings{ MaPe-DL14, address = {Vienna, Austria}, author = {Yue {Ma} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 27th International Workshop on Description Logics ({DL'14})}, editor = {Meghyn {Bienvenu} and Magdalena {Ortiz} and Riccardo {Rosati} and Mantas {Simkus}}, pages = {633--645}, series = {CEUR Workshop Proceedings}, title = {Towards Parallel Repair: An Ontology Decomposition-based Approach}, volume = {1193}, year = {2014}, }

Theofilos Mailis, Rafael Peñaloza, and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Conjunctive Query Answering in Finitely-valued Fuzzy Description Logics**. In Roman Kontchakov and Marie-Laure Mugnier, editors,*Proceedings of the 8th International Conference on Web Reasoning and Rule Systems (RR 2014)*, pages 124–139. Springer, 2014.Abstract BibTeX Entry PDF File ©Springer-Verlag

Fuzzy Description Logics (DLs) generalize crisp ones by providing membership degree semantics for concepts and roles. A popular technique for reasoning in fuzzy DL ontologies is by providing a reduction to crisp DLs and then employ reasoning in the crisp DL. In this paper we adopt this approach to solve conjunctive query (CQ) answering problems for fuzzy DLs. We give reductions for Gödel and Łukasiewicz variants of fuzzy SROIQ and two kinds of fuzzy CQs. The correctness of the proposed reduction is proved and its complexity is studied for different fuzzy variants of SROIQ.

@inproceedings{ MaPe-RR-14, author = {Theofilos {Mailis} and Rafael {Pe\~naloza} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of the 8th International Conference on Web Reasoning and Rule Systems (RR 2014)}, editor = {Roman {Kontchakov} and Marie-Laure {Mugnier}}, pages = {124--139}, publisher = {Springer}, title = {Conjunctive Query Answering in Finitely-valued Fuzzy Description Logics}, volume = {8741}, year = {2014}, }

Theofilos Mailis and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Employing DL-LiteR-Reasoners for Fuzzy Query Answering**. In Thepchai Supnithi and Takahira Yamaguchi, editors,*Proceedings of the 4th Joint International Semantic Technology Conference (JIST2014)*. Lecture Notes in Computer Science, 2014.Abstract BibTeX Entry PDF File ©Springer-Verlag

Recently, answering of conjunctive queries has been investigated and implemented in optimized reasoner systems based on the rewriting approach for crisp DLs. In this paper we investigate how to employ such existing implementations for query answering in DL-LiteR over fuzzy ontologies. To this end we give an extended rewriting algorithm for the case of fuzzy DL-LiteR-ABoxes that employs the one for crisp DL-LiteR and investigate the limitations of this approach. We also tested the performance of our proto-type implementation FLite of this method.

@inproceedings{ MaTu-JIST-14, author = {Theofilos {Mailis} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of the 4th Joint International Semantic Technology Conference (JIST2014)}, editor = {Thepchai {Supnithi} and Takahira {Yamaguchi}}, publisher = {Lecture Notes in Computer Science}, title = {Employing DL-LiteR-Reasoners for Fuzzy Query Answering}, year = {2014}, }

Francisco Martin-Recuerda and Dirk Walther:

Abstract BibTeX Entry PDF File

**Axiom Dependency Hypergraphs for Fast Modularisation and Atomic Decomposition**. In Meghyn Bienvenu, Magdalena Ortiz, Riccardo Rosati, and Mantas Simkus, editors,*Proceedings of the 27th International Workshop on Description Logics (DL'14)*, volume 1193 of*CEUR Workshop Proceedings*, pages 299–310, 2014.Abstract BibTeX Entry PDF File

In this paper we use directed hypergraphs to represent the locality-based dependencies between the axioms of an OWL ontology. We define a notion of an axiom dependency hypergraph, where axioms are represented as nodes and dependencies between axioms as hyper- edges connecting possibly several nodes with one node. We show that a locality-based module of an ontology corresponds to a connected compo- nent in the hypergraph, and an atom of an ontology to a strongly con- nected component. Collapsing the strongly connected components into single nodes yields a condensed axiom dependency hypergraph, which contains the atomic decomposition of the ontology. To condense the ax- iom dependency hypergraph we exploit linear time graph algorithms on its graph fragment. This optimization can significantly reduce the time needed to compute the atomic decomposition of an ontology. We provide an experimental evaluation for computing the atomic decomposition of large biomedical ontologies, and for computing syntactic locality-based modules using the condensed axiom dependency hypergraph.

@inproceedings{ MaWa-DL14, author = {Francisco {Martin-Recuerda} and Dirk {Walther}}, booktitle = {Proceedings of the 27th International Workshop on Description Logics ({DL'14})}, editor = {Meghyn {Bienvenu} and Magdalena {Ortiz} and Riccardo {Rosati} and Mantas {Simkus}}, pages = {299--310}, series = {CEUR Workshop Proceedings}, title = {Axiom Dependency Hypergraphs for Fast Modularisation and Atomic Decomposition}, volume = {1193}, year = {2014}, }

Francisco Martin-Recuerda and Dirk Walther:

Abstract BibTeX Entry PDF File

**Fast Modularisation and Atomic Decomposition of Ontologies using Axiom Dependency Hypergraphs**. In Peter Mika, Tania Tudorache, Abraham Bernstein, Chris Welty, Craig Knoblock, Denny Vrandecic, Paul Groth, Natasha Noy, Krzysztof Janowicz, and Carole Goble, editors,*Proceedings of the 13th International Semantic Web Conference (ISWC 2014), Part II*, volume 8797 of*Lecture Notes in Computer Science*, pages 49–64. Springer-Verlag, 2014.Abstract BibTeX Entry PDF File

In this paper we define the notion of an axiom dependency hypergraph, which explicitly represents how axioms are included into a module by the algorithm for computing locality-based modules. A locality-based module of an ontology corresponds to a set of connected nodes in the hypergraph, and atoms of an ontology to strongly connected components. Collapsing the strongly connected components into single nodes yields a condensed hypergraph that comprises a representation of the atomic decomposition of the ontology. To speed up the condensation of the hypergraph, we first reduce its size by collapsing the strongly connected components of its graph fragment employing a linear time graph algorithm. This approach helps to significantly reduce the time needed for computing the atomic decomposition of an ontology. We provide an experimental evaluation for computing the atomic decomposition of large biomedical ontologies. We also demonstrate a significant improvement in the time needed to extract locality-based modules from an axiom dependency hypergraph and its condensed version.

@inproceedings{ MaWa-ISWC14, author = {Francisco {Martin-Recuerda} and Dirk {Walther}}, booktitle = {Proceedings of the 13th International Semantic Web Conference (ISWC 2014), Part II}, editor = {Peter {Mika} and Tania {Tudorache} and Abraham {Bernstein} and Chris {Welty} and Craig {Knoblock} and Denny {Vrandecic} and Paul {Groth} and Natasha {Noy} and Krzysztof {Janowicz} and Carole {Goble}}, pages = {49--64}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Fast Modularisation and Atomic Decomposition of Ontologies using Axiom Dependency Hypergraphs}, volume = {8797}, year = {2014}, }

Dorian Merz, Rafael Peñaloza, and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File

**Reasoning in**\(\mathcal{ALC}\)**with Fuzzy Concrete Domains**. In Carsten Lutz and Michael Thielscher, editors,*Proceedings of 37th edition of the German Conference on Artificial Intelligence (KI'14)*, volume 8736 of*Lecture Notes in Artificial Intelligence*, pages 171–182. Springer Verlag, 2014.Abstract BibTeX Entry PDF File

In the context of Description Logics (DLs) concrete domains allow to model concepts and facts by the use of concrete values and predicates between them. For reasoning in the DL ALC with general TBoxes concrete domains may cause undecidability. Under certain restrictions of the concrete domains decidability can be regained. Typically, the concrete domain predicates are crisp, which is a limitation for some applications. In this paper we investigate crisp ALC in combination with fuzzy concrete domains for general TBoxes, devise conditions for decidability, and give a tableau-based reasoning algorithm.

@inproceedings{ MePeTu-KI-14, author = {Dorian {Merz} and Rafael {Pe{\~n}aloza} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of 37th edition of the German Conference on Artificial Intelligence (KI'14)}, editor = {Carsten {Lutz} and Michael {Thielscher}}, pages = {171--182}, publisher = {Springer Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Reasoning in {$\mathcal{ALC}$} with Fuzzy Concrete Domains}, volume = {8736}, year = {2014}, }

Rafael Peñaloza:

BibTeX Entry PDF File

**Automata-based Reasoning in Fuzzy Description Logics**. In Tommaso Flaminio, Lluis Godo, Siegfried Gottlob, and Erich Peter Klement, editors,*Proceedings of the 35th Linz Seminar on Fuzzy Set Theory*, pages 106–106, 2014.BibTeX Entry PDF File

@inproceedings{ Pena-LINZ14, address = {Linz, Austria}, author = {Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 35th Linz Seminar on Fuzzy Set Theory}, editor = {Tommaso {Flaminio} and Lluis {Godo} and Siegfried {Gottlob} and Erich Peter {Klement}}, pages = {106--106}, title = {Automata-based Reasoning in Fuzzy Description Logics}, year = {2014}, }

Rafael Peñaloza, Veronika Thost, and Anni-Yasmin Turhan:

BibTeX Entry PDF File

**Certain Answers in a Rough World**. In Meghyn Bienvenu, Magdalena Ortiz, Riccardo Rosati, and Mantas Simkus, editors,*Proceedings of the 27th International Workshop on Description Logics (DL'14)*, volume 1193 of*CEUR Workshop Proceedings*, pages 709–712, 2014.BibTeX Entry PDF File

@inproceedings{ PeTT-DL14, address = {Vienna, Austria}, author = {Rafael {Pe{\~n}aloza} and Veronika {Thost} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of the 27th International Workshop on Description Logics ({DL'14})}, editor = {Meghyn {Bienvenu} and Magdalena {Ortiz} and Riccardo {Rosati} and Mantas {Simkus}}, pages = {709--712}, series = {CEUR Workshop Proceedings}, title = {Certain Answers in a Rough World}, volume = {1193}, year = {2014}, }

Rafael Peñaloza and Aparna Saisree Thuluva:

BibTeX Entry PDF File

**COBRA, a Demo**. In C. Maria Keet and Valentina Tamma, editors,*Proceedings of the 11th International Workshop on OWL: Experiences and Directions (OWLED 2014)*, volume 1265 of*CEUR Workshop Proceedings*, 2014.BibTeX Entry PDF File

@inproceedings{ PeTh-OWLED14, author = {Rafael {Pe{\~n}aloza} and Aparna Saisree {Thuluva}}, booktitle = {Proceedings of the 11th International Workshop on OWL: Experiences and Directions (OWLED 2014)}, editor = {C. Maria {Keet} and Valentina {Tamma}}, series = {CEUR Workshop Proceedings}, title = {COBRA, a Demo}, volume = {1265}, year = {2014}, }

Benjamin Zarrieß and Jens Claßen:

Abstract BibTeX Entry PDF File

**On the Decidability of Verifying LTL Properties of Golog Programs**. In*Technical Report of the AAAI 2014 Spring Symposium: Knowledge Representation and Reasoning in Robotics (KRR14)*. Palo Alto, California, USA, AAAI Press, 2014.Abstract BibTeX Entry PDF File

The high-level action programming language Golog is a useful means for modeling the behavior of autonomous agents such as mobile robots. It relies on a representation given in terms of a logic-based action theory in the Situation Calculus (SC). To guarantee that the possibly non-terminating execution of a Golog program leads to the desired behavior of the agent, it is desirable to (automatically) verify that it satisfies certain requirements given in terms of temporal formulas. However, due to the high (first-order) expressiveness of the Golog language, the verification problem is in general undecidable. In this paper we show that for a fragment of the Golog language defined on top of the decidable logic C^{2}, the verification problem for linear time temporal properties becomes decidable, which extends earlier results to a more expressive fragment of the input formalism. Moreover, we justify the involved restrictions on program constructs and action theory by showing that relaxing any of these restrictions instantly renders the verification problem undecidable again.

@inproceedings{ ZaCla-KRR14, address = {Palo Alto, California, USA}, author = {Benjamin {Zarrie{\ss}} and Jens {Cla{\ss}en}}, booktitle = {Technical Report of the AAAI 2014 Spring Symposium: Knowledge Representation and Reasoning in Robotics (KRR{\textquoteright}14)}, publisher = {AAAI Press}, title = {On the Decidability of Verifying LTL Properties of Golog Programs}, year = {2014}, }

Benjamin Zarrieß and Jens Claßen:

Abstract BibTeX Entry

**Verifying CTL* Properties of Golog Programs over Local-Effect Actions**. In*Proceedings of the Twenty-First European Conference on Artificial Intelligence (ECAI 2014)*, 2014.Abstract BibTeX Entry

Golog is a high-level action programming language for controlling autonomous agents such as mobile robots. It is defined on top of a logic-based action theory expressed in the Situation Calculus. Before a program is deployed onto an actual robot and executed in the physical world, it is desirable, if not crucial, to verify that it meets certain requirements (typically expressed through temporal formulas) and thus indeed exhibits the desired behaviour. However, due to the high (first-order) expressiveness of the language, the corresponding verification problem is in general undecidable. In this paper, we extend earlier results to identify a large, non-trivial fragment of the formalism where verification is decidable. In particular, we consider properties expressed in a first-order variant of the branching-time temporal logic CTL*. Decidability is obtained by (1) resorting to the decidable first-order fragment C^{2}as underlying base logic, (2) using a fragment of Golog with ground actions only, and (3) requiring the action theory to only admit local effects.

@inproceedings{ ZC-ECAI14, address = {Prague, Czech Republic}, author = {Benjamin {Zarrie{\ss}} and Jens {Cla{\ss}en}}, booktitle = {Proceedings of the Twenty-First European Conference on Artificial Intelligence (ECAI 2014)}, title = {Verifying CTL* Properties of Golog Programs over Local-Effect Actions}, year = {2014}, }

## 2013

Ignasi Abío, Robert Nieuwenhuis, Albert Oliveras, and Enric Rodríguez-Carbonell:

BibTeX Entry

**A Parametric Approach for Smaller and Better Encodings of Cardinality Constraints**. In*19th International Conference on Principles and Practice of Constraint Programming*,*CP'13*, 2013.BibTeX Entry

@inproceedings{ parametricCardinalityConstraint, author = {Ignasi {Ab{\'\i}o} and Robert {Nieuwenhuis} and Albert {Oliveras} and Enric {Rodr\'{\i}guez-Carbonell}}, booktitle = {19th International Conference on Principles and Practice of Constraint Programming}, series = {CP'13}, title = {{A Parametric Approach for Smaller and Better Encodings of Cardinality Constraints}}, year = {2013}, }

Ignasi Abío, Robert Nieuwenhuis, Albert Oliveras, Enric Rodríguez-Carbonell, and Peter J. Stuckey:

BibTeX Entry

**To Encode or to Propagate? The Best Choice for Each Constraint in SAT**. In*19th International Conference on Principles and Practice of Constraint Programming*,*CP'13*, 2013.BibTeX Entry

@inproceedings{ encodeOrPropagate, author = {Ignasi {Ab{\'\i}o} and Robert {Nieuwenhuis} and Albert {Oliveras} and Enric {Rodr\'{\i}guez-Carbonell} and Peter J. {Stuckey}}, booktitle = {19th International Conference on Principles and Practice of Constraint Programming}, series = {CP'13}, title = {{To Encode or to Propagate? The Best Choice for Each Constraint in SAT}}, year = {2013}, }

Mario Alviano and Rafael Peñaloza:

Abstract BibTeX Entry PDF File DOI ©Cambridge University Press

**Fuzzy Answer Sets Approximations**.*Theory and Practice of Logic Programming*, 13(4–5):753–767, 2013.Abstract BibTeX Entry PDF File DOI ©Cambridge University Press

Fuzzy answer set programming (FASP) is a recent formalism for knowledge representation that enriches the declarativity of answer set programming by allowing propositions to be graded. To now, no implementations of FASP solvers are available and all current proposals are based on compilations of logic programs into different paradigms, like mixed integer programs or bilevel programs. These approaches introduce many auxiliary variables which might affect the performance of a solver negatively. To limit this downside, operators for approximating fuzzy answer sets can be introduced: Given a FASP program, these operators compute lower and upper bounds for all atoms in the program such that all answer sets are between these bounds. This paper analyzes several operators of this kind which are based on linear programming, fuzzy unfounded sets and source pointers. Furthermore, the paper reports on a prototypical implementation, also describing strategies for avoiding computations of these operators when they are guaranteed to not improve current bounds. The operators and their implementation can be used to obtain more constrained mixed integer or bilevel programs, or even for providing a basis for implementing a native FASP solver. Interestingly, the semantics of relevant classes of programs with unique answer sets, like positive programs and programs with stratified negation, can be already computed by the prototype without the need for an external tool.

@article{ AlPe-TPLP13, author = {Mario {Alviano} and Rafael {Pe{\~n}aloza}}, doi = {http://dx.doi.org/10.1017/S1471068413000471}, journal = {Theory and Practice of Logic Programming}, number = {4--5}, pages = {753--767}, publisher = {Cambridge University Press}, title = {Fuzzy Answer Sets Approximations}, volume = {13}, year = {2013}, }

Jamal Atif, Isabelle Bloch, Felix Distel, and Céline Hudelot:

Abstract BibTeX Entry

**A fuzzy extension of explanatory relations based on mathematical morphology**. In Gabriella Pasi and Javier Montero, editors,*Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2013)*, 2013.Abstract BibTeX Entry

In this paper, we build upon previous work defining explanatory relations based on mathematical morphology operators on logical formulas in propositional logics. We propose to extend such relations to the case where the set of models of a formula is fuzzy, as a first step towards morphological fuzzy abduction. The membership degrees may represent degrees of satisfaction of the formula, preferences, vague information for instance related to a partially observed situation, imprecise knowledge, etc. The proposed explanatory relations are based on successive fuzzy erosions of the set of models, conditionally to a theory, while the maximum membership degree in the results remains higher than a threshold. Two explanatory relations are proposed, one based on the erosion of the conjunction of the theory and the formula to be explained, and the other based on the erosion of the theory, while remaining consistent with the formula at least to some degree. Extensions of the rationality postulates introduced by Pino-Perez and Uzcategui are proposed. As in the classical crisp case, we show that the second explanatory relation exhibits stronger properties than the first one.

@inproceedings{ AtEtAl-EUSFLAT13, author = {Jamal {Atif} and Isabelle {Bloch} and Felix {Distel} and C\'{e}line {Hudelot}}, booktitle = {Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology {(EUSFLAT-2013)}}, editor = {Gabriella {Pasi} and Javier {Montero}}, title = {A fuzzy extension of explanatory relations based on mathematical morphology}, year = {2013}, }

Jamal Atif, Isabelle Bloch, Felix Distel, and Céline Hudelot:

Abstract BibTeX Entry PDF File ©Springer-Verlag (The final publication is available at link.springer.com)

**Mathematical Morphology Operators over Concept Lattices**. In Peggy Cellier, Felix Distel, and Bernhard Ganter, editors,*Proceedings of the 11th International Conference on Formal Concept Analysis (ICFCA'13)*, volume 7880 of*Lecture Notes in Computer Science*, pages 28–43. Springer-Verlag, 2013.Abstract BibTeX Entry PDF File ©Springer-Verlag (The final publication is available at link.springer.com)

Although mathematical morphology and formal concept analysis are two lattice-based data analysis theories, they are still developed in two disconnected research communities. The aim of this paper is to contribute to fill this gap, beyond the classical relationship between the Galois connections defined by the derivation operators and the adjunctions underlying the algebraic mathematical morphology framework. In particular we define mathematical morphology operators over concept lattices, based on distances, valuations, or neighborhood relations in concept lattices. Their properties are also discussed. These operators provide new tools for reasoning over concept lattices.

@inproceedings{ AtEtAl-ICFCA13, author = {Jamal {Atif} and Isabelle {Bloch} and Felix {Distel} and C\'{e}line {Hudelot}}, booktitle = {Proceedings of the 11th International Conference on Formal Concept Analysis {(ICFCA'13)}}, editor = {Peggy {Cellier} and Felix {Distel} and Bernhard {Ganter}}, pages = {28--43}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Mathematical Morphology Operators over Concept Lattices}, volume = {7880}, year = {2013}, }

Franz Baader, Stefan Borgwardt, and Marcel Lippmann:

Abstract BibTeX Entry PDF File (The final publication is available at link.springer.com)

**Temporalizing Ontology-Based Data Access**. In Maria Paola Bonacina, editor,*Proceedings of the 24th International Conference on Automated Deduction (CADE-24)*, volume 7898 of*Lecture Notes in Artificial Intelligence*, pages 330–344. Lake Placid, NY, USA, Springer-Verlag, 2013.Abstract BibTeX Entry PDF File (The final publication is available at link.springer.com)

Ontology-based data access (OBDA) generalizes query answering in databases towards deduction since (i) the fact base is not assumed to contain complete knowledge (i.e., there is no closed world assumption), and (ii) the interpretation of the predicates occurring in the queries is constrained by axioms of an ontology. OBDA has been investigated in detail for the case where the ontology is expressed by an appropriate Description Logic (DL) and the queries are conjunctive queries. Motivated by situation awareness applications, we investigate an extension of OBDA to the temporal case. As query language we consider an extension of the well-known propositional temporal logic LTL where conjunctive queries can occur in place of propositional variables, and as ontology language we use the prototypical expressive DL ALC. For the resulting instance of temporalized OBDA, we investigate both data complexity and combined complexity of the query entailment problem.

@inproceedings{ BaBL-CADE13, address = {Lake Placid, NY, USA}, author = {Franz {Baader} and Stefan {Borgwardt} and Marcel {Lippmann}}, booktitle = {Proceedings of the 24th International Conference on Automated Deduction (CADE-24)}, editor = {Maria Paola {Bonacina}}, pages = {330--344}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Temporalizing Ontology-Based Data Access}, volume = {7898}, year = {2013}, }

Franz Baader, Oliver Fernández Gil, and Barbara Morawska:

Abstract BibTeX Entry PDF File

**Hybrid Unification in the Description Logic**\(\mathcal{EL}\). In Barbara Morawska and Konstantin Korovin, editors,*Proceedings of the 27th International Workshop on Unification (UNIF'13)*, 2013.Abstract BibTeX Entry PDF File

Unification in Description Logics (DLs) has been proposed as an inference service that can, for example, be used to detect redundancies in ontologies. For the DL EL, which is used to define several large biomedical ontologies, unification is NP-complete. However, the unification algorithms for EL developed until recently could not deal with ontologies containing general concept inclusions (GCIs). In a series of recent papers we have made some progress towards addressing this problem, but the ontologies the developed unification algorithms can deal with need to satisfy a certain cycle restriction. In the present paper, we follow a different approach. Instead of restricting the input ontologies, we generalize the notion of unifiers to so-called hybrid unifiers. Whereas classical unifiers can be viewed as acyclic TBoxes, hybrid unifiers are cyclic TBoxes, which are interpreted together with the ontology of the input using a hybrid semantics that combines fixpoint and descriptive semantics. We show that hybrid unification in EL is NP-complete.

@inproceedings{ BaBM-UNIF13, address = {Eindhoven, The Netherlands}, author = {Franz {Baader} and Oliver {Fern\'andez Gil} and Barbara {Morawska}}, booktitle = {Proceedings of the 27th International Workshop on Unification (UNIF'13)}, editor = {Barbara {Morawska} and Konstantin {Korovin}}, title = {Hybrid Unification in the Description Logic {$\mathcal{EL}$}}, year = {2013}, }

Franz Baader, Oliver Fernández Gil, and Barbara Morawska:

Abstract BibTeX Entry PDF File

**Hybrid Unification in the Description Logic**\(\mathcal{EL}\). In Pascal Fontaine, Christophe Ringeissen, and Renate A. Schmidt, editors,*Proceedings of the 9th International Symposium on Frontiers of Combining Systems (FroCoS 2013)*, volume 8152 of*Lecture Notes in Computer Science*, pages 295–310. Nancy, France, Springer-Verlag, September 2013.Abstract BibTeX Entry PDF File

Unification in Description Logics (DLs) has been proposed as an inference service that can, for example, be used to detect redundancies in ontologies. For the DL EL, which is used to define several large biomedical ontologies, unification is NP-complete. However, the unification algorithms for EL developed until recently could not deal with ontologies containing general concept inclusions (GCIs). In a series of recent papers we have made some progress towards addressing this problem, but the ontologies the developed unification algorithms can deal with need to satisfy a certain cycle restriction. In the present paper, we follow a different approach. Instead of restricting the input ontologies, we generalize the notion of unifiers to so-called hybrid unifiers. Whereas classical unifiers can be viewed as acyclic TBoxes, hybrid unifiers are cyclic TBoxes, which are interpreted together with the ontology of the input using a hybrid semantics that combines fixpoint and descriptive semantics. We show that hybrid unification in EL is NP-complete and introduce a goal-oriented algorithm for computing hybrid unifiers.

@inproceedings{ BaFM-FroCoS13, address = {Nancy, France}, author = {Franz {Baader} and Oliver {Fern\'andez Gil} and Barbara {Morawska}}, booktitle = {Proceedings of the 9th International Symposium on Frontiers of Combining Systems ({FroCoS 2013})}, editor = {Pascal {Fontaine} and Christophe {Ringeissen} and Renate A. {Schmidt}}, month = {September}, pages = {295--310}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Hybrid Unification in the Description Logic {$\mathcal{EL}$}}, volume = {8152}, year = {2013}, }

Franz Baader, Oliver Fernández Gil, and Barbara Morawska:

Abstract BibTeX Entry PDF File

**Hybrid**\(\mathcal{EL}\)**-Unification is NP-Complete**. In Thomas Eiter, Birte Glimm, Yevgeny Kazakov, and Markus Krötzsch, editors,*Proceedings of the 26th International Workshop on Description Logics (DL-2013)*, volume 1014 of*CEUR Workshop Proceedings*, pages 29–40, July 2013.Abstract BibTeX Entry PDF File

@inproceedings{ BaFM-DL13, author = {Franz {Baader} and Oliver {Fern\'andez Gil} and Barbara {Morawska}}, booktitle = {Proceedings of the 26th International Workshop on Description Logics ({DL-2013})}, editor = {Thomas {Eiter} and Birte {Glimm} and Yevgeny {Kazakov} and Markus {Kr{\"o}tzsch}}, month = {July}, pages = {29--40}, series = {CEUR Workshop Proceedings}, title = {Hybrid {$\mathcal{EL}$}-Unification is NP-Complete}, venue = {Ulm, Germany}, volume = {1014}, year = {2013}, }

Franz Baader and Alexander Okhotin:

Abstract BibTeX Entry PDF File

**On Language Equations with One-sided Concatenation**.*Fundamenta Informaticae*, 126(1):1–35, 2013.Abstract BibTeX Entry PDF File

Language equations are equations where both the constants occurring in the equations and the solutions are formal languages. They have first been introduced in formal language theory, but are now also considered in other areas of computer science. In the present paper, we restrict the attention to language equations with one-sided concatenation, but in contrast to previous work on these equations, we allow not just union but all Boolean operations to be used when formulating them. In addition, we are not just interested in deciding solvability of such equations, but also in deciding other properties of the set of solutions, like its cardinality (finite, infinite, uncountable) and whether it contains least/greatest solutions. We show that all these decision problems are ExpTime-complete.

@article{ BaOk-FI13, author = {Franz {Baader} and Alexander {Okhotin}}, journal = {Fundamenta Informaticae}, number = {1}, pages = {1--35}, title = {On Language Equations with One-sided Concatenation}, volume = {126}, year = {2013}, }

Franz Baader and Benjamin Zarrieß:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Verification of Golog Programs over Description Logic Actions**. In Pascal Fontaine, Christophe Ringeissen, and Renate A. Schmidt, editors,*Proceedings of the 9th International Symposium on Frontiers of Combining Systems (FroCoS 2013)*, volume 8152 of*Lecture Notes in Computer Science*, pages 181–196. Nancy, France, Springer-Verlag, September 2013.Abstract BibTeX Entry PDF File ©Springer-Verlag

High-level action programming languages such as Golog have successfully been used to model the behavior of autonomous agents. In addition to a logic-based action formalism for describing the environment and the effects of basic actions, they enable the construction of complex actions using typical programming language constructs. To ensure that the execution of such complex actions leads to the desired behavior of the agent, one needs to specify the required properties in a formal way, and then verify that these requirements are met by any execution of the program. Due to the expressiveness of the action formalism underlying Golog (Situation Calculus), the verification problem for Golog programs is in general undecidable. Action formalisms based on Description Logic (DL) try to achieve decidability of inference problems such as the projection problem by restricting the expressiveness of the underlying base logic. However, until now these formalisms have not been used within Golog programs. In the present paper, we introduce a variant of Golog where basic actions are defined using such a DL-based formalism, and show that the verification problem for such programs is decidable. This improves on our previous work on verifying properties of infinite sequences of DL actions in that it considers (finite and infinite) sequences of DL actions that correspond to (terminating and non-terminating) runs of a Golog program rather than just infinite sequences accepted by a Büchi automaton abstracting the program.

@inproceedings{ BaZa-FroCoS13, address = {Nancy, France}, author = {Franz {Baader} and Benjamin {Zarrie{\ss}}}, booktitle = {Proceedings of the 9th International Symposium on Frontiers of Combining Systems ({FroCoS 2013})}, editor = {Pascal {Fontaine} and Christophe {Ringeissen} and Renate A. {Schmidt}}, month = {September}, pages = {181--196}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Verification of Golog Programs over Description Logic Actions}, volume = {8152}, year = {2013}, }

Daniel Borchmann:

Abstract BibTeX Entry

**Axiomatizing**\(\mathcal{E\!L}^{\bot}_{\mathrm{gfp}}\)**-General Concept Inclusions in the Presence of Untrusted Individuals**. In*Proceedings of the 26th International Workshop on Description Logics (DL-2013)*, volume 1014 of*CEUR Workshop Proceedings*, pages 65–79. CEUR-WS.org, July 2013.Abstract BibTeX Entry

To extract terminological knowledge from data, Baader and Distel have proposed an effective method that allows for the extraction of a base of all valid general concept inclusions of a given finite interpretation. In previous works, to be able to handle small amounts of errors in our data, we have extended this approach to also extract general concept inclusions which are ``almost valid'' in the interpretation. This has been done by demanding that general concept inclusions which are ``almost valid'' are those having only an allowed percentage of counterexamples in the interpretation. In this work, we shall further extend our previous work to allow the interpretation to contain both trusted and untrusted individuals, i.e. individuals from which we know and do not know that they are correct, respectively. The problem we then want to solve is to find a compact representation of all terminological knowledge that is valid for all trusted individuals and is almost valid for all others.

@inproceedings{ Borc-DL13, author = {Daniel {Borchmann}}, booktitle = {Proceedings of the 26th International Workshop on Description Logics ({DL-2013})}, month = {July}, pages = {65--79}, publisher = {CEUR-WS.org}, series = {CEUR Workshop Proceedings}, title = {Axiomatizing $\mathcal{E\!L}^{\bot}_{\mathrm{gfp}}$-General Concept Inclusions in the Presence of Untrusted Individuals}, venue = {Ulm, Germany}, volume = {1014}, year = {2013}, }

Daniel Borchmann:

Abstract BibTeX Entry

**Axiomatizing**\(\mathcal{E}\!\mathcal{L}^{\bot}\)**-Expressible Terminological Knowledge from Erroneous Data**. In*Proceedings of the Seventh International Conference on Knowledge Capture*, pages 1–8. ACM, 2013.Abstract BibTeX Entry

In a recent approach, Baader and Distel proposed an algorithm to axiomatize all terminological knowledge that is valid in a given data set and is expressible in the description logic \(\mathcal{EL}^{\bot}\). This approach is based on the mathematical theory of formal concept analysis. However, this algorithm requires the initial data set to be free of errors, an assumption that normally cannot be made for real-world data. In this work, we propose a first extension of the work of Baader and Distel to handle errors in the data set. The approach we present here is based on the notion of confidence, as it has been developed and used in the area of data mining.

@inproceedings{ Borc-KCAP13, author = {Daniel {Borchmann}}, booktitle = {Proceedings of the Seventh International Conference on Knowledge Capture}, pages = {1--8}, publisher = {ACM}, title = {Axiomatizing $\mathcal{E}\!\mathcal{L}^{\bot}$-Expressible Terminological Knowledge from Erroneous Data}, venue = {Banff, Canada}, year = {2013}, }

Daniel Borchmann:

Abstract BibTeX Entry PDF File

**Towards an Error-Tolerant Construction of**\(\mathcal{EL}^{\bot}\)**-Ontologies from Data Using Formal Concept Analysis**. In Peggy Cellier, Felix Distel, and Bernhard Ganter, editors,*Formal Concept Analysis, 11th International Conference, ICFCA 2013, Dresden, Germany, May 21-24, 2013. Proceedings*, volume 7880 of*Lecture Notes in Computer Science*, pages 60–75. Springer, 2013.Abstract BibTeX Entry PDF File

In the work of Baader and Distel, a method has been proposed to axiomatize all general concept inclusions (GCIs) expressible in the description logic \(\mathcal{EL}^{\bot}\) and valid in a given interpretation \(\mathcal{I}\). This provides us with an effective method to learn \(\mathcal{EL}^{\bot}-ontologies from interpretations. In this work, we want to extend this approach in the direction of handling errors, which might be present in the data-set. We shall do so by not only considering valid GCIs but also those whose confidence is above a given threshold \)c\(. We shall give the necessary definitions and show some first results on the axiomatization of all GCIs with confidence at least \)c$. Finally, we shall provide some experimental evidence based on real-world data that supports our approach.

@inproceedings{ Borc-ICFCA13, author = {Daniel {Borchmann}}, booktitle = {Formal Concept Analysis, 11th International Conference, ICFCA 2013, Dresden, Germany, May 21-24, 2013. Proceedings}, editor = {Peggy {Cellier} and Felix {Distel} and Bernhard {Ganter}}, pages = {60--75}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Towards an Error-Tolerant Construction of $\mathcal{EL}^{\bot}$ -Ontologies from Data Using Formal Concept Analysis}, volume = {7880}, year = {2013}, }

Stefan Borgwardt, Marcel Lippmann, and Veronika Thost:

Abstract BibTeX Entry PDF File (The final publication is available at link.springer.com)

**Temporal Query Answering in the Description Logic DL-Lite**. In Pascal Fontaine, Christophe Ringeissen, and Renate A. Schmidt, editors,*Proceedings of the 9th International Symposium on Frontiers of Combining Systems (FroCoS 2013)*, volume 8152 of*Lecture Notes in Computer Science*, pages 165–180. Nancy, France, Springer-Verlag, 2013.Abstract BibTeX Entry PDF File (The final publication is available at link.springer.com)

Ontology-based data access (OBDA) generalizes query answering in relational databases. It allows to query a database by using the language of an ontology, abstracting from the actual relations of the database. For ontologies formulated in Description Logics of the DL-Lite family, OBDA can be realized by rewriting the query into a classical first-order query, e.g. an SQL query, by compiling the information of the ontology into the query. The query is then answered using classical database techniques. In this paper, we consider a temporal version of OBDA. We propose a temporal query language that combines a linear temporal logic with queries over DL-Lite_{c}ore-ontologies. This language is well-suited to express temporal properties of dynamical systems and is useful in context-aware applications that need to detect specific situations. Using a first-order rewriting approach, we transform our temporal queries into queries over a temporal database. We then present three approaches to answering the resulting queries, all having different advantages and drawbacks.

@inproceedings{ BoLiTh-FroCoS13, address = {Nancy, France}, author = {Stefan {Borgwardt} and Marcel {Lippmann} and Veronika {Thost}}, booktitle = {Proceedings of the 9th International Symposium on Frontiers of Combining Systems ({FroCoS 2013})}, editor = {Pascal {Fontaine} and Christophe {Ringeissen} and Renate A. {Schmidt}}, pages = {165--180}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Temporal Query Answering in the Description Logic {\textit{DL-Lite}}}, volume = {8152}, year = {2013}, }

Stefan Borgwardt, Marcel Lippmann, and Veronika Thost:

BibTeX Entry PDF File

**Temporal Query Answering in DL-Lite**. In Thomas Eiter, Birte Glimm, Yevgeny Kazakov, and Markus Krötzsch, editors,*Proceedings of the 26th International Workshop on Description Logics (DL-2013)*, volume 1014 of*CEUR Workshop Proceedings*. Ulm, Germany, CEUR-WS.org, July 2013.BibTeX Entry PDF File

@inproceedings{ BoLiTh-DL13, address = {Ulm, Germany}, author = {Stefan {Borgwardt} and Marcel {Lippmann} and Veronika {Thost}}, booktitle = {Proceedings of the 26th International Workshop on Description Logics ({DL-2013})}, editor = {Thomas {Eiter} and Birte {Glimm} and Yevgeny {Kazakov} and Markus {Kr{\"o}tzsch}}, month = {July}, publisher = {CEUR-WS.org}, series = {CEUR Workshop Proceedings}, title = {Temporal Query Answering in {\textit{DL-Lite}}}, volume = {1014}, year = {2013}, }

Stefan Borgwardt and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**About Subsumption in Fuzzy**\(\mathcal{EL}\). In Thomas Eiter, Birte Glimm, Yevgeny Kazakov, and Markus Krötzsch, editors,*Proceedings of the 2013 International Workshop on Description Logics (DL'13)*, volume 1014 of*CEUR-WS*, pages 526–538, 2013.Abstract BibTeX Entry PDF File

The Description Logic EL is used to formulate several large biomedical ontologies. Fuzzy extensions of EL can express the vagueness inherent in many biomedical concepts. We consider fuzzy EL with semantics based on general t-norms, and study the reasoning problems of deciding positive subsumption and 1-subsumption and computing the best subsumption degree.

@inproceedings{ BoPe-DL13, address = {Ulm, Germany}, author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 2013 International Workshop on Description Logics ({DL'13})}, editor = {Thomas {Eiter} and Birte {Glimm} and Yevgeny {Kazakov} and Markus {Kr{\"o}tzsch}}, pages = {526--538}, series = {CEUR-WS}, title = {About Subsumption in Fuzzy $\mathcal{EL}$}, volume = {1014}, year = {2013}, }

Stefan Borgwardt and Rafael Peñaloza:

Abstract BibTeX Entry PDF File ©IJCAI

**Positive Subsumption in Fuzzy**\(\mathcal{EL}\)**with General t-norms**. In Francesca Rossi, editor,*Proceedings of the 23rd International Joint Conference on Artificial Intelligence (IJCAI'13)*, pages 789–795. Beijing, China, AAAI Press, 2013.Abstract BibTeX Entry PDF File ©IJCAI

The Description Logic EL is used to formulate several large biomedical ontologies. Fuzzy extensions of EL can express the vagueness inherent in many biomedical concepts. We study the reasoning problem of deciding positive subsumption in fuzzy EL with semantics based on general t-norms. We show that the complexity of this problem depends on the specific t-norm chosen. More precisely, if the t-norm has zero divisors, then the problem is co-NP-hard; otherwise, it can be decided in polynomial time. We also show that the best subsumption degree cannot be computed in polynomial time if the t-norm contains the Łukasiewicz t-norm.

@inproceedings{ BoPe-IJCAI13, address = {Beijing, China}, author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 23rd International Joint Conference on Artificial Intelligence (IJCAI'13)}, editor = {Francesca {Rossi}}, pages = {789--795}, publisher = {AAAI Press}, title = {Positive Subsumption in Fuzzy $\mathcal{EL}$ with General t-norms}, year = {2013}, }

Stefan Borgwardt and Rafael Peñaloza:

Abstract BibTeX Entry PDF File ©Springer-Verlag (The final publication is available at link.springer.com)

**The Complexity of Lattice-Based Fuzzy Description Logics**.*Journal on Data Semantics*, 2(1):1–19, 2013.Abstract BibTeX Entry PDF File ©Springer-Verlag (The final publication is available at link.springer.com)

We study the complexity of reasoning in fuzzy description logics with semantics based on finite residuated lattices. For the logic SHI, we show that deciding satisfiability and subsumption of concepts, with or without a TBox, are ExpTime-complete problems. In ALCHI and a variant of SI, these decision problems become PSpace-complete when restricted to acyclic TBoxes. This matches the known complexity bounds for reasoning in crisp description logics between ALC and SHI.

@article{ BoPe-JoDS12, author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}}, journal = {Journal on Data Semantics}, number = {1}, pages = {1--19}, title = {The Complexity of Lattice-Based Fuzzy Description Logics}, volume = {2}, year = {2013}, }

Waltenegus Dargie, Eldora, Julian Mendez, Christoph Möbius, Kateryna Rybina, Veronika Thost, and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File ©IEEE Press

**Situation Recognition for Service Management Systems Using OWL 2 Reasoners**. In*Proceedings of the 10th IEEE Workshop on Context Modeling and Reasoning 2013*, pages 31–36. San Diego, California, IEEE Computer Society, March 2013.Abstract BibTeX Entry PDF File ©IEEE Press

For service management systems the early recognition of situations that necessitate a rebinding or a migration of services is an important task. To describe these situations on differing levels of detail and to allow their recognition even if only incomplete information is available, we employ the ontology language OWL 2 and the reasoning services defined for it. In this paper we provide a case study on the performance of state of the art OWL 2 reasoning systems for answering class queries and conjunctive queries modeling the relevant situations for service rebinding or migration in the differing OWL 2 profiles.

@inproceedings{ DelMe13, address = {San Diego, California}, author = {Waltenegus {Dargie} and {Eldora} and Julian {Mendez} and Christoph {M{\"o}bius} and Kateryna {Rybina} and Veronika {Thost} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of the 10th IEEE Workshop on Context Modeling and Reasoning 2013}, month = {March}, pages = {31--36}, publisher = {IEEE Computer Society}, title = {Situation Recognition for Service Management Systems Using OWL 2 Reasoners}, year = {2013}, }

Felix Distel and Yue Ma:

Abstract BibTeX Entry

**A hybrid approach for learning SNOMED CT definitions from text**. In*Proceedings of the 2013 International Workshop on Description Logics (DL'13)*,*CEUR-WS*, 2013.Abstract BibTeX Entry

In recent years approaches for extracting formal definitions from natural language have been developed. These approaches typically use methods from natural language processing, such as relation extraction or syntax parsing. They make only limited use of description logic reasoning. We propose a hybrid approach combining natural language processing methods and description logic reasoning. In a first step description candidates are obtained using a natural language processing method. Description logic reasoning is used in a post-processing step to select good quality candidate definitions. We identify the corresponding reasoning problem and examine its complexity.

@inproceedings{ DiMa-DL13, address = {Ulm, Germany}, author = {Felix {Distel} and Yue {Ma}}, booktitle = {Proceedings of the 2013 International Workshop on Description Logics ({DL'13})}, series = {CEUR-WS}, title = {A hybrid approach for learning SNOMED CT definitions from text}, year = {2013}, }

Andreas Ecke, Michel Ludwig, and Dirk Walther:

Abstract BibTeX Entry PDF File

**The Concept Difference for**\(\mathcal{EL}\)**-Terminologies using Hypergraphs**. In*Proceedings of the International workshop on (Document) Changes: modeling, detection, storage and visualization (DChanges 2013)*, volume 1008 of*CEUR-WS*, 2013.Abstract BibTeX Entry PDF File

Ontologies are used to represent and share knowledge. Numerous ontologies have been developed so far, especially in knowledge intensive areas such as the biomedical domain. As the size of ontologies increases, their continued development and maintenance is becoming more challenging as well. Detecting and representing semantic differences between versions of ontologies is an important task for which automated tool support is needed. In this paper we investigate the logical difference problem using a hypergraph representation of EL-terminologies. We focus solely on the concept difference wrt. a signature. For computing this difference it suffices to check the existence of simulations between hypergraphs whereas previous approaches required a combination of different methods.

@inproceedings{ EcLuWa-DChanges2013, author = {Andreas {Ecke} and Michel {Ludwig} and Dirk {Walther}}, booktitle = {Proceedings of the International workshop on (Document) Changes: modeling, detection, storage and visualization ({DChanges 2013})}, series = {CEUR-WS}, title = {The Concept Difference for $\mathcal{EL}$-Terminologies using Hypergraphs}, venue = {Florence, Italy}, volume = {1008}, year = {2013}, }

Andreas Ecke, Rafael Peñaloza, and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File PDF File (Extended Technical Report)

**Computing Role-depth Bounded Generalizations in the Description Logic**\(\mathcal{ELOR}\). In Ingo J. Timm and Matthias Thimm, editors,*Proceedings of the 36th German Conference on Artificial Intelligence (KI 2013)*, volume 8077 of*Lecture Notes in Artificial Intelligence*, pages 49–60. Koblenz, Germany, Springer-Verlag, 2013.Abstract BibTeX Entry PDF File PDF File (Extended Technical Report)

Description Logics (DLs) are a family of knowledge representation formalisms, that provides the theoretical basis for the standard web ontology language OWL. Generalization services like the least common subsumer (lcs) and the most specific concept (msc) are the basis of several ontology design methods, and form the core of similarity measures. For the DL ELOR, which covers most of the OWL 2 EL profile, the lcs and msc need not exist in general, but they always exist if restricted to a given role-depth. We present algorithms that compute these role-depth bounded generalizations. Our method is easy to implement, as it is based on the polynomial-time completion algorithm for ELOR.

@inproceedings{ EcPeTu-KI-13, address = {Koblenz, Germany}, author = {Andreas {Ecke} and Rafael {Pe{\~n}aloza} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of the 36th German Conference on Artificial Intelligence (KI 2013)}, editor = {Ingo J. {Timm} and Matthias {Thimm}}, pages = {49--60}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Computing Role-depth Bounded Generalizations in the Description Logic {$\mathcal{ELOR}$}}, volume = {8077}, year = {2013}, }

Andreas Ecke, Rafael Peñaloza, and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File

**Role-depth bounded Least Common Subsumer in Prob-**\(\mathcal{EL}\)**with Nominals**. In Thomas Eiter, Birte Glimm, Yevgeny Kazakov, and Markus Krötzsch, editors,*Proceedings of the 26th International Workshop on Description Logics (DL-2013)*, volume 1014 of*CEUR-WS*, pages 670–688, July 2013.Abstract BibTeX Entry PDF File

Completion-based algorithms can be employed for computing the least common subsumer of two concepts up to a given role-depth, in extensions of the lightweight DL EL. This approach has been applied also to the probabilistic DL Prob-EL, which is variant of EL with subjective probabilities. In this paper we extend the completion-based lcs-computation algorithm to nominals, yielding a procedure for the DL Prob-ELO⁰¹.

@inproceedings{ EcPeTu-DL-13, address = {Ulm, Germany}, author = {Andreas {Ecke} and Rafael {Pe{\~n}aloza} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of the 26th International Workshop on Description Logics ({DL-2013})}, editor = {Thomas {Eiter} and Birte {Glimm} and Yevgeny {Kazakov} and Markus {Kr{\"o}tzsch}}, month = {July}, pages = {670--688}, series = {CEUR-WS}, title = {Role-depth bounded Least Common Subsumer in Prob-{$\mathcal{EL}$} with Nominals}, volume = {1014}, year = {2013}, }

Andreas Ecke, Rafael Peñaloza, and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File

**Towards Instance Query Answering for Concepts Relaxed by Similarity Measures**. In*Workshop on Weighted Logics for AI (in conjunction with IJCAI'13)*, 2013.Abstract BibTeX Entry PDF File

In Description Logics (DL) knowledge bases (KBs) information is typically captured by crisp concept descriptions. However, for many practical applications querying the KB by crisp concepts is too restrictive. A controlled way of gradually relaxing a query concept can be achieved by the use of similarity measures. To this end we formalize the task of instance query answering for crisp DL KBs using concepts relaxed by similarity measures. We identify relevant properties for the similarity measure and give first results on a computation algorithm.

@inproceedings{ EcPeTu-WL4AI-13, address = {Beijing, China}, author = {Andreas {Ecke} and Rafael {Pe{\~n}aloza} and Anni-Yasmin {Turhan}}, booktitle = {Workshop on {W}eighted {L}ogics for {AI} (in conjunction with IJCAI'13)}, title = {Towards Instance Query Answering for Concepts Relaxed by Similarity Measures}, year = {2013}, }

Sebastian Goetz, Julian Mendez, Veronika Thost, and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File

**OWL 2 Reasoning To Detect Energy-Efficient Software Variants From Context**. In Kavitha Srinivas and Simon Jupp, editors,*Proceedings of the 10th OWL: Experiences and Directions Workshop (OWLED 2013)*, May 2013.Abstract BibTeX Entry PDF File

Runtime variability management of component-based software systems allows to consider the current context of a system for system configuration to achieve energy-efficiency. For optimizing the system configuration at runtime, the early recognition of situations apt to reconfiguration is an important task. To describe these situations on differing levels of detail and to allow their recognition even if only incomplete information is available, we employ the ontology language OWL 2 and the reasoning services defined for it. In this paper, we show that the relevant situations for optimizing the current system configuration can be modeled in the different OWL 2 profiles. We further provide a case study on the performance of state of the art OWL 2 reasoning systems for answering concept queries and conjunctive queries modeling the situations to be detected.

@inproceedings{ GoMeT13, address = {Montpellier, France}, author = {Sebastian {Goetz} and Julian {Mendez} and Veronika {Thost} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of the 10th OWL: Experiences and Directions Workshop (OWLED 2013)}, editor = {Kavitha {Srinivas} and Simon {Jupp}}, month = {May}, title = {OWL 2 Reasoning To Detect Energy-Efficient Software Variants From Context}, year = {2013}, }

Sebastian Götz, René Schöne, Claas Wilke, Julian Mendez, and Uwe Aßmann:

Abstract BibTeX Entry PDF File

**Towards Predictive Self-optimization by Situation Recognition**.*2nd Workshop EASED@ BUIS 2013*11, 2013.Abstract BibTeX Entry PDF File

Abstract: Energy efficiency of software is an increasingly important topic. To achieve energy efficiency, a system should automatically optimize itself to provide the best possible utility to the user for the least possible cost in terms of energy consumption. To reach this goal, the system has to continuously decide whether and how to adapt itself, which takes time and consumes energy by itself. During this time, the system could be in an inefficient state and waste energy. We envision the application of predictive situation recognition to initiate decision making before it is actually needed. Thus, the time of the system being in an inefficient state is reduced, leading to a more energy-efficient reconfiguration.

@article{ GoScWiMeAs13, author = {Sebastian {G{\"o}tz} and Ren{\'e} {Sch{\"o}ne} and Claas {Wilke} and Julian {Mendez} and Uwe {A{\ss}mann}}, journal = {2nd Workshop EASED@ BUIS 2013}, pages = {11}, title = {Towards Predictive Self-optimization by Situation Recognition}, year = {2013}, }

Andreas Herzig, Emiliano Lorini, and Dirk Walther:

BibTeX Entry PDF File

**Reasoning about Actions Meets Strategic Logics**. In Davide Grossi, Olivier Roy, and Huaxin Huang, editors,*Logic, Rationality, and Interaction - 4th International Workshop, LORI 2013, Hangzhou, China, October 9-12, 2013, Proceedings*, volume 8196 of*Lecture Notes in Computer Science*, pages 162–175. Springer, 2013.BibTeX Entry PDF File

@inproceedings{ HLW-LORI-13, author = {Andreas {Herzig} and Emiliano {Lorini} and Dirk {Walther}}, booktitle = {Logic, Rationality, and Interaction - 4th International Workshop, LORI 2013, Hangzhou, China, October 9-12, 2013, Proceedings}, editor = {Davide {Grossi} and Olivier {Roy} and Huaxin {Huang}}, pages = {162--175}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Reasoning about Actions Meets Strategic Logics}, volume = {8196}, year = {2013}, }

Michel Ludwig and Boris Konev:

Abstract BibTeX Entry PDF File

**Towards Practical Uniform Interpolation and Forgetting for**\(\mathcal{ALC}\)**TBoxes**. In*Proceedings of the 26th International Workshop on Description Logics (DL-2013)*, volume 1014 of*CEUR-WS*, pages 377–389, 2013.Abstract BibTeX Entry PDF File

We develop a clausal resolution-based approach for computing uniform interpolants of TBoxes formulated in the description logic when such uniform interpolants exist. We also present an experimental evaluation of our approach and its applications to concept forgetting, ontology obfuscation and logical difference on real-life \(\mathcal{ALC}\) ontologies. Our results indicate that in many practical cases a uniform interpolant exists and can be computed with the presented algorithm.

@inproceedings{ LuKo-DL-2013, author = {Michel {Ludwig} and Boris {Konev}}, booktitle = {Proceedings of the 26th International Workshop on Description Logics ({DL-2013})}, pages = {377--389}, series = {CEUR-WS}, title = {Towards Practical Uniform Interpolation and Forgetting for~$\mathcal{ALC}$ TBoxes}, venue = {Ulm, Germany}, volume = {1014}, year = {2013}, }

Yue Ma and Qingfeng Chang:

Abstract BibTeX Entry

**Measuring Incompleteness under Multi-Valued Semantics by Partial MaxSAT Solvers**. In*The 12th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty*, 2013.Abstract BibTeX Entry

Knowledge base metrics provide a useful way to analyze and compare knowledge bases. For example, inconsistency measurements have been proposed to distinguish different inconsistent knowledge bases. Whilst inconsistency degrees have been widely developed, the incompleteness of a knowledge base is rarely studied due to the difficulty of formalizing incompleteness. For this, we propose an incompleteness degree based on multi-valued semantics and show that it satisfies some desired properties. Moreover, we develop an algorithm to compute the proposed metric by reducing the problem to an instance of partial MaxSAT problem such that we can benefit from highly optimized partial MaxSAT solvers. We finally examine the approach over a set of knowledge bases from real applications, which experimentally shows that the proposed incompleteness metric can be computed pratically.

@inproceedings{ MaChang-Ecsquaru13, address = {Dresden, Germany}, author = {Yue {Ma} and Qingfeng {Chang}}, booktitle = {The 12th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty}, title = {Measuring Incompleteness under Multi-Valued Semantics by Partial MaxSAT Solvers}, year = {2013}, }

Yue Ma and Felix Distel:

Abstract BibTeX Entry PDF File

**Concept Adjustment for Description Logics**. In Mathieu d'Aquin and Andrew Gordon, editors,*Proceedings of the 7th International Conference on Knowledge Capture*. ACM, 2013.Abstract BibTeX Entry PDF File

There exist a handful of natural language processing and machine learning approaches for extracting Description Logic concept definitions from natural language texts. Typically, for a single target concept several textual sentences are used, from which candidate concept descriptions are obtained. These candidate descriptions may have confidence values associated with them. In a final step, the candidates need to be combined into a single concept, in the easiest case by selecting a relevant subset and taking its conjunction. However, concept descriptions generated in this manner can contain false information, which is harmful when added to a formal knowledge base. In this paper, we claim that this can be improved by considering formal constraints that the target concept needs to satisfy. We first formalize a reasoning problem for the selection of relevant candidates and examine its computational complexity. Then, we show how it can be reduced to SAT, yielding a practical algorithm for its solution. Furthermore, we describe two ways to construct formal constraints, one is automatic and the other interactive. Applying this approach to the SNOMED CT ontology construction scenario, we show that the proposed framework brings a visible benefit for SNOMED CT development.

@inproceedings{ MaDi-KCap13, author = {Yue {Ma} and Felix {Distel}}, booktitle = {Proceedings of the 7th International Conference on Knowledge Capture}, editor = {Mathieu {d'Aquin} and Andrew {Gordon}}, publisher = {ACM}, title = {Concept Adjustment for Description Logics}, year = {2013}, }

Yue Ma and Felix Distel:

Abstract BibTeX Entry PDF File ©Springer-Verlag (The final publication is available at link.springer.com)

**Learning Formal Definitions for Snomed CT from Text**. In Niels Peek, Roque Marín Morales, and Mor Peleg, editors,*Artificial Intelligence in Medicine*, volume 7885 of*Lecture Notes in Computer Science*, pages 73–77. Springer-Verlag, 2013.Abstract BibTeX Entry PDF File ©Springer-Verlag (The final publication is available at link.springer.com)

Snomed CT is a widely used medical ontology which is formally expressed in a fragment of the Description Logic EL++. The underlying logics allow for expressive querying, yet make it costly to maintain and extend the ontology. In this paper we present an approach for the extraction of Snomed CT definitions from natural language text. We test and evaluate the approach using two types of texts.

@inproceedings{ MaDi-AIME13, author = {Yue {Ma} and Felix {Distel}}, booktitle = {Artificial Intelligence in Medicine}, editor = {Niels {Peek} and Roque {Mar{\'i}n Morales} and Mor {Peleg}}, pages = {73--77}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Learning Formal Definitions for Snomed CT from Text}, volume = {7885}, year = {2013}, }

Yue Ma and Adelina Nazarenko François Lévy:

Abstract BibTeX Entry

**Semantic Annotation in Specific Domains with rich Ontologies (in French)**. In*20ème conférence du Traitement Automatique du Langage Naturel*, 2013. To appear.Abstract BibTeX Entry

Technical documentations are generally difficult to explore and maintain. Powerful tools could help users, provided the documents have been semantically annotated. However, the annotations must be sufficiently specialized, rich and consistent, relying on some explicit semantic model – usually an ontology – that represents the semantics of the target domain. In this paper, we analyze that traditional approaches have limited success for this task. Hence, we propose a novel approach, named phrase-based statistical semantic annotation, for predicting semantic annotations from limited training data. Such a modeling makes the challenging problem, domain specific semantic annotation regarding arbitrarily rich semantic models, easily handled. We used several evaluation metrics on two different business regulatory texts, for which our approach achieved a good performance. In particular, it obtained \(91.9\%\sim97.65\%\) F-measure in the label and position predictions with different settings. This suggests that human annotators can be highly supported in domain specific semantic annotation tasks.

@inproceedings{ MaLeNa-TALN13, address = {Dresden, Germany}, author = {Yue {Ma} and Adelina Nazarenko {Fran\c{c}ois L\'evy}}, booktitle = {20\`eme conf\'erence du Traitement Automatique du Langage Naturel}, note = {To appear.}, title = {Semantic Annotation in Specific Domains with rich Ontologies (in French)}, year = {2013}, }

Yue Ma and Julian Mendez:

Abstract BibTeX Entry

**High Quality Data Generation: An Ontology Reasoning based Approach**. In*International Workshop on Artificial Intelligence for Big Data (in conjunction with IJCAI'13)*, 2013. To appear.Abstract BibTeX Entry

As Big Data is getting increasingly more helpful for different applications, the problem of obtaining reliable data becomes important. The importance is more obvious for domain specific applications because of their abstruse domain knowledge. Most of the Big Data based techniques manipulate directly datasets under the assumption that data quantity can lead to a good system quality. In this paper, we show that the quality can be improved by automatically enriching a given dataset with more high-quality data beforehand. This is achieved by a tractable reasoning technique over the widely used biomedical ontology SNOMED CT. Our approach is evaluated by the scenario of formal definition generation from natural language texts, where the average precision of learned definitions is improved by 5.3%.

@inproceedings{ MaMe-AIBD13, address = {Dresden, Germany}, author = {Yue {Ma} and Julian {Mendez}}, booktitle = {International Workshop on {A}rtificial {I}ntelligence for {B}ig {D}ata (in conjunction with IJCAI'13)}, note = {To appear.}, title = {High Quality Data Generation: An Ontology Reasoning based Approach}, year = {2013}, }

Francisco Martin-Recuerda and Dirk Walther:

BibTeX Entry PDF File

**Towards Fast Atomic Decomposition using Axiom Dependency Hypergraphs**. In Chiara Del Vescovo, Torsten Hahmann, David Pearce, and Dirk Walther, editors,*Proceedings of the 7th International Workshop on Modular Ontologies co-located with the 12th International Conference on Logic Programming and Non-monotonic Reasoning (LPNMR 2013), Corunna, Spain, September 15, 2013*, volume 1081 of*CEUR Workshop Proceedings*. CEUR-WS.org, 2013.BibTeX Entry PDF File

@inproceedings{ MRW-WOMO-13, author = {Francisco {Martin-Recuerda} and Dirk {Walther}}, booktitle = {Proceedings of the 7th International Workshop on Modular Ontologies co-located with the 12th International Conference on Logic Programming and Non-monotonic Reasoning (LPNMR 2013), Corunna, Spain, September 15, 2013}, editor = {Chiara Del {Vescovo} and Torsten {Hahmann} and David {Pearce} and Dirk {Walther}}, publisher = {CEUR-WS.org}, series = {CEUR Workshop Proceedings}, title = {Towards Fast Atomic Decomposition using Axiom Dependency Hypergraphs}, volume = {1081}, year = {2013}, }

Rafael Peñaloza and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File ©Springer-Verlag (The final publication is available at link.springer.com)

**Instance-based Non-standard Inferences in**\(\mathcal{EL}\)**with Subjective Probabilities**. In Fernando Bobillo, Paulo C. G. Costa, Claudia d'Amato, Nicola Fanizzi, Kathryn B. Laskey, Kenneth J. Laskey, Thomas Lukasiewicz, Matthias Nickles, and Michael Pool, editors,*Uncertainty Reasoning for the Semantic Web II, International Workshops URSW 2008-2010 Held at ISWC and UniDL 2010 Held at FLoC, Revised Selected Papers*, number 7123 in*Lecture Notes in Computer Science*, pages 80–98. Springer-Verlag, 2013.Abstract BibTeX Entry PDF File ©Springer-Verlag (The final publication is available at link.springer.com)

For practical ontology-based applications representing and reasoning with probabilities is an essential task. For Description Logics with subjective probabilities reasoning procedures for testing instance relations based on the completion method have been developed. In this paper we extend this technique to devise algorithms for solving non-standard inferences for EL and its probabilistic extension Prob-EL^{0}1: computing the most specific concept of an individual and finding explanations for instance relations.

@inproceedings{ PeTu12, author = {Rafael {Pe{\~n}aloza} and Anni-Yasmin {Turhan}}, booktitle = {Uncertainty Reasoning for the Semantic Web II, International Workshops URSW 2008-2010 Held at ISWC and UniDL 2010 Held at FLoC, Revised Selected Papers}, editor = {Fernando {Bobillo} and Paulo C. G. {Costa} and Claudia {d'Amato} and Nicola {Fanizzi} and Kathryn B. {Laskey} and Kenneth J. {Laskey} and Thomas {Lukasiewicz} and Matthias {Nickles} and Michael {Pool}}, number = {7123}, pages = {80--98}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Instance-based Non-standard Inferences in $\mathcal{EL}$ with Subjective Probabilities}, year = {2013}, }

Rafael Peñaloza and Tingting Zou:

Abstract BibTeX Entry PDF File

**Rough**\(\mathcal{EL}\)**Classification**. In Thomas Eiter, Birte Glimm, Yevgeny Kazakov, and Markus Krötzsch, editors,*Proceedings of the 2013 International Workshop on Description Logics (DL'13)*, volume 1014 of*CEUR-WS*, pages 415–427, 2013.Abstract BibTeX Entry PDF File

Rough Description Logics (DLs) have been studied as a means for representing and reasoning with imprecise knowledge. It has been shown that reasoning in rough DLs can be reduced to reasoning in a classical DL that allows value restrictions, and transitive and inverse roles. This shows that for propositionally closed DLs, the complexity of reasoning is not increased by the inclusion of rough constructors. However, applying such a reduction to rough EL yields an exponential time upper bound. We show that this blow-up in complexity can be avoided, providing a polynomial-time completion-based algorithm for classifying rough EL ontologies.

@inproceedings{ PeZo-DL13, address = {Ulm, Germany}, author = {Rafael {Pe{\~n}aloza} and Tingting {Zou}}, booktitle = {Proceedings of the 2013 International Workshop on Description Logics ({DL'13})}, editor = {Thomas {Eiter} and Birte {Glimm} and Yevgeny {Kazakov} and Markus {Kr{\"o}tzsch}}, pages = {415--427}, series = {CEUR-WS}, title = {Rough $\mathcal{EL}$ Classification}, volume = {1014}, year = {2013}, }

Rafael Peñaloza and Tingting Zou:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Roughening the**\(\mathcal{EL}\)**Envelope**. In P. Fontaine, C. Ringeissen, and R. A. Schmidt, editors,*Proceedings of the 2013 International Symposium on Frontiers of Combining Systems (FroCoS 2013)*, volume 8152 of*Lecture Notes in Computer Science*, pages 71–86. Nancy, France, Springer-Verlag, 2013.Abstract BibTeX Entry PDF File ©Springer-Verlag

The EL family of description logics (DLs) has been successfully applied for representing the knowledge of several domains, specially from the bio-medical fields. One of its principal characteristics is that its reasoning tasks have polynomial complexity, which makes them suitable for large-scale knowledge bases. In their classical form, these logics cannot handle imprecise concepts in a satisfactory manner. Rough sets have been studied as a method for describing imprecise notions, by providing a lower and an upper approximation, which are defined through classes of indiscernible elements. In this paper we study the combination of the EL family of DLs with the notion of rough sets, thus obtaining a family of rough DLs. We show that the rough extension of these DLs maintains the polynomial-time complexity enjoyed by its classical counterpart. We also present a completion-based algorithm that is a strict generalization of the known method for the DL EL++.

@inproceedings{ PeZo-FroCoS13, address = {Nancy, France}, author = {Rafael {Pe{\~n}aloza} and Tingting {Zou}}, booktitle = {Proceedings of the 2013 International Symposium on Frontiers of Combining Systems ({FroCoS 2013})}, editor = {P. {Fontaine} and C. {Ringeissen} and R. A. {Schmidt}}, pages = {71--86}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Roughening the $\mathcal{EL}$ Envelope}, volume = {8152}, year = {2013}, }

Uwe Ryssel, Felix Distel, and Daniel Borchmann:

Abstract BibTeX Entry PDF File (The final publication is available at link.springer.com)

**Fast algorithms for implication bases and attribute exploration using proper premises**.*Annals of Mathematics and Artificial Intelligence*, Special Issue 65:1–29, 2013.Abstract BibTeX Entry PDF File (The final publication is available at link.springer.com)

A central task in formal concept analysis is the enumeration of a small base for the implications that hold in a formal context. The usual stem base algorithms have been proven to be costly in terms of runtime. Proper premises are an alternative to the stem base. We present a new algorithm for the fast computation of proper premises. It is based on a known link between proper premises and minimal hypergraph transversals. Two further improvements are made, which reduce the number of proper premises that are obtained multiple times and redundancies within the set of proper premises. We have evaluated our algorithms within an application related to refactoring of model variants. In this application an implicational base needs to be computed, and runtime is more crucial than minimal cardinality. In addition to the empirical tests, we provide heuristic evidence that an approach based on proper premises will also be beneficial for other applications. Finally, we show how our algorithms can be extended to an exploration algorithm that is based on proper premises.

@article{ RyDiBo-AMAI13, author = {Uwe {Ryssel} and Felix {Distel} and Daniel {Borchmann}}, journal = {Annals of Mathematics and Artificial Intelligence}, pages = {1--29}, publisher = {Springer Netherlands}, title = {Fast algorithms for implication bases and attribute exploration using proper premises}, volume = {Special Issue 65}, year = {2013}, }

Veronika Thost, Konrad Voigt, and Daniel Schuster:

Abstract BibTeX Entry PDF File

**Query Matching for Report Recommendation**. In*Proceedings of the 22Nd ACM International Conference on Conference on Information and Knowledge Management*,*CIKM '13*, pages 1391–1400. San Francisco, California, USA, ACM, 2013.Abstract BibTeX Entry PDF File

Today, reporting is an essential part of everyday business life. But the preparation of complex Business Intelligence data by formulating relevant queries and presenting them in meaningful visualizations, so-called reports, is a challenging task for non-expert database users. To support these users with report creation, we leverage existing queries and present a system for query recommendation in a reporting environment, which is based on query matching. Targeting at large-scale, real-world reporting scenarios, we propose a scalable, index-based query matching approach. Moreover, schema matching is applied for a more fine-grained, structural comparison of the queries. In addition to interactively providing content-based query recommendations of good quality, the system works independent of particular data sources or query languages. We evaluate our system with an empirical data set and show that it achieves an F1-Measure of 0.56 and outperforms the approaches applied by state-of-the-art reporting tools (e.g., keyword search) by up to 30%.

@inproceedings{ ThoSchVo-CIKM13, address = {San Francisco, California, USA}, author = {Veronika {Thost} and Konrad {Voigt} and Daniel {Schuster}}, booktitle = {Proceedings of the 22Nd ACM International Conference on Conference on Information and Knowledge Management}, pages = {1391--1400}, publisher = {ACM}, series = {CIKM '13}, title = {Query Matching for Report Recommendation}, year = {2013}, }

George Tsatsaronis, Alina Petrova, Maria Kissa, Yue Ma, Felix Distel, Franz Baader, and Michael Schroeder:

Abstract BibTeX Entry PDF File

**Learning Formal Definitions for Biomedical Concepts**. In Kavitha Srinivas and Simon Jupp, editors,*Proceedings of the 10th OWL: Experiences and Directions Workshop (OWLED 2013)*, May 2013.Abstract BibTeX Entry PDF File

Ontologies such as the SNOMED Clinical Terms (SNOMED CT), and the Medical Subject Headings (MeSH) play a major role in life sciences. Modeling formally the concepts and the roles in this domain is a crucial process to allow for the integration of biomedical knowledge across applications. In this direction we propose a novel methodology to learn formal definitions for biomedical concepts from unstructured text. We evaluate experimentally the suggested methodology in learning formal definitions of SNOMED CT concepts, using their text definitions from MeSH. The evaluation is focused on the learning of three roles which are among the most populated roles in SNOMED CT: Associated Morphology, Finding Site and Causative Agent. Results show that our methodology may provide an Accuracy of up to 75%. For the representation of the instances three main approaches are suggested, namely, Bag of Words, word n-grams and character n-grams.

@inproceedings{ TsaEtAl-OWLED13, address = {Montpellier, France}, author = {George {Tsatsaronis} and Alina {Petrova} and Maria {Kissa} and Yue {Ma} and Felix {Distel} and Franz {Baader} and Michael {Schroeder}}, booktitle = {Proceedings of the 10th OWL: Experiences and Directions Workshop (OWLED 2013)}, editor = {Kavitha {Srinivas} and Simon {Jupp}}, month = {May}, title = {Learning Formal Definitions for Biomedical Concepts}, year = {2013}, }

Anni-Yasmin Turhan:

Abstract BibTeX Entry

**Introductions to Description Logics - A Guided Tour**. In Sebastian Rudolph, Georg Gottlob, Ian Horrocks, and Frank van Harmelen, editors,*In Proceedings of Reasoning Web. Semantic Technologies for Intelligent Data Access - 9th International Summer School*, volume 8067 of*Lecture Notes in Computer Science*, pages 150–161. Springer, 2013.Abstract BibTeX Entry

Description Logics (DLs) are the logical formalism underlying the standard web ontology language OWL 2. DLs have formal semantics which are the basis for many powerful reasoning services. This paper provides an overview of basic topics in the field of Description Logics by surveying the introductory literature and course material with a focus on DL reasoning services. The resulting compilation also gives a historical perspective on DLs as a research area.

@inproceedings{ Tu-RW-13, author = {Anni-Yasmin {Turhan}}, booktitle = {In Proceedings of Reasoning Web. Semantic Technologies for Intelligent Data Access - 9th International Summer School}, editor = {Sebastian {Rudolph} and Georg {Gottlob} and Ian {Horrocks} and Frank van {Harmelen}}, pages = {150--161}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Introductions to Description Logics - A Guided Tour}, volume = {8067}, year = {2013}, }

Anni-Yasmin Turhan and Benjamin Zarrieß:

Abstract BibTeX Entry PDF File

**Computing the lcs w.r.t. General**\(\mathcal{E\!L}^+\)**TBoxes**. In Thomas Eiter, Birte Glimm, Yevgeny Kazakov, and Markus Krötzsch, editors,*Proceedings of the 26th International Workshop on Description Logics (DL-2013)*,*CEUR Workshop Proceedings*, pages 477–488. Ulm, Germany, CEUR-WS.org, July 2013.Abstract BibTeX Entry PDF File

Recently, exact conditions for the existence of the least common subsumer (lcs) computed w.r.t. general \(\mathcal{EL}\)-TBoxes have been devised. This paper extends these results and provides necessary and suffcient conditions for the existence of the lcs w.r.t. \(\mathcal{EL}^+\)-TBoxes. We show decidability of the existence in PTime and polynomial bounds on the maximal role-depth of the lcs, which in turn yields a computation algorithm for the lcs w.r.t. \(\mathcal{EL}^+\)-TBoxes.

@inproceedings{ TuZa-DL13, address = {Ulm, Germany}, author = {Anni-Yasmin {Turhan} and Benjamin {Zarrie{\ss}}}, booktitle = {Proceedings of the 26th International Workshop on Description Logics ({DL-2013})}, editor = {Thomas {Eiter} and Birte {Glimm} and Yevgeny {Kazakov} and Markus {Kr{\"o}tzsch}}, month = {July}, pages = {477--488}, publisher = {CEUR-WS.org}, series = {CEUR Workshop Proceedings}, title = {Computing the lcs w.r.t.\ General $\mathcal{E\!L}^+$ {TB}oxes}, year = {2013}, }

Benjamin Zarrieß and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File ©IJCAI

**Most Specific Generalizations w.r.t. General**\(\mathcal{EL}\)**-TBoxes**. In*Proceedings of the 23rd International Joint Conference on Artificial Intelligence (IJCAI'13)*. Beijing, China, AAAI Press, 2013.Abstract BibTeX Entry PDF File ©IJCAI

In the area of Description Logics the least common subsumer (lcs) and the most specific concept (msc) are inferences that generalize a set of concepts or an individual, respectively, into a single concept. If computed w.r.t. a general -TBox neither the lcs nor the msc need to exist. So far in this setting no exact conditions for the existence of lcs- or msc-concepts are known. This paper provides necessary and suffcient conditions for the existence of these two kinds of concepts. For the lcs of a fixed number of concepts and the msc we show decidability of the existence in PTime and polynomial bounds on the maximal role-depth of the lcs- and msc-concepts. The latter allows to compute the lcs and the msc, respectively.

@inproceedings{ ZaTu-IJCAI13, address = {Beijing, China}, author = {Benjamin {Zarrie{\ss}} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of the 23rd International Joint Conference on Artificial Intelligence (IJCAI'13)}, publisher = {AAAI Press}, title = {Most Specific Generalizations w.r.t.\ General $\mathcal{EL}$-TBoxes}, year = {2013}, }

Thomas Zerjatke and Monika Sturm:

Abstract BibTeX Entry DOI

**Solving a PSPACE-complete problem by gene assembly**.*Journal of Logic and Computation*, 23(4):897–908, 2013.Abstract BibTeX Entry DOI

Gene assembly is a natural process of genome re-arrangement that occurs during sexual reproduction of unicellular organisms called ciliates. Two computational models adapting this process of gene assembly have been proposed: the intramolecular, e.g. (Ehrenfeucht et al., 2004, Computation in Living Cells: Gene Assembly in Ciliates), and the intermolecular model, e.g. (Landweber and Kari, 2001, Evolution as Computation). A context sensitive version of the intramolecular model introduced by Ishdorj and Petre (2007, Proceedings of the 6th International Conference on Unconventional Computation) was shown to be computationally universal and efficient for solving NP-complete problems. In this article we show that within this model PSPACE-complete problems can also be solved in linear time.

@article{ ZeSt-JLC-13, author = {Thomas {Zerjatke} and Monika {Sturm}}, doi = {http://dx.doi.org/10.1093/logcom/exr052}, journal = {Journal of Logic and Computation}, number = {4}, pages = {897--908}, publisher = {Oxford University Press}, title = {Solving a {PSPACE}-complete problem by gene assembly}, volume = {23}, year = {2013}, }

## 2012

Franz Baader, Stefan Borgwardt, Julian Alfredo Mendez, and Barbara Morawska:

Abstract BibTeX Entry PDF File

**UEL: Unification Solver for**\(\mathcal{EL}\). In Yevgeny Kazakov, Domenico Lembo, and Frank Wolter, editors,*Proceedings of the 25th International Workshop on Description Logics (DL'12)*, volume 846 of*CEUR Workshop Proceedings*, pages 26–36, 2012.Abstract BibTeX Entry PDF File

UEL is a system that computes unifiers for unification problems formulated in the description logic EL. EL is a description logic with restricted expressivity, but which is still expressive enough for the formal representation of biomedical ontologies, such as the large medical ontology SNOMED CT. We propose to use UEL as a tool to detect redundancies in such ontologies by computing unifiers of two formal concepts suspected of expressing the same concept of the application domain. UEL provides access to two different unification algorithms and can be used as a plug-in of the popular ontology editor Protégé, or stand-alone.

@inproceedings{ BBMM-DL-12, address = {Rome, Italy}, author = {Franz {Baader} and Stefan {Borgwardt} and Julian Alfredo {Mendez} and Barbara {Morawska}}, booktitle = {Proceedings of the 25th International Workshop on Description Logics (DL'12)}, editor = {Yevgeny {Kazakov} and Domenico {Lembo} and Frank {Wolter}}, pages = {26--36}, series = {CEUR Workshop Proceedings}, title = {{UEL}: Unification Solver for {$\mathcal{EL}$}}, volume = {846}, year = {2012}, }

Franz Baader, Stefan Borgwardt, and Barbara Morawska:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**A Goal-Oriented Algorithm for Unification in**\(\mathcal{ELH}_{R^+}\)**w.r.t. Cycle-Restricted Ontologies**. In Michael Thielscher and Dongmo Zhang, editors,*Proceedings of the 25th Australasian Joint Conference on Artificial Intelligence (AI'12)*, volume 7691 of*Lecture Notes in Artificial Intelligence*, pages 493–504. Sydney, Australia, Springer-Verlag, 2012.Abstract BibTeX Entry PDF File ©Springer-Verlag

Unification in Description Logics (DLs) has been proposed as an inference service that can, for example, be used to detect redundancies in ontologies. For the DL EL, which is used to define several large biomedical ontologies, unification is NP-complete. A goal-oriented NP unification algorithm for EL that uses nondeterministic rules to transform a given unification problem into solved form has recently been presented. In this paper, we extend this goal-oriented algorithm in two directions: on the one hand, we add general concept inclusion axioms (GCIs), and on the other hand, we add role hierarchies (H) and transitive roles (R+). For the algorithm to be complete, however, the ontology consisting of the GCIs and role axioms needs to satisfy a certain cycle restriction.

@inproceedings{ BaBM-AI12, address = {Sydney, Australia}, author = {Franz {Baader} and Stefan {Borgwardt} and Barbara {Morawska}}, booktitle = {Proceedings of the 25th Australasian Joint Conference on Artificial Intelligence (AI'12)}, editor = {Michael {Thielscher} and Dongmo {Zhang}}, pages = {493--504}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {A Goal-Oriented Algorithm for Unification in {$\mathcal{ELH}_{R^+}$} w.r.t. Cycle-Restricted Ontologies}, volume = {7691}, year = {2012}, }

Franz Baader, Stefan Borgwardt, and Barbara Morawska:

Abstract BibTeX Entry PDF File

**A Goal-Oriented Algorithm for Unification in**\(\mathcal{EL}\)**w.r.t. Cycle-Restricted TBoxes**. In Yevgeny Kazakov, Domenico Lembo, and Frank Wolter, editors,*Proceedings of the 25th International Workshop on Description Logics (DL'12)*, volume 846 of*CEUR Workshop Proceedings*, pages 37–47, 2012.Abstract BibTeX Entry PDF File

Unification in Description Logics (DLs) has been proposed as an inference service that can, for example, be used to detect redundancies in ontologies. The inexpressive Description Logic EL is of particular interest in this context since, on the one hand, several large biomedical ontologies are defined using EL. On the other hand, unification in EL has been shown to be NP-complete, and thus of significantly lower complexity than unification in other DLs of similarly restricted expressive power. Recently, a brute-force NP-unification algorithm for EL w.r.t. a restricted form of general concept inclusion axioms was developed. This paper introduces a goal-oriented algorithm that reduces the amount of nondeterministic guesses considerably.

@inproceedings{ BaBM-DL-12, address = {Rome, Italy}, author = {Franz {Baader} and Stefan {Borgwardt} and Barbara {Morawska}}, booktitle = {Proceedings of the 25th International Workshop on Description Logics (DL'12)}, editor = {Yevgeny {Kazakov} and Domenico {Lembo} and Frank {Wolter}}, pages = {37--47}, series = {CEUR Workshop Proceedings}, title = {A Goal-Oriented Algorithm for Unification in {$\mathcal{EL}$} w.r.t. Cycle-Restricted {TB}oxes}, volume = {846}, year = {2012}, }

Franz Baader, Stefan Borgwardt, and Barbara Morawska:

Abstract BibTeX Entry PDF File

**Computing Minimal**\(\mathcal{EL}\)**-unifiers is Hard**. In Silvio Ghilardi and Lawrence Moss, editors,*Proceedings of the 9-th International Conference on Advances in Modal Logic (AiML'12)*, 2012.Abstract BibTeX Entry PDF File

Unification has been investigated both in modal logics and in description logics, albeit with different motivations. In description logics, unification can be used to detect redundancies in ontologies. In this context, it is not sufficient to decide unifiability, one must also compute appropriate unifiers and present them to the user. For the description logic EL, which is used to define several large biomedical ontologies, deciding unifiability is an NP-complete problem. It is known that every solvable EL-unification problem has a minimal unifier, and that every minimal unifier is a local unifier. Existing unification algorithms for EL compute all minimal unifiers, but additionally (all or some) non-minimal local unifiers. Computing only the minimal unifiers would be better since there are considerably less minimal unifiers than local ones, and their size is usually also quite small. In this paper we investigate the question whether the known algorithms for EL-unification can be modified such that they compute exactly the minimal unifiers without changing the complexity and the basic nature of the algorithms. Basically, the answer we give to this question is negative.

@inproceedings{ BaBM-AiML12, author = {Franz {Baader} and Stefan {Borgwardt} and Barbara {Morawska}}, booktitle = {Proceedings of the 9-th International Conference on Advances in Modal Logic ({AiML'12})}, editor = {Silvio {Ghilardi} and Lawrence {Moss}}, title = {Computing Minimal {$\mathcal{EL}$}-unifiers is Hard}, year = {2012}, }

Franz Baader, Stefan Borgwardt, and Barbara Morawska:

Abstract BibTeX Entry PDF File

**Extending Unification in**\(\mathcal{EL}\)**Towards General TBoxes**. In Gerhard Brewka, Thomas Eiter, and Sheila A. McIlraith, editors,*Proceedings of the Thirteenth International Conference on Principles of Knowledge Representation and Reasoning (KR'12)*, pages 568–572. AAAI Press, 2012.Abstract BibTeX Entry PDF File

Unification in Description Logics (DLs) has been proposed as an inference service that can, for example, be used to detect redundancies in ontologies. The inexpressive Description Logic EL is of particular interest in this context since, on the one hand, several large biomedical ontologies are defined using EL. On the other hand, unification in EL has recently been shown to be NP-complete, and thus of significantly lower complexity than unification in other DLs of similarly restricted expressive power. However, the unification algorithms for EL developed so far cannot deal with general concept inclusion axioms (GCIs). This paper makes a considerable step towards addressing this problem, but the GCIs our new unification algorithm can deal with still need to satisfy a certain cycle restriction.

@inproceedings{ BaBM-KR12, author = {Franz {Baader} and Stefan {Borgwardt} and Barbara {Morawska}}, booktitle = {Proceedings of the Thirteenth International Conference on Principles of Knowledge Representation and Reasoning ({KR'12})}, editor = {Gerhard {Brewka} and Thomas {Eiter} and Sheila A. {McIlraith}}, pages = {568--572}, publisher = {AAAI Press}, title = {Extending Unification in {$\mathcal{EL}$} Towards General {TBoxes}}, year = {2012}, }

Franz Baader, Stefan Borgwardt, and Barbara Morawska:

Abstract BibTeX Entry PDF File

**Recent Advances in Unification for the**\(\mathcal{EL}\)**Family**. In Santiago Escobar, Konstantin Korovin, and Vladimir Rybakov, editors,*Proceedings of the 26th International Workshop on Unification (UNIF'12)*, 2012.Abstract BibTeX Entry PDF File

Unification in Description Logics (DLs) has been proposed as an inference service that can, for example, be used to detect redundancies in ontologies. For the DL EL, which is used to define several large biomedical ontologies, unification is NP-complete. Several algorithms that solve unification in EL have previously been presented. In this paper, we summarize recent extensions of these algorithms that can deal with general concept inclusion axioms (GCIs), role hierarchies(H), and transitive roles (R+). For the algorithms to be complete, however, the ontology consisting of the GCIs and role axioms needs to satisfy a certain cycle restriction.

@inproceedings{ BaBM-UNIF12, address = {Manchester, UK}, author = {Franz {Baader} and Stefan {Borgwardt} and Barbara {Morawska}}, booktitle = {Proceedings of the 26th International Workshop on Unification (UNIF'12)}, editor = {Santiago {Escobar} and Konstantin {Korovin} and Vladimir {Rybakov}}, title = {Recent Advances in Unification for the {$\mathcal{EL}$} Family}, year = {2012}, }

Franz Baader, Stefan Borgwardt, and Barbara Morawska:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**SAT-Encoding of Unification in**\(\mathcal{ELH}_{R^+}\)**w.r.t. Cycle-Restricted Ontologies**. In*Proceedings of the 6th International Joint Conference on Automated Reasoning (IJCAR'12)*, volume 7364 of*Lecture Notes in Artificial Intelligence*, pages 30–44. Manchester, UK, Springer-Verlag, 2012.Abstract BibTeX Entry PDF File ©Springer-Verlag

Unification in Description Logics has been proposed as an inference service that can, for example, be used to detect redundancies in ontologies. For the Description Logic EL, which is used to define several large biomedical ontologies, unification is NP-complete. An NP unification algorithm for EL based on a translation into propositional satisfiability (SAT) has recently been presented. In this paper, we extend this SAT encoding in two directions: on the one hand, we add general concept inclusion axioms, and on the other hand, we add role hierarchies (H) and transitive roles (R+). For the translation to be complete, however, the ontology needs to satisfy a certain cycle restriction. The SAT translation depends on a new rewriting-based characterization of subsumption w.r.t. ELHR+-ontologies.

@inproceedings{ BaBM-IJCAR-12, address = {Manchester, UK}, author = {Franz {Baader} and Stefan {Borgwardt} and Barbara {Morawska}}, booktitle = {Proceedings of the 6th International Joint Conference on Automated Reasoning (IJCAR'12)}, pages = {30--44}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {{SAT}-Encoding of Unification in {$\mathcal{ELH}_{R^+}$} w.r.t. Cycle-Restricted Ontologies}, volume = {7364}, year = {2012}, }

Franz Baader, Silvio Ghilardi, and Carsten Lutz:

Abstract BibTeX Entry PDF File

**LTL over Description Logic Axioms**.*ACM Trans. Comput. Log.*, 13(3), 2012.Abstract BibTeX Entry PDF File

Most of the research on temporalized Description Logics (DLs) has concentrated on the case where temporal operators can be applied to concepts, and sometimes additionally to TBox axioms and ABox assertions. The aim of this paper is to study temporalized DLs where temporal operators on TBox axioms and ABox assertions are available, but temporal operators on concepts are not. While the main application of existing temporalized DLs is the representation of conceptual models that explicitly incorporate temporal aspects, the family of DLs studied in this paper addresses applications that focus on the temporal evolution of data and of ontologies. Our results show that disallowing temporal operators on concepts can significantly decrease the complexity of reasoning. In particular, reasoning with rigid roles (whose interpretation does not change over time) is typically undecidable without such a syntactic restriction, whereas our logics are decidable in elementary time even in the presence of rigid roles. We analyze the effects on computational complexity of dropping rigid roles, dropping rigid concepts, replacing temporal TBoxes with global ones, and restricting the set of available temporal operators. In this way, we obtain a novel family of temporalized DLs whose complexity ranges from 2-ExpTime-complete via NExpTime-complete to ExpTime-complete.

@article{ BaaderGL12, author = {Franz {Baader} and Silvio {Ghilardi} and Carsten {Lutz}}, journal = {ACM Trans. Comput. Log.}, number = {3}, title = {{LTL} over Description Logic Axioms}, volume = {13}, year = {2012}, }

Franz Baader, Martin Knechtel, and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Context-Dependent Views to Axioms and Consequences of Semantic Web Ontologies**.*Journal of Web Semantics*, 12–13:22–40, 2012. Available at http://dx.doi.org/10.1016/j.websem.2011.11.006Abstract BibTeX Entry PDF File

The framework developed in this paper can deal with scenarios where selected sub-ontologies of a large ontology are offered as views to users, based on contexts like the access rights of a user, the trust level required by the application, or the level of detail requested by the user. Instead of materializing a large number of different sub-ontologies, we propose to keep just one ontology, but equip each axiom with a label from an appropriate context lattice. The different contexts of this ontology are then also expressed by elements of this lattice. For large-scale ontologies, certain consequences (like the subsumption hierarchy) are often pre-computed. Instead of pre-computing these consequences for every context, our approach computes just one label (called a boundary) for each consequence such that a comparison of the user label with the consequence label determines whether the consequence follows from the sub-ontology determined by the context. We describe different black-box approaches for computing boundaries, and present first experimental results that compare the efficiency of these approaches on large real-world ontologies. Black-box means that, rather than requiring modifications of existing reasoning procedures, these approaches can use such procedures directly as sub-procedures, which allows us to employ existing highly-optimized reasoners. Similar to designing ontologies, the process of assigning axiom labels is error-prone. For this reason, we also address the problem of how to repair the labelling of an ontology in case the knowledge engineer notices that the computed boundary of a consequence does not coincide with her intuition regarding in which context the consequence should or should not be visible.

@article{ BaKP-JWS12, author = {Franz {Baader} and Martin {Knechtel} and Rafael {Pe{\~n}aloza}}, journal = {Journal of Web Semantics}, note = {Available at http://dx.doi.org/10.1016/j.websem.2011.11.006}, pages = {22--40}, title = {Context-Dependent Views to Axioms and Consequences of Semantic Web Ontologies}, volume = {12--13}, year = {2012}, }

Franz Baader, Julian Mendez, and Barbara Morawska:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**UEL: Unification Solver for the Description Logic EL – System Description**. In*Proceedings of the 6th International Joint Conference on Automated Reasoning (IJCAR'12)*, volume 7364 of*Lecture Notes in Artificial Intelligence*, pages 45–51. Manchester, UK, Springer-Verlag, 2012.Abstract BibTeX Entry PDF File ©Springer-Verlag

UEL is a system that computes unifiers for unification problems formulated in the description logic EL. EL is a description logic with restricted expressivity, but which is still expressive enough for the formal representation of biomedical ontologies, such as the large medical ontology SNOMED CT. We propose to use UEL as a tool to detect redundancies in such ontologies by computing unifiers of two formal concepts suspected of expressing the same concept of the application domain. UEL can be used as a plug-in of the popular ontology editor Protege, or as a standalone unification application.

@inproceedings{ BaMM-IJCAR-12, address = {Manchester, UK}, author = {Franz {Baader} and Julian {Mendez} and Barbara {Morawska}}, booktitle = {Proceedings of the 6th International Joint Conference on Automated Reasoning (IJCAR'12)}, pages = {45--51}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {UEL: Unification Solver for the Description Logic EL -- System Description}, volume = {7364}, year = {2012}, }

Franz Baader and Alexander Okhotin:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Solving language equations and disequations with applications to disunification in description logics and monadic set constraints**. In Nikolaj Bjørner and Andrei Voronkov, editors,*Proceedings of the 18th International Conference on Logic for Programming, Artifical Intelligence, and Reasoning (LPAR-12)*, volume 7180 of*Lecture Notes in Computer Science*, pages 107–121. Mérida, Venezuela, Springer-Verlag, 2012.Abstract BibTeX Entry PDF File ©Springer-Verlag

We extend previous results on the complexity of solving language equations with one-sided concatenation and all Boolean operations to the case where also disequations (i.e., negated equations) may occur. To show that solvability of systems of equations and disequations is still in ExpTime, we introduce a new type of automata working on infinite trees, which we call looping automata with colors. As applications of these results, we show new complexity results for disunification in the description logic FL0 and for monadic set constraints with negation. We believe that looping automata with colors may also turn out to be useful in other applications.

@inproceedings{ BaOk-LPAR18, address = {M{\'e}rida, Venezuela}, author = {Franz {Baader} and Alexander {Okhotin}}, booktitle = {Proceedings of the 18th International Conference on Logic for Programming, Artifical Intelligence, and Reasoning {(LPAR-12)}}, editor = {Nikolaj {Bj{\o}rner} and Andrei {Voronkov}}, pages = {107--121}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Solving language equations and disequations with applications to disunification in description logics and monadic set constraints}, volume = {7180}, year = {2012}, }

Stefan Borgwardt, Felix Distel, and Rafael Peñaloza:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**How Fuzzy is my Fuzzy Description Logic?**. In Bernhard Gramlich, Dale Miller, and Ulrike Sattler, editors,*Proceedings of the 6th International Joint Conference on Automated Reasoning (IJCAR'12)*, volume 7364 of*Lecture Notes in Artificial Intelligence*, pages 82–96. Manchester, UK, Springer-Verlag, 2012.Abstract BibTeX Entry PDF File ©Springer-Verlag

Fuzzy Description Logics (DLs) with t-norm semantics have been studied as a means for representing and reasoning with vague knowledge. Recent work has shown that even fairly inexpressive fuzzy DLs become undecidable for a wide variety of t-norms. We complement those results by providing a class of t-norms and an expressive fuzzy DL for which ontology consistency is linearly reducible to crisp reasoning, and thus has its same complexity. Surprisingly, in these same logics crisp models are insufficient for deciding fuzzy subsumption.

@inproceedings{ BoDP-IJCAR-12, address = {Manchester, UK}, author = {Stefan {Borgwardt} and Felix {Distel} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 6th International Joint Conference on Automated Reasoning (IJCAR'12)}, editor = {Bernhard {Gramlich} and Dale {Miller} and Ulrike {Sattler}}, pages = {82--96}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {How Fuzzy is my Fuzzy Description Logic?}, volume = {7364}, year = {2012}, }

Stefan Borgwardt, Felix Distel, and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Gödel Negation Makes Unwitnessed Consistency Crisp**. In Yevgeny Kazakov, Domenico Lembo, and Frank Wolter, editors,*Proceedings of the 2012 International Workshop on Description Logics (DL'12)*, volume 846 of*CEUR-WS*, pages 103–113, 2012.Abstract BibTeX Entry PDF File

Ontology consistency has been shown to be undecidable for a wide variety of fairly inexpressive fuzzy Description Logics (DLs). In particular, for any t-norm "starting with" the Lukasiewicz t-norm, consistency of crisp ontologies (w.r.t. witnessed models) is undecidable in any fuzzy DL with conjunction, existential restrictions, and (residual) negation. In this paper we show that for any t-norm with Gödel negation, that is, any t-norm not starting with Lukasiewicz, ontology consistency for a variant of fuzzy SHOI is linearly reducible to crisp reasoning, and hence decidable in exponential time. Our results hold even if reasoning is not restricted to the class of witnessed models only.

@inproceedings{ BoDP-DL12, address = {Rome, Italy}, author = {Stefan {Borgwardt} and Felix {Distel} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 2012 International Workshop on Description Logics ({DL'12})}, editor = {Yevgeny {Kazakov} and Domenico {Lembo} and Frank {Wolter}}, pages = {103--113}, series = {CEUR-WS}, title = {{G{\"o}}del Negation Makes Unwitnessed Consistency Crisp}, volume = {846}, year = {2012}, }

Stefan Borgwardt and Barbara Morawska:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Finding Finite Herbrand Models**. In Nikolaj Bjørner and Andrei Voronkov, editors,*Proceedings of the 18th International Conference on Logic for Programming, Artifical Intelligence, and Reasoning (LPAR'12)*, volume 7180 of*Lecture Notes in Computer Science*, pages 138–152. Mérida, Venezuela, Springer-Verlag, 2012.Abstract BibTeX Entry PDF File ©Springer-Verlag

We show that finding finite Herbrand models for a restricted class of first-order clauses is ExpTime-complete. A Herbrand model is called finite if it interprets all predicates by finite subsets of the Herbrand universe. The restricted class of clauses consists of anti-Horn clauses with monadic predicates and terms constructed over unary function symbols and constants. The decision procedure can be used as a new goal-oriented algorithm to solve linear language equations and unification problems in the description logic FL0. The new algorithm has only worst-case exponential runtime, in contrast to the previous one which was even best-case exponential.

@inproceedings{ BoMo-LPAR-12, address = {M{\'e}rida, Venezuela}, author = {Stefan {Borgwardt} and Barbara {Morawska}}, booktitle = {Proceedings of the 18th International Conference on Logic for Programming, Artifical Intelligence, and Reasoning (LPAR'12)}, editor = {Nikolaj {Bj{\o}rner} and Andrei {Voronkov}}, pages = {138--152}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Finding Finite {H}erbrand Models}, volume = {7180}, year = {2012}, }

Stefan Borgwardt and Rafael Peñaloza:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**A Tableau Algorithm for Fuzzy Description Logics over Residuated De Morgan Lattices**. In Markus Krötzsch and Umberto Straccia, editors,*Proceedings of the 6th International Conference on Web Reasoning and Rule Systems (RR 2012)*, volume 7497 of*Lecture Notes in Computer Science*, pages 9–24. Springer, 2012.Abstract BibTeX Entry PDF File ©Springer-Verlag

Fuzzy description logics can be used to model vague knowledge in application domains. This paper analyses the consistency and satisfiability problems in the description logic SHI with semantics based on a complete residuated De Morgan lattice. The problems are undecidable in the general case, but can be decided by a tableau algorithm when restricted to finite lattices. For some sublogics of SHI, we provide upper complexity bounds that match the complexity of crisp reasoning.

@inproceedings{ BoPeRR12, author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 6th International Conference on Web Reasoning and Rule Systems (RR 2012)}, editor = {Markus {Kr{\"o}tzsch} and Umberto {Straccia}}, pages = {9--24}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {A Tableau Algorithm for Fuzzy Description Logics over Residuated De Morgan Lattices}, volume = {7497}, year = {2012}, }

Stefan Borgwardt and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Non-Gödel Negation Makes Unwitnessed Consistency Undecidable**. In Yevgeny Kazakov, Domenico Lembo, and Frank Wolter, editors,*Proceedings of the 2012 International Workshop on Description Logics (DL'12)*, volume 846 of*CEUR-WS*, pages 411–421, 2012.Abstract BibTeX Entry PDF File

Recent results show that ontology consistency is undecidable for a wide variety of fuzzy Description Logics (DLs). Most notably, undecidability arises for a family of inexpressive fuzzy DLs using only conjunction, existential restrictions, and residual negation, even if the ontology itself is crisp. All those results depend on restricting reasoning to witnessed models. In this paper, we show that ontology consistency for inexpressive fuzzy DLs using any t-norm starting with the Łukasiewicz t-norm is also undecidable w.r.t. general models.

@inproceedings{ BoPe-DL12, address = {Rome, Italy}, author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 2012 International Workshop on Description Logics ({DL'12})}, editor = {Yevgeny {Kazakov} and Domenico {Lembo} and Frank {Wolter}}, pages = {411--421}, series = {CEUR-WS}, title = {Non-{G{\"o}}del Negation Makes Unwitnessed Consistency Undecidable}, volume = {846}, year = {2012}, }

Stefan Borgwardt and Rafael Peñaloza:

Abstract BibTeX Entry PDF File ©AAAI

**Undecidability of Fuzzy Description Logics**. In Gerhard Brewka, Thomas Eiter, and Sheila A. McIlraith, editors,*Proceedings of the 13th International Conference on Principles of Knowledge Representation and Reasoning (KR 2012)*, pages 232–242. Rome, Italy, AAAI Press, 2012.Abstract BibTeX Entry PDF File ©AAAI

Fuzzy description logics (DLs) have been investigated for over two decades, due to their capacity to formalize and reason with imprecise concepts. Very recently, it has been shown that for several fuzzy DLs, reasoning becomes undecidable. Although the proofs of these results differ in the details of each specific logic considered, they are all based on the same basic idea. In this paper, we formalize this idea and provide sufficient conditions for proving undecidability of a fuzzy DL. We demonstrate the effectiveness of our approach by strengthening all previously-known undecidability results and providing new ones. In particular, we show that undecidability may arise even if only crisp axioms are considered.

@inproceedings{ BoPe-KR12, address = {Rome, Italy}, author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 13th International Conference on Principles of Knowledge Representation and Reasoning (KR 2012)}, editor = {Gerhard {Brewka} and Thomas {Eiter} and Sheila A. {McIlraith}}, pages = {232--242}, publisher = {AAAI Press}, title = {Undecidability of Fuzzy Description Logics}, year = {2012}, }

Felix Distel:

Abstract BibTeX Entry PDF File

**Adapting Fuzzy Formal Concept Analysis for Fuzzy Description Logics**. In*Proceedings of the 9th international conference on concept lattices and their applications (CLA 2012)*, 2012.Abstract BibTeX Entry PDF File

Fuzzy Logics have been applied successfully within both Formal Concept Analysis and Description Logics. Especially in the latter field, Fuzzy Logics have been gaining significant momentum during the last two years. Unfortunately, the research on fuzzy logics within the two communities has been conducted independently from each other, leading to different approaches being pursued. We show that if we look at a restricted variant of fuzzy formal concept analysis, then the differences between the two approaches can be reconciled. Moreover, an implicational base can be computed even when the identity hedge is used.

@inproceedings{ Dis-CLA-2012, author = {Felix {Distel}}, booktitle = {Proceedings of the 9th international conference on concept lattices and their applications (CLA 2012)}, title = {Adapting Fuzzy Formal Concept Analysis for Fuzzy Description Logics}, year = {2012}, }

Andreas Ecke and Anni-Yasmin Turhan:

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**Optimizations for the role-depth bounded least common subsumer in**\(\mathcal{el}+\). In Matthew Horridge and Pavel Klinov, editors,*Proc. of 9th OWL: Experiences and Directions Workshop (OWLED 2012)*, 2012.Abstract BibTeX Entry PDF File

Computing the least common subsumer (lcs) yields a generalization of a collection of concepts, computing such generalizations is a useful reasoning task for many ontology-based applications. Since the lcs need not exist, if computed w.r.t. general TBoxes, an approximative approach, the role-depth bounded lcs, has been proposed. Recently, this approach has been extended to the Description logic , which covers most of the OWL 2 EL profile. In this paper we present two kinds of optimizations for the computation of such approximative lcs: one to obtain succinct rewritings of \(\mathcal{el}+\)-concepts and the other to speed-up the k-lcs computation. The evaluation of these optimizations give evidence that they can improve the computation of the role-depth bounded lcs by orders of magnitude.

@inproceedings{ EcTu-OWLED-12, author = {Andreas {Ecke} and Anni-Yasmin {Turhan}}, booktitle = {Proc. of 9th OWL: Experiences and Directions Workshop (OWLED 2012)}, editor = {Matthew {Horridge} and Pavel {Klinov}}, title = {Optimizations for the role-depth bounded least common subsumer in $\mathcal{el}+$}, volume = {849}, year = {2012}, }

Andreas Ecke and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File

**Role-depth Bounded Least Common Subsumers for**\(\mathcal{EL}\)**+ and**\(\mathcal{ELI}\). In Yevgeny Kazakhov and Frank Wolter, editors,*Proc. of Description Logics Workshop*, volume 846 of*CEUR*, 2012.Abstract BibTeX Entry PDF File

For \(\mathcal{EL}\) the least common subsumer (lcs) need not exist, if computed w.r.t. general TBoxes. In case the role-depth of the lcs concept description is bounded, an approximate solution can be obtained. In this paper we extend the completion-based method for computing such approximate solutions to \(\mathcal{ELI}\) and \(\mathcal{EL}\)+. For \(\mathcal{ELI}\) the extension needs to be able to treat complex node labels. For a naive method generates highly redundant concept descriptions for which we devise a heuristic that produces smaller, but equivalent concept descriptions. We demonstrate the usefulness of this heuristic by an evaluation.

@inproceedings{ EcTu-DL-12, author = {Andreas {Ecke} and Anni-Yasmin {Turhan}}, booktitle = {Proc.\ of Description Logics Workshop}, editor = {Yevgeny {Kazakhov} and Frank {Wolter}}, series = {CEUR}, title = {Role-depth Bounded Least Common Subsumers for $\mathcal{EL}$+ and $\mathcal{ELI}$}, volume = {846}, year = {2012}, }

Weili Fu and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Adding Context to Tableaux for DLs**. In Yevgeny Kazakov, Domenico Lembo, and Frank Wolter, editors,*Proceedings of the 2012 International Workshop on Description Logics (DL'12)*, volume 846 of*CEUR-WS*, 2012.Abstract BibTeX Entry PDF File

We consider the problem of reasoning with ontologies where every axiom is associated to a context, and contexts are related through a total order. These contexts could represent, for example, a degree of trust associated to the axiom, or a level of granularity for the knowledge provided. We describe an extension of tableaux-based decision procedures into methods that compute the best-fitting context for the consequences of an ontology, and apply it to the tableaux algorithm for ALC. We also describe an execution strategy that preserves most of the standard optimizations used in modern DL reasoners.

@inproceedings{ FuPe-DL12, address = {Rome, Italy}, author = {Weili {Fu} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 2012 International Workshop on Description Logics ({DL'12})}, editor = {Yevgeny {Kazakov} and Domenico {Lembo} and Frank {Wolter}}, series = {CEUR-WS}, title = {Adding Context to Tableaux for {DLs}}, volume = {846}, year = {2012}, }

Karsten Lehmann and Rafael Peñaloza:

BibTeX Entry PDF File

**The Complexity of Computing the Behaviour of Weighted Büchi Automata over Lattices**. In Heiko Vogler and Manfred Droste, editors,*Proceedings of the 6th International Workshop Weighted Automata: Theory and Applications (WATA'12)*, 2012.BibTeX Entry PDF File

@inproceedings{ LePe12, author = {Karsten {Lehmann} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 6th International Workshop Weighted Automata: Theory and Applications ({WATA'12})}, editor = {Heiko {Vogler} and Manfred {Droste}}, title = {The Complexity of Computing the Behaviour of Weighted B{\"u}chi Automata over Lattices}, year = {2012}, }

Karsten Lehmann and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File

**A Framework for Semantic-based Similarity Measures for**\(\mathcal{ELH}\)**-Concepts**. In Luis Fariñas del Cerro, Andreas Herzig, and Jérôme Mengin, editors,*Proceedings of the 13th European Conference on Logics in Artificial Intelligence*,*Lecture Notes in Artificial Intelligence*, pages 307–319. Springer Verlag, 2012.Abstract BibTeX Entry PDF File

Similarity measures for concepts written in Description Logics (DLs) are often devised based on the syntax of concepts or simply by adjusting them to a set of instance data. These measures do not take the semantics of the concepts into account and can thus lead to unintuitive results. It even remains unclear how these measures behave if applied to new domains or new sets of instance data. In this paper we develop a framework for similarity measures for ELH-concept descriptions based on the semantics of the DL ELH. We show that our framework ensures that the measures resulting from instantiations fulfill fundamental properties, such as equivalence invariance, yet the framework provides the flexibility to adjust measures to specifics of the modelled domain.

@inproceedings{ LeTu-Jelia12, author = {Karsten {Lehmann} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of the 13th European Conference on Logics in Artificial Intelligence}, editor = {Luis Fari{\~n}as del {Cerro} and Andreas {Herzig} and J{\'e}r{\^o}me {Mengin}}, pages = {307--319}, publisher = {Springer Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {A Framework for Semantic-based Similarity Measures for {$\mathcal{ELH}$}-Concepts}, year = {2012}, }

Frederick Maier, Yue Ma, and Pascal Hitzler:

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**Paraconsistent OWL and Related Logics**. In*Semantic Web journal*, March 2012.BibTeX Entry PDF File

@inproceedings{ MaMaHi-JSW-12, author = {Frederick {Maier} and Yue {Ma} and Pascal {Hitzler}}, booktitle = {Semantic Web journal}, month = {March}, title = {Paraconsistent OWL and Related Logics}, year = {2012}, }

Julian Mendez:

Abstract BibTeX Entry PDF File

**jcel: A Modular Rule-based Reasoner**.*In Proceedings of the 1st International Workshop on OWL Reasoner Evaluation (ORE 2012)*, 858, 2012.Abstract BibTeX Entry PDF File

jcel is a reasoner for the description logic EL+ that uses a rule-based completion algorithm. These algorithms are used to get subsumptions in the lightweight description logic EL and its extensions. One of these extensions is EL+, a description logic with restricted expressivity, but used in formal representation of biomedical ontologies. These ontologies can be encoded using the Web Ontology Language (OWL), and through the OWL API, edited using the popular ontology editor Protege. jcel implements a subset of the OWL 2 EL profile, and can be used as a Java library or as a Protege plug-in. This system description presents the architecture and main features of jcel, and reports some of the challenges and limitations faced in its development.

@article{ Me-ORE12, author = {Julian {Mendez}}, journal = {In Proceedings of the 1st International Workshop on OWL Reasoner Evaluation (ORE 2012)}, title = {jcel: A Modular Rule-based Reasoner}, volume = {858}, year = {2012}, }

Guohui Xiao and Yue Ma:

Abstract BibTeX Entry PDF File

**Inconsistency Measurement based on Variables in Minimal Unsatisfiable Subsets**. In*Proceedings of European Conference on Artificial Intelligence (ECAI'12)*, pages 864–869, 2012.Abstract BibTeX Entry PDF File

Measuring inconsistency degrees of knowledge bases (KBs) provides important context information for facilitating inconsistency handling. Several semantic and syntax based measures have been proposed separately. In this paper, we propose a new way to define inconsistency measurements by combining semantic and syntax based approaches. It is based on counting the variables of minimal unsatisfiable subsets (MUSes) and minimal correction subsets (MCSes), which leads to two equivalent inconsistency degrees, named IDMUS and IDMCS. We give the theoretical and experimental comparisons between them and two purely semantic-based inconsistency degrees: 4-valued and the Quasi Classical semantics based inconsistency degrees. Moreover, the computational complexities related to our new inconsistency measurements are studied. As it turns out that computing the exact inconsistency degrees is intractable in general, we then propose and evaluate an anytime algorithm to make IDMUS and IDMCS usable in knowledge management applications. In particular, as most of syntax based measures tend to be difficult to compute in reality due to the exponential number of MUSes, our new inconsistency measures are practical because the numbers of variables in MUSes are often limited or easily to be approximated. We evaluate our approach on the DC benchmark. Our encouraging experimental results show that these new inconsistency measurements or their approximations are efficient to handle large knowledge bases and to better distinguish inconsistent knowledge bases.

@inproceedings{ XiMa-ECAI-12, author = {Guohui {Xiao} and Yue {Ma}}, booktitle = {Proceedings of European Conference on Artificial Intelligence (ECAI'12)}, pages = {864--869}, title = {Inconsistency Measurement based on Variables in Minimal Unsatisfiable Subsets}, year = {2012}, }

Wael Yehia, Hongkai Liu, Marcel Lippmann, Franz Baader, and Mikhail Soutchanski:

Abstract BibTeX Entry PDF File

**Experimental Results on Solving the Projection Problem in Action Formalisms Based on Description Logics**. In Yevgeny Kazakov, Domenico Lembo, and Frank Wolter, editors,*Proceedings of the 25th International Workshop on Description Logics (DL-2012)*, volume 846 of*CEUR Workshop Proceedings*. Rome, Italy, CEUR-WS.org, June 2012.Abstract BibTeX Entry PDF File

In the reasoning about actions community, one of the most basic reasoning problems is the projection problem: the question whether a certain assertion holds after executing a sequence of actions. While undecidable for general action theories based on the situation calculus, the projection problem was shown to be decidable in two different restrictions of the situation calculus to theories formulated using description logics. In this paper, we compare our implementations of projection procedures for these two approaches on random testing data for several realistic application domains. Important contributions of this work are not only the obtained experimental results, but also the approach for generating test cases. By using patterns extracted from the respective application domains, we ensure that the randomly generated input data make sense and are not inconsistent.

@inproceedings{ YeLiLi-DL-12, address = {Rome, Italy}, author = {Wael {Yehia} and Hongkai {Liu} and Marcel {Lippmann} and Franz {Baader} and Mikhail {Soutchanski}}, booktitle = {Proceedings of the 25th International Workshop on Description Logics ({DL-2012})}, editor = {Yevgeny {Kazakov} and Domenico {Lembo} and Frank {Wolter}}, month = {June}, publisher = {CEUR-WS.org}, series = {CEUR Workshop Proceedings}, title = {Experimental Results on Solving the Projection Problem in Action Formalisms Based on Description Logics}, volume = {846}, year = {2012}, }

## 2011

F. Baader and S. Ghilardi:

Abstract BibTeX Entry PDF File

**Unification in Modal and Description Logics**.*Logic Journal of the IGPL*, 19(6):705–730, 2011. Available at http://jigpal.oxfordjournals.org/content/19/6/705.abstractAbstract BibTeX Entry PDF File

Unification was originally introduced in automated deduction and term rewriting, but has recently also found applications in other fields. In this article, we give a survey of the results on unification obtained in two closely related, yet different, application areas of unification: description logics and modal logics.

@article{ BaaderGhilardi2011, author = {F. {Baader} and S. {Ghilardi}}, journal = {Logic Journal of the IGPL}, note = {Available at http://jigpal.oxfordjournals.org/content/19/6/705.abstract}, number = {6}, pages = {705--730}, title = {Unification in Modal and Description Logics}, volume = {19}, year = {2011}, }

Franz Baader:

Abstract BibTeX Entry (The final publication is available at link.springer.com)

**What's new in Description Logics**.*Informatik-Spektrum*, 34(5):434–442, 2011.Abstract BibTeX Entry (The final publication is available at link.springer.com)

Mainstream research in Description Logics (DLs) until recently concentrated on increasing the expressive power of the employed description language while keeping standard inference problems like subsumption and instance manageable in the sense that highly optimized reasoning procedures for them behave well in practice. One of the main successes of this line of research was the adoption of OWL DL, which is based on an expressive DL, as the standard ontology language for the Semantic Web. More recently, there has been a growing interest in more light-weight DLs, and in other kinds of inference problems, mainly triggered by need in applications with large-scale ontologies. In this paper, we first review the DL research leading to the very expressive DLs with practical inference procedures underlying OWL, and then sketch the recent development of light-weight DLs and novel inference procedures.

@article{ BaaderSpektrum2011, author = {Franz {Baader}}, journal = {Informatik-Spektrum}, number = {5}, pages = {434--442}, title = {What's new in Description Logics}, volume = {34}, year = {2011}, }

Franz Baader, Nguyen Thanh Binh, Stefan Borgwardt, and Barbara Morawska:

BibTeX Entry PDF File

**Computing Local Unifiers in the Description Logic**\(\mathcal{EL}\)**without the Top Concept**. In Franz Baader, Barbara Morawska, and Jan Otop, editors,*Proceedings of the 25th International Workshop on Unification (UNIF'11)*, pages 2–8, 2011.BibTeX Entry PDF File

@inproceedings{ BBBM-UNIF11, address = {Wroc{\l}aw, Poland}, author = {Franz {Baader} and Nguyen Thanh {Binh} and Stefan {Borgwardt} and Barbara {Morawska}}, booktitle = {Proceedings of the 25th International Workshop on Unification (UNIF'11)}, editor = {Franz {Baader} and Barbara {Morawska} and Jan {Otop}}, pages = {2--8}, title = {Computing Local Unifiers in the Description Logic {$\mathcal{EL}$} without the Top Concept}, year = {2011}, }

Franz Baader, Nguyen Thanh Binh, Stefan Borgwardt, and Barbara Morawska:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Unification in the Description Logic**\(\mathcal{EL}\)**without the Top Concept**. In Nikolaj Bjørner and Viorica Sofronie-Stokkermans, editors,*Proceedings of the 23rd International Conference on Automated Deduction (CADE 2011)*, volume 6803 of*Lecture Notes in Computer Science*, pages 70–84. Wroclaw, Poland, Springer-Verlag, 2011.Abstract BibTeX Entry PDF File ©Springer-Verlag

Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. The inexpressive Description Logic EL is of particular interest in this context since, on the one hand, several large biomedical ontologies are defined using EL. On the other hand, unification in EL has recently been shown to be NP-complete, and thus of considerably lower complexity than unification in other DLs of similarly restricted expressive power. However, EL allows the use of the top concept, which represents the whole interpretation domain, whereas the large medical ontology SNOMED CT makes no use of this feature. Surprisingly, removing the top concept from EL makes the unification problem considerably harder. More precisely, we will show in this paper that unification in EL without the top concept is PSpace-complete.

@inproceedings{ BaBiBoMoCADE11, address = {Wroclaw, Poland}, author = {Franz {Baader} and Nguyen Thanh {Binh} and Stefan {Borgwardt} and Barbara {Morawska}}, booktitle = {Proceedings of the 23rd International Conference on Automated Deduction ({CADE 2011})}, editor = {Nikolaj {Bj{\o}rner} and Viorica {Sofronie-Stokkermans}}, pages = {70--84}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Unification in the Description Logic $\mathcal{EL}$\\ without the Top Concept}, volume = {6803}, year = {2011}, }

Franz Baader, Nguyen Thanh Binh, Stefan Borgwardt, and Barbara Morawska:

Abstract BibTeX Entry PDF File

**Unification in the Description Logic**\(\mathcal{EL}\)**without the Top Concept**. In Riccardo Rosati, Sebastian Rudolph, and Michael Zakharyaschev, editors,*Proceedings of the 24th International Workshop on Description Logics (DL 2011)*, volume 745 of*CEUR-WS*, pages 26–36, 2011.Abstract BibTeX Entry PDF File

Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. The inexpressive Description Logic EL is of particular interest in this context since, on the one hand, several large biomedical ontologies are defined using EL. On the other hand, unification in EL has recently been shown to be NP-complete, and thus of considerably lower complexity than unification in other DLs of similarly restricted expressive power. However, EL allows the use of the top concept, which represents the whole interpretation domain, whereas the large medical ontology SNOMED CT makes no use of this feature. Surprisingly, removing the top concept from EL makes the unification problem considerably harder. More precisely, we will show that unification in EL without the top concept is PSpace-complete.

@inproceedings{ BBBM-DL-11, author = {Franz {Baader} and Nguyen Thanh {Binh} and Stefan {Borgwardt} and Barbara {Morawska}}, booktitle = {Proceedings of the 24th International Workshop on Description Logics (DL 2011)}, editor = {Riccardo {Rosati} and Sebastian {Rudolph} and Michael {Zakharyaschev}}, pages = {26--36}, series = {CEUR-WS}, title = {Unification in the Description Logic {$\mathcal{EL}$} without the Top Concept}, volume = {745}, year = {2011}, }

Franz Baader and Rafael Peñaloza:

Abstract BibTeX Entry PDF File ©IEEE Press

**Are Fuzzy Description Logics with General Concept Inclusion Axioms Decidable?**. In*Proceedings of 2011 IEEE International Conference on Fuzzy Systems (Fuzz-IEEE 2011)*, pages 1735–1742. IEEE Press, 2011.Abstract BibTeX Entry PDF File ©IEEE Press

This paper concentrates on a fuzzy Description Logic with product t-norm and involutive negation. It does not answer the question posed in its title for this logic, but it gives strong indications that the answer might in fact be "no." On the one hand, it shows that an algorithm that was claimed to answer the question affirmatively for this logic is actually incorrect. On the other hand, it proves undecidability of a variant of this logic.

@inproceedings{ BaPe-FuzzIEEE11, author = {Franz {Baader} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of 2011 IEEE International Conference on Fuzzy Systems ({Fuzz-IEEE 2011})}, pages = {1735--1742}, publisher = {IEEE Press}, title = {Are Fuzzy Description Logics with General Concept Inclusion Axioms Decidable?}, year = {2011}, }

Franz Baader and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**GCIs Make Reasoning in Fuzzy DL with the Product T-norm Undecidable**. In Riccardo Rosati, Sebastian Rudolph, and Michael Zakharyaschev, editors,*Proceedings of the 24th International Workshop on Description Logics (DL 2011)*, volume 745 of*CEUR-WS*, 2011.Abstract BibTeX Entry PDF File

Fuzzy Description Logics (DLs) have been investigated for at least two decades because they can be used to formalize imprecise concepts. In particular, tableau algorithm for crisp DLs have been extended to reason also with their fuzzy counterparts. Recently, it has been shown that, in the presence of GCIs, some of these fuzzy DLs do not have the finite model property, thus throwing doubt on the correctness of tableau algorithms claimed to handle fuzzy DLs with GCIs. Previously, we have shown that these doubts are indeed justified, by proving that a certain fuzzy DL with product t-norm and involutive negation is undecidable. In this paper, we show that undecidability also holds if we consider a fuzzy DL where disjunction and involutive negation are replaced by the constructor implication, interpreted as the residuum.

@inproceedings{ BaPe-DL11, address = {Barcelona, Spain}, author = {Franz {Baader} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 24th International Workshop on Description Logics (DL 2011)}, editor = {Riccardo {Rosati} and Sebastian {Rudolph} and Michael {Zakharyaschev}}, series = {CEUR-WS}, title = {GCIs Make Reasoning in Fuzzy DL with the Product T-norm Undecidable}, volume = {745}, year = {2011}, }

Franz Baader and Rafael Peñaloza:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**On the Undecidability of Fuzzy Description Logics with GCIs and Product t-norm**. In Cesare Tinelli and Viorica Sofronie-Stokkermans, editors,*Proceedings of 8th International Symposium Frontiers of Combining Systems (FroCoS 2011)*, volume 6989 of*Lecture Notes in Aritificial Intelligence*, pages 55–70. Saarbrücken, Germany, Springer-Verlag, 2011.Abstract BibTeX Entry PDF File ©Springer-Verlag

The combination of Fuzzy Logics and Description Logics (DLs) has been investigated for at least two decades because such fuzzy DLs can be used to formalize imprecise concepts. In particular, tableau algorithms for crisp Description Logics have been extended to reason also with their fuzzy counterparts. Recently, it has been shown that, in the presence of general concept inclusion axioms (GCIs), some of these fuzzy DLs actually do not have the finite model property, thus throwing doubt on the correctness of tableau algorithm for which it was claimed that they can handle fuzzy DLs with GCIs. In a previous paper, we have shown that these doubts are indeed justified, by proving that a certain fuzzy DL with product t-norm and involutive negation is undecidable. In the present paper, we show that undecidability also holds if we consider a t-norm-based fuzzy DL where disjunction and involutive negation are replaced by the constructor implication, which is interpreted as the residuum. The only condition on the t-norm is that it is a continuous t-norm "starting" with the product t-norm, which covers an uncountable family of t-norms.

@inproceedings{ BaPe-FroCoS11, address = {Saarbr{\"u}cken, Germany}, author = {Franz {Baader} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of 8th International Symposium Frontiers of Combining Systems ({FroCoS 2011})}, editor = {Cesare {Tinelli} and Viorica {Sofronie-Stokkermans}}, pages = {55--70}, publisher = {Springer-Verlag}, series = {Lecture Notes in Aritificial Intelligence}, title = {On the Undecidability of Fuzzy Description Logics with GCIs and Product t-norm}, volume = {6989}, year = {2011}, }

Daniel Borchmann and Felix Distel:

Abstract BibTeX Entry PDF File ©IEEE Press

**Mining of**\(\mathcal{EL}\)**-GCIs**. In*The 11th IEEE International Conference on Data Mining Workshops*. Vancouver, Canada, IEEE Computer Society, 11 December 2011.Abstract BibTeX Entry PDF File ©IEEE Press

We consider an existing approach for mining general inclusion axioms written in the lightweight Description Logic EL. In comparison to classical association rule mining, this approach allows more complex patterns to be obtained. Ours is the first implementation of these algorithms for learning Description Logic axioms. We use our implementation for a case study on two real world datasets. We discuss the outcome and examine what further research will be needed for this approach to be applied in a practical setting.

@inproceedings{ BorDi11, address = {Vancouver, Canada}, author = {Daniel {Borchmann} and Felix {Distel}}, booktitle = {The 11th IEEE International Conference on Data Mining Workshops}, month = {11 December}, publisher = {IEEE Computer Society}, title = {Mining of $\mathcal{EL}$-GCIs}, year = {2011}, }

Stefan Borgwardt and Rafael Peñaloza:

Abstract BibTeX Entry PDF File ©IJCAI

**Description Logics over Lattices with Multi-valued Ontologies**. In Toby Walsh, editor,*Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence (IJCAI'11)*, pages 768–773. Barcelona, Spain, AAAI Press, 2011.Abstract BibTeX Entry PDF File ©IJCAI

Uncertainty is unavoidable when modeling most application domains. In medicine, for example, symptoms (such as pain, dizziness, or nausea) are always subjective, and hence imprecise and incomparable. Additionally, concepts and their relationships may be inexpressible in a crisp, clear-cut manner. We extend the description logic ALC with multi-valued semantics based on lattices that can handle uncertainty on concepts as well as on the axioms of the ontology. We introduce reasoning methods for this logic w.r.t. general concept inclusions and show that the complexity of reasoning is not increased by this new semantics.

@inproceedings{ BoPe-IJCAI11, address = {Barcelona, Spain}, author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence ({IJCAI'11})}, editor = {Toby {Walsh}}, pages = {768--773}, publisher = {AAAI Press}, title = {Description Logics over Lattices with Multi-valued Ontologies}, year = {2011}, }

Stefan Borgwardt and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Finite Lattices Do Not Make Reasoning in**\(\mathcal{ALCI}\)**Harder**. In Fernando Bobillo et.al., editor,*Proceedings of the 7th International Workshop on Uncertainty Reasoning for the Semantic Web (URSW'11)*, volume 778 of*CEUR-WS*, pages 51–62, 2011.Abstract BibTeX Entry PDF File

We consider the fuzzy logic ALCI with semantics based on a finite residuated lattice. We show that the problems of satisfiability and subsumption of concepts in this logic are ExpTime-complete w.r.t. general TBoxes and PSpace-complete w.r.t. acyclic TBoxes. This matches the known complexity bounds for reasoning in crisp ALCI.

@inproceedings{ BoPe-URSW11, address = {Bonn, Germany}, author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 7th International Workshop on Uncertainty Reasoning for the Semantic Web ({URSW'11})}, editor = {Fernando Bobillo {et.al.}}, pages = {51--62}, series = {CEUR-WS}, title = {Finite Lattices Do Not Make Reasoning in $\mathcal{ALCI}$ Harder}, volume = {778}, year = {2011}, }

Stefan Borgwardt and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Fuzzy Ontologies over Lattices with T-norms**. In Riccardo Rosati, Sebastian Rudolph, and Michael Zakharyaschev, editors,*Proceedings of the 24th International Workshop on Description Logics (DL 2011)*, volume 745 of*CEUR Workshop Proceedings*, pages 70–80. Barcelona, Spain, CEUR-WS.org, 2011.Abstract BibTeX Entry PDF File

Although fuzzy description logics over total orders and De Morgan lattices have been studied for nearly two decades, only a few, very specific instances of these logics are able to deal with general concept inclusion axioms. In this paper, we describe a general approach for extending description logic semantics to lattice-based fuzzy sets t-norms. We show that this logic is undecidable for a very simple class of infinite lattices, and describe an optimal automata-based algorithm for deciding satisfiability when the lattice is finite.

@inproceedings{ BoPe-DL11, address = {Barcelona, Spain}, author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 24th International Workshop on Description Logics (DL 2011)}, editor = {Riccardo {Rosati} and Sebastian {Rudolph} and Michael {Zakharyaschev}}, pages = {70--80}, publisher = {CEUR-WS.org}, series = {CEUR Workshop Proceedings}, title = {Fuzzy Ontologies over Lattices with T-norms}, volume = {745}, year = {2011}, }

Stefan Borgwardt and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**The Inclusion Problem for Weighted Automata on Infinite Trees**. In Pál Dömösi and Szabolcs Iván, editors,*Proceedings of the 13th International Conference on Automata and Formal Languages (AFL'11)*, pages 108–122. Debrecen, Hungary, College of Nyíregyháza, 2011.Abstract BibTeX Entry PDF File

Weighted automata can be seen as a natural generalization of finite state automata to more complex algebraic structures. The standard reasoning tasks for unweighted automata can also be generalized to the weighted setting. In this paper we study the problems of intersection, complementation and inclusion for weighted automata on infinite trees and show that they are not harder complexity-wise than reasoning with unweighted automata. We also present explicit methods for solving these problems optimally.

@inproceedings{ BoPe-AFL11, address = {Debrecen, Hungary}, author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 13th International Conference on Automata and Formal Languages (AFL'11)}, editor = {P{\'a}l {D{\"o}m{\"o}si} and Szabolcs {Iv{\'a}n}}, pages = {108--122}, publisher = {College of Ny{\'i}regyh{\'a}za}, title = {The Inclusion Problem for Weighted Automata on Infinite Trees}, year = {2011}, }

Felix Distel:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Some Complexity Results about Essential Closed Sets**. In Petko Valtchev and Robert J\"aschke, editors,*International Conference on Formal Concept Analysis*, volume 6628 of*LNCS*, pages 81–92, 2011.Abstract BibTeX Entry PDF File ©Springer-Verlag

We examine the enumeration problem for essential closed sets of a formal context. Essential closed sets are sets that can be written as the closure of a pseudo-intent. The results for enumeration of essential closed sets are similar to existing results for pseudo-intents, albeit some differences exist. For example, while it is possible to compute the lectically first pseudo-intent in polynomial time, we show that it is not possible to compute the lectically first essential closed set in polynomial time unless P = NP. This also proves that essential closed sets cannot be enumerated in the lectic order with polynomial delay unless P = NP. We also look at minimal essential closed sets and show that they cannot be enumerated in output polynomial time unless P = NP.

@inproceedings{ Diste11, author = {Felix {Distel}}, booktitle = {International Conference on Formal Concept Analysis}, editor = {Petko {Valtchev} and Robert {J{\"{}a}schke}}, pages = {81--92}, series = {LNCS}, title = {Some Complexity Results about Essential Closed Sets}, volume = {6628}, year = {2011}, }

Felix Distel and Barış Sertkaya:

Abstract BibTeX Entry ©Elsevier

**On the complexity of enumerating pseudo-intents**.*Discrete Applied Mathematics*, 159(6):450–466, 2011.Abstract BibTeX Entry ©Elsevier

We investigate whether the pseudo-intents of a given formal context can efficiently be enumerated. We show that they cannot be enumerated in a specified lexicographic order with polynomial delay unless P = NP. Furthermore we show that if the restriction on the order of enumeration is removed, then the problem becomes at least as hard as enu- merating minimal transversals of a given hypergraph. We introduce the notion of minimal pseudo-intents and show that recognizing minimal pseudo-intents is polynomial. Despite their less complicated nature, surprisingly it turns out that minimal pseudo-intents cannot be enumerated in output-polynomial time unless P = NP.

@article{ DisSe11, author = {Felix {Distel} and Bar\i{}\c{s} {Sertkaya}}, journal = {Discrete Applied Mathematics}, number = {6}, pages = {450--466}, title = {On the complexity of enumerating pseudo-intents}, volume = {159}, year = {2011}, }

Eldora, Martin Knechtel, and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Correcting Access Restrictions to a Consequence More Flexibly**. In Riccardo Rosati, Sebastian Rudolph, and Michael Zakharyaschev, editors,*Proceedings of the 24th International Workshop on Description Logics (DL 2011)*, volume 745 of*CEUR Workshop Proceedings*, 2011.Abstract BibTeX Entry PDF File

Recent research has shown that labeling ontologies can be useful for restricting the access to some of the axioms and their implicit consequences. However, the labeling of the axioms is an error-prone and highly sensible task. In previous work we have shown how to correct the access restrictions if the security administrator knows the precise access level that a consequence must receive, and axioms are relabeled to that same access level. In this paper, we look at a more general situation in which access rights can be granted or denied to some specific users, without having to fully specify the precise access level. We also allow a more flexible labeling function, where the new access level of the relabeled axioms may differ from the level of the restriction. We provide black-box algorithms for computing suggestions of axioms to be relabeled.

@inproceedings{ ElKP-DL11, author = {{Eldora} and Martin {Knechtel} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 24th International Workshop on Description Logics (DL 2011)}, editor = {Riccardo {Rosati} and Sebastian {Rudolph} and Michael {Zakharyaschev}}, series = {CEUR Workshop Proceedings}, title = {Correcting Access Restrictions to a Consequence More Flexibly}, volume = {745}, year = {2011}, }

Hongkai Liu, Carsten Lutz, Maja Milicic, and Frank Wolter:

Abstract BibTeX Entry PDF File

**Foundations of instance level updates in expressive description logics**.*Artificial Intelligence*, 175(18):2170–2197, 2011.Abstract BibTeX Entry PDF File

In description logic (DL), ABoxes are used for describing the state of affairs in an application domain. We consider the problem of updating ABoxes when the state changes, assuming that update information is described at an atomic level, i.e., in terms of possibly negated ABox assertions that involve only atomic concepts and roles. We analyze such basic ABox updates in several standard DLs, in particular addressing questions of expressibility and succinctness: can updated ABoxes always be expressed in the DL in which the original ABox was formulated and, if so, what is the size of the updated ABox? It turns out that DLs have to include nominals and the ‘@’ constructor of hybrid logic for updated ABoxes to be expressible, and that this still holds when updated ABoxes are approximated. Moreover, the size of updated ABoxes is exponential in the role depth of the original ABox and the size of the update. We also show that this situation improves when updated ABoxes are allowed to contain additional auxiliary symbols. Then, DLs only need to include nominals for updated ABoxes to exist, and the size of updated ABoxes is polynomial in the size of both the original ABox and the update.

@article{ LiLuMiWo-AIJ11, author = {Hongkai {Liu} and Carsten {Lutz} and Maja {Milicic} and Frank {Wolter}}, journal = {Artificial Intelligence}, number = {18}, pages = {2170--2197}, title = {Foundations of instance level updates in expressive description logics}, volume = {175}, year = {2011}, }

Julian Mendez, Andreas Ecke, and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File

**Implementing completion-based inferences for the**\(\mathcal{el}\)**-family**. In Riccardo Rosati, Sebastian Rudolph, and Michael Zakharyaschev, editors,*Proceedings of the international Description Logics workshop*. CEUR, 2011.Abstract BibTeX Entry PDF File

Completion algorithms for subsumption are investigated for many extensions of the description logic EL. While for several of them subsumption is tractable, this is no longer the case, if inverse roles are admitted. In this paper we present an optimized version of the completion algorithm for ELIHFR, which is implemented in jCEL. The completion sets computed during classification are a good substrate for implementing other reasoning services such as generalizations. We report on an extension of jCEL that computes role-depth bounded least common subsumers and most specific concepts based on completion sets.

@inproceedings{ MeEcTu-DL11, author = {Julian {Mendez} and Andreas {Ecke} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of the international Description Logics workshop}, editor = {Riccardo {Rosati} and Sebastian {Rudolph} and Michael {Zakharyaschev}}, publisher = {CEUR}, title = {Implementing completion-based inferences for the {$\mathcal{el}$}-family}, volume = {745}, year = {2011}, }

R. Peñaloza and A.-Y. Turhan:

Abstract BibTeX Entry PDF File

**A Practical Approach for Computing Generalization Inferences in**\({\mathcal{EL}}\). In Marko Grobelnik and Elena Simperl, editors,*Proceedings of the 8th European Semantic Web Conference (ESWC'11)*,*Lecture Notes in Computer Science*. Springer-Verlag, 2011.Abstract BibTeX Entry PDF File

We present methods that compute generalizations of concepts or individuals described in ontologies written in the Description Logic EL. These generalizations are the basis of methods for ontology design and are the core of concept similarity measures. The reasoning service least common subsumer (lcs) generalizes a set of concepts. Similarly, the most specific concept (msc) generalizes an individual into a concept description. For EL the lcs and the msc do not need to exist, if computed w.r.t. general EL-TBoxes. However, it is possible to find a concept description that is the lcs (msc) up to a certain role-depth. In this paper we present a practical approach for computing the role-depth bounded lcs and msc, based on the polynomial-time completion algorithm for EL and describe its implementation.

@inproceedings{ PeTu-ESWC11, author = {R. {Pe{\~n}aloza} and A.-Y. {Turhan}}, booktitle = {Proceedings of the 8th European Semantic Web Conference ({ESWC'11})}, editor = {Marko {Grobelnik} and Elena {Simperl}}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {A Practical Approach for Computing Generalization Inferences in {${\mathcal{EL}}$}}, year = {2011}, }

Uwe Ryssel, Felix Distel, and Daniel Borchmann:

Abstract BibTeX Entry PDF File

**Fast Computation of Proper Premises**. In Amedeo Napoli and Vilem Vychodil, editors,*International Conference on Concept Lattices and Their Applications*, pages 101–113. INRIA Nancy – Grand Est and LORIA, 2011.Abstract BibTeX Entry PDF File

This work is motivated by an application related to refactoring of model variants. In this application an implicational base needs to be computed, and runtime is more crucial than minimal cardinality. Since the usual stem base algorithms have proven to be too costly in terms of runtime, we have developed a new algorithm for the fast computation of proper premises. It is based on a known link between proper premises and minimal hypergraph transversals. Two further improvements are made, which reduce the number of proper premises that are obtained multiple times and redundancies within the set of proper premises. We provide heuristic evidence that an approach based on proper premises will also be beneficial for other applications.

@inproceedings{ RyDiB11, author = {Uwe {Ryssel} and Felix {Distel} and Daniel {Borchmann}}, booktitle = {International Conference on Concept Lattices and Their Applications}, editor = {Amedeo {Napoli} and Vilem {Vychodil}}, pages = {101--113}, publisher = {INRIA Nancy -- Grand Est and LORIA}, title = {Fast Computation of Proper Premises}, year = {2011}, }

Anni-Yasmin Turhan:

BibTeX Entry PDF File

**Description Logic reasoning for Semantic Web Ontologies – Extended abstract**. In Rajendra Akerkar, editor,*Proceedings of the first International Conference on Web Intelligence, Mining and Semantics*. ACM, 2011.BibTeX Entry PDF File

@inproceedings{ Tu-WIMS11, author = {Anni-Yasmin {Turhan}}, booktitle = {Proceedings of the first International Conference on Web Intelligence, Mining and Semantics}, editor = {Rajendra {Akerkar}}, publisher = {ACM}, title = {Description Logic reasoning for Semantic Web Ontologies -- Extended abstract}, year = {2011}, }

## 2010

Franz Baader, Bernhard Beckert, and Tobias Nipkow:

BibTeX Entry (The final publication is available at link.springer.com)

**Deduktion: von der Theorie zur Anwendung**.*Informatik-Spektrum*, 33(5):444–451, 2010.BibTeX Entry (The final publication is available at link.springer.com)

@article{ BaBeNi-IS-10, author = {Franz {Baader} and Bernhard {Beckert} and Tobias {Nipkow}}, journal = {Informatik-Spektrum}, number = {5}, pages = {444--451}, title = {Deduktion: von der {T}heorie zur {A}nwendung}, volume = {33}, year = {2010}, }

Franz Baader, Meghyn Bienvenu, Carsten Lutz, and Frank Wolter:

Abstract BibTeX Entry PDF File

**Query and Predicate Emptiness in Description Logics**. In Fangzhen Lin and Ulrike Sattler, editors,*Proceedings of the 12th International Conference on Principles of Knowledge Representation and Reasoning (KR2010)*. AAAI Press, 2010.Abstract BibTeX Entry PDF File

Ontologies can be used to provide an enriched vocabulary for the formulation of queries over instance data. We identify query emptiness and predicate emptiness as two central reasoning services in this context. Query emptiness asks whether a given query has an empty answer over all data sets formulated in a given signature. Predicate emptiness is defined analogously, but quantifies universally over all queries that contain a given predicate. In this paper, we determine the computational complexity of query emptiness and predicate emptiness in the EL, DL-Lite, and ALC-families of description logics, investigate the connection to ontology modules, and perform a practical case study to evaluate the new reasoning services.

@inproceedings{ BaaderBLW10, author = {Franz {Baader} and Meghyn {Bienvenu} and Carsten {Lutz} and Frank {Wolter}}, booktitle = {Proceedings of the 12th International Conference on Principles of Knowledge Representation and Reasoning ({KR2010})}, editor = {Fangzhen {Lin} and Ulrike {Sattler}}, publisher = {AAAI Press}, title = {Query and Predicate Emptiness in Description Logics}, year = {2010}, }

Franz Baader, Marcel Lippmann, and Hongkai Liu:

Abstract BibTeX Entry PDF File (The final publication is available at link.springer.com)

**Using Causal Relationships to Deal with the Ramification Problem in Action Formalisms Based on Description Logics**. In Christian G. Fermüller and Andrei Voronkov, editors,*Proceedings of the 17th International Conference on Logic for Programming, Artifical Intelligence, and Reasoning (LPAR-17)*, volume 6397 of*Lecture Notes in Computer Science (subline Advanced Research in Computing and Software Science)*, pages 82–96. Yogyakarta, Indonesia, Springer-Verlag, October 2010.Abstract BibTeX Entry PDF File (The final publication is available at link.springer.com)

In the reasoning about actions community, causal relationships have been proposed as a possible approach for solving the ramification problem, i.e., the problem of how to deal with indirect effects of actions. In this paper, we show that causal relationships can be added to action formalisms based on Description Logics (DLs) without destroying the decidability of the consistency and the projection problem. We investigate the complexity of these decision problems based on which DL is used as base logic for the action formalism.

@inproceedings{ BaLiLi-LPAR-10, address = {Yogyakarta, Indonesia}, author = {Franz {Baader} and Marcel {Lippmann} and Hongkai {Liu}}, booktitle = {Proceedings of the 17th International Conference on Logic for Programming, Artifical Intelligence, and Reasoning ({LPAR-17})}, editor = {Christian G. {Ferm{\"u}ller} and Andrei {Voronkov}}, month = {October}, pages = {82--96}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science (subline Advanced Research in Computing and Software Science)}, title = {Using Causal Relationships to Deal with the Ramification Problem in Action Formalisms Based on Description Logics}, volume = {6397}, year = {2010}, }

Franz Baader, Hongkai Liu, and Anees ul Mehdi:

Abstract BibTeX Entry PDF File

**Verifying Properties of Infinite Sequences of Description Logic Actions**. In Helder Coelho, Rudi Studer, and Michael Wooldridge, editors,*Proceedings of the 19th European Conference on Artificial Intelligence (ECAI10)*, volume 215 of*Frontiers in Artificial Intelligence and Applications*, pages 53–58. IOS Press, 2010.Abstract BibTeX Entry PDF File

The verification problem for action logic programs with non-terminating behaviour is in general undecidable. In this paper, we consider a restricted setting in which the problem becomes decidable. On the one hand, we abstract from the actual execution sequences of a non-terminating program by considering infinite sequences of actions defined by a Buechi automaton. On the other hand, we assume that the logic underlying our action formalism is a decidable description logic rather than full first-order predicate logic.

@inproceedings{ BaLiMe-ECAI10, author = {Franz {Baader} and Hongkai {Liu} and Anees ul {Mehdi}}, booktitle = {Proceedings of the 19th European Conference on Artificial Intelligence ({ECAI10})}, editor = {Helder {Coelho} and Rudi {Studer} and Michael {Wooldridge}}, pages = {53--58}, publisher = {IOS Press}, series = {Frontiers in Artificial Intelligence and Applications}, title = {Verifying Properties of Infinite Sequences of Description Logic Actions}, volume = {215}, year = {2010}, }

Franz Baader, Carsten Lutz, and Anni-Yasmin Turhan:

BibTeX Entry PDF File (The final publication is available at link.springer.com)

**Small is again Beautiful in Description Logics**.*KI – Künstliche Intelligenz*, 24(1):25–33, 2010.BibTeX Entry PDF File (The final publication is available at link.springer.com)

@article{ BaLuTu-KIJ-10, author = {Franz {Baader} and Carsten {Lutz} and Anni-Yasmin {Turhan}}, journal = {KI -- K{\"u}nstliche Intelligenz}, month = {April}, number = {1}, pages = {25--33}, title = {Small is again Beautiful in Description Logics}, volume = {24}, year = {2010}, }

Franz Baader and Barbara Morawska:

Abstract BibTeX Entry PDF File (The final publication is available at link.springer.com)

**SAT Encoding of Unification in EL**. In Christian G. Fermüller and Andrei Voronkov, editors,*Proceedings of the 17th International Conference on Logic for Programming, Artifical Intelligence, and Reasoning (LPAR-17)*, volume 6397 of*Lecture Notes in Computer Science (subline Advanced Research in Computing and Software Science)*, pages 97–111. Yogyakarta, Indonesia, Springer-Verlag, October 2010.Abstract BibTeX Entry PDF File (The final publication is available at link.springer.com)

Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. In a recent paper, we have shown that unification in EL is NP-complete, and thus of a complexity that is considerably lower than in other Description Logics of comparably restricted expressive power. In this paper, we introduce a new NP-algorithm for solving unification problems in EL, which is based on a reduction to satisfiability in propositional logic (SAT). The advantage of this new algorithm is, on the one hand, that it allows us to employ highly optimized state-of-the-art SAT solvers when implementing an EL-unification algorithm. On the other hand, this reduction provides us with a proof of the fact that EL-unification is in NP that is much simpler than the one given in our previous paper on EL-unification.

@inproceedings{ BaMo-LPAR-10, address = {Yogyakarta, Indonesia}, author = {Franz {Baader} and Barbara {Morawska}}, booktitle = {Proceedings of the 17th International Conference on Logic for Programming, Artifical Intelligence, and Reasoning ({LPAR-17})}, editor = {Christian G. {Ferm{\"u}ller} and Andrei {Voronkov}}, month = {October}, pages = {97--111}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science (subline Advanced Research in Computing and Software Science)}, title = {SAT Encoding of Unification in EL}, volume = {6397}, year = {2010}, }

Franz Baader and Barbara Morawska:

Abstract BibTeX Entry PDF File

**Unification in the Description Logic**\(\mathcal{EL}\).*Logical Methods in Computer Science*, 6(3), 2010. Special Issue of the 20th International Conference on Rewriting Techniques and Applications; also available at http://arxiv.org/abs/1006.2289Abstract BibTeX Entry PDF File

Abstract: The Description Logic EL has recently drawn considerable attention since, on the one hand, important inference problems such as the subsumption problem are polynomial. On the other hand, EL is used to define large biomedical ontologies. Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. The main result of this paper is that unification in EL is decidable. More precisely, EL-unification is NP-complete, and thus has the same complexity as EL-matching. We also show that, w.r.t. the unification type, EL is less well-behaved: it is of type zero, which in particular implies that there are unification problems that have no finite complete set of unifiers.

@article{ Ba-Mo-LMCS-10, author = {Franz {Baader} and Barbara {Morawska}}, journal = {Logical Methods in Computer Science}, note = {Special Issue of the 20th International Conference on Rewriting Techniques and Applications; also available at http://arxiv.org/abs/1006.2289}, number = {3}, title = {Unification in the Description Logic {$\mathcal{EL}$}}, volume = {6}, year = {2010}, }

Franz Baader and Rafael Peñaloza:

Abstract BibTeX Entry PDF File (The final publication is available at link.springer.com)

**Automata-based Axiom Pinpointing**.*Journal of Automated Reasoning*, 45(2):91–129, 2010. Special Issue: Selected Papers from IJCAR 2008Abstract BibTeX Entry PDF File (The final publication is available at link.springer.com)

Axiom pinpointing has been introduced in description logics (DL) to help the user understand the reasons why consequences hold by computing minimal subsets of the knowledge base that have the consequence in question (MinA). Most of the pinpointing algorithms described in the DL literature are obtained as extensions of tableau-based reasoning algorithms for computing consequences from DL knowledge bases. In this paper, we show that automata-based algorithms for reasoning in DLs and other logics can also be extended to pinpointing algorithms. The idea is that the tree automaton constructed by the automata-based approach can be transformed into a weighted tree automaton whose so-called behaviour yields a pinpointing formula, i.e., a monotone Boolean formula whose minimal valuations correspond to the MinAs. We also develop an approach for computing the behaviour of a given weighted tree automaton. We use the DL İ as well as Linear Temporal Logic (LTL) to illustrate our new pinpointing approach.

@article{ BaPe-JAR09, author = {Franz {Baader} and Rafael {Pe{\~n}aloza}}, journal = {Journal of Automated Reasoning}, month = {August}, note = {Special Issue: Selected Papers from IJCAR~2008}, number = {2}, pages = {91--129}, title = {Automata-based Axiom Pinpointing}, volume = {45}, year = {2010}, }

Franz Baader and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Axiom Pinpointing in General Tableaux**.*Journal of Logic and Computation*, 20(1):5–34, 2010. Special Issue: Tableaux and Analytic Proof MethodsAbstract BibTeX Entry PDF File

Axiom pinpointing has been introduced in description logics (DLs) to help the user to understand the reasons why consequences hold and to remove unwanted consequences by computing minimal (maximal) subsets of the knowledge base that have (do not have) the consequence in question. Most of the pinpointing algorithms described in the DLliterature are obtained as extensions of the standard tableau-based reasoning algorithms for computing consequences from DL knowledge bases. Although these extensions are based on similar ideas, they are all introduced for a particular tableau-based algorithm for a particular DL. The purpose of this article is to develop a general approach for extending a tableau-based algorithm to a pinpointing algorithm. This approach is based on a general definition of tableau algorithms, which captures many of the known tableau-based algorithms employed in DLs, but also other kinds of reasoning procedures.

@article{ BaaPen-JLC10, author = {Franz {Baader} and Rafael {Pe{\~n}aloza}}, journal = {Journal of Logic and Computation}, note = {Special Issue: Tableaux and Analytic Proof Methods}, number = {1}, pages = {5--34}, title = {Axiom Pinpointing in General Tableaux}, volume = {20}, year = {2010}, }

Felix Distel:

Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

**An Approach to Exploring Description Logic Knowledge Bases**. In Barış Sertkaya and Léonard Kwuida, editors,*Proceedings of the 8th International Conference on Formal Concept Analysis, (ICFCA 2010)*, volume 5986 of*Lecture Notes in Artificial Intelligence*, pages 209–224. Springer, 2010.Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

This paper is the successor to two previous papers published at the ICFCA conference. In the first paper we have shown that in the Description Logics EL and ELgfp , the set of general concept inclusions holding in a finite model always has a finite basis. An exploration formalism that can be used to obtain this basis was presented in the second paper. In this paper we show how this formalism can be modified such that counterexamples to GCIs can be provided in the form of ABox- individuals. In a second part of the paper we examine which description logics can be used for this ABox.

@inproceedings{ Distel-ICFCA-10b, author = {Felix {Distel}}, booktitle = {Proceedings of the 8th International Conference on Formal Concept Analysis, (ICFCA 2010)}, editor = {Bar\i{}{\c{s}} {Sertkaya} and L\'eonard {Kwuida}}, pages = {209--224}, publisher = {Springer}, series = {Lecture Notes in Artificial Intelligence}, title = {An Approach to Exploring Description Logic Knowledge Bases}, volume = {5986}, year = {2010}, }

Felix Distel:

Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

**Hardness of Enumerating Pseudo-Intents in the Lectic Order**. In Barış Sertkaya and Léonard Kwuida, editors,*Proceedings of the 8th International Conference on Formal Concept Analysis, (ICFCA 2010)*, volume 5986 of*Lecture Notes in Artificial Intelligence*, pages 124–137. Springer, 2010.Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

We investigate the complexity of enumerating pseudo-intents in the lectic order. We look at the following decision problem: Given a formal context and a set of n pseudo-intents determine whether they are the lectically first n pseudo-intents. We show that this problem is coNP-hard. We thereby show that there cannot be an algorithm with a good theoretical complexity for enumerating pseudo-intents in a lectic order. In a second part of the paper we introduce the notion of minimal pseudo-intents, i.e. pseudo-intents that do not strictly contain a pseudo-intent. We provide some complexity results about minimal pseudo-intents that are readily obtained from the previous result.

@inproceedings{ Distel-ICFCA-10, author = {Felix {Distel}}, booktitle = {Proceedings of the 8th International Conference on Formal Concept Analysis, (ICFCA 2010)}, editor = {Bar\i{}{\c{s}} {Sertkaya} and L\'eonard {Kwuida}}, pages = {124--137}, publisher = {Springer}, series = {Lecture Notes in Artificial Intelligence}, title = {Hardness of Enumerating Pseudo-Intents in the Lectic Order}, volume = {5986}, year = {2010}, }

Martin Knechtel and Rafael Peñaloza:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**A Generic Approach for Correcting Access Restrictions to a Consequence**. In Lora Aroyo, Grigoris Antoniou, Eero Hyvönen, Annette ten Teije, Heiner Stuckenschmidt, Liliana Cabral, and Tania Tudorache, editors,*Proceedings of the 7th Extended Semantic Web Conference (ESWC 2010)*, volume 6088 of*Lecture Notes in Computer Science*, pages 167–182, 2010.Abstract BibTeX Entry PDF File ©Springer-Verlag

Recent research has shown that annotations are useful for representing access restrictions to the axioms of an ontology and their implicit consequences. Previous work focused on assigning a label, representing its access level, to each consequence from a given ontology. However, a security administrator might not be satisfied with the access level obtained through these methods. In this case, one is interested in finding which axioms would need to get their access restrictions modified in order to get the desired label for the consequence. In this paper we look at this problem and present algorithms for solving it with a variety of optimizations. We also present first experimental results on large scale ontologies, which show that our methods perform well in practice.

@inproceedings{ KnPe-ESWC-10, author = {Martin {Knechtel} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 7th Extended Semantic Web Conference (ESWC 2010)}, editor = {Lora {Aroyo} and Grigoris {Antoniou} and Eero {Hyv{\"o}nen} and Annette ten {Teije} and Heiner {Stuckenschmidt} and Liliana {Cabral} and Tania {Tudorache}}, pages = {167--182}, series = {Lecture Notes in Computer Science}, title = {A Generic Approach for Correcting Access Restrictions to a Consequence}, volume = {6088}, year = {2010}, }

Martin Knechtel and Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Correcting Access Restrictions to a Consequence**. In Volker Haarslev, David Toman, and Grant Weddell, editors,*Proceedings of the 23rd International Workshop on Description Logics (DL 2010)*, volume 573 of*CEUR-WS*, pages 220–231, 2010.Abstract BibTeX Entry PDF File

Recent research has shown that annotations are useful for representing access restrictions to the axioms of an ontology and their implicit consequences. Previous work focused on computing a consequence's access restriction efficiently from the restrictions of its implying axioms. However, a security administrator might not be satisfied since the intended restriction differs from the one obtained through these methods. In this case, one is interested in finding a minimal set of axioms which need changed restrictions. In this paper we look at this problem and present algorithms based on ontology repair for solving it. Our first experimental results on large scale ontologies show that our methods perform well in practice.

@inproceedings{ KnPe-DL-10, author = {Martin {Knechtel} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 23rd International Workshop on Description Logics (DL 2010)}, editor = {Volker {Haarslev} and David {Toman} and Grant {Weddell}}, pages = {220--231}, series = {CEUR-WS}, title = {Correcting Access Restrictions to a Consequence}, volume = {573}, year = {2010}, }

Martin Knechtel and Heiner Stuckenschmidt:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Query-Based Access Control for Ontologies**. In P. Hitzler and T. Lukasiewicz, editors,*Proceedings of the 4th International Conference on Web Reasoning and Rule Systems (RR 2010)*, volume 6333 of*Lecture Notes in Computer Science*, pages 73–87, 2010.Abstract BibTeX Entry PDF File ©Springer-Verlag

Role-based access control is a standard mechanism in information systems. Based on the role a user has, certain information is kept from the user even if requested. For ontologies representing knowledge, deciding what can be told to a user without revealing secrets is more difficult as the user might be able to infer secret knowledge using logical reasoning. In this paper, we present two approaches to solving this problem: query rewriting vs. axiom filtering, and show that while both approaches prevent the unveiling of secret knowledge, axiom filtering is more complete in the sense that it does not suppress knowledge the user is allowed to see while this happens frequently in query rewriting. Axiom filtering requires that each axiom carries a label representing its access level. We present methods to find an optimal axiom labeling to enforce query-based access restrictions and report experiments on real world data showing that a significant number of results are retained using the axiom filtering method.

@inproceedings{ KnSt-RR-10, author = {Martin {Knechtel} and Heiner {Stuckenschmidt}}, booktitle = {Proceedings of the 4th International Conference on Web Reasoning and Rule Systems (RR 2010)}, editor = {P. {Hitzler} and T. {Lukasiewicz}}, pages = {73--87}, series = {Lecture Notes in Computer Science}, title = {Query-Based Access Control for Ontologies}, volume = {6333}, year = {2010}, }

Thomas Lukasiewicz, Rafael Peñaloza, and Anni-Yasmin Turhan, editors:

Abstract BibTeX Entry

**Proceedings of the First International Workshop on Uncertainty in Description Logics**, number 613 in CEUR, July 2010. UniDL is a IJCAR collocated FLoC workshop. See http://sunsite.informatik.rwth-aachen.de/Publications/CEUR-WS/Vol-613/Abstract BibTeX Entry

During the recent decade, handling uncertainty has started to play an important role in ontology languages, especially in application areas like the Semantic Web, biomedicine, and artificial intelligence. For this reason, there is currently a strong research interest in description logics (DLs) that allow for dealing with uncertainty. The subject of the workshop is how to deal with uncertainty and imprecision in DLs. This encompasses approaches that enable probabilistic or fuzzy reasoning in DLs, but the workshop is also open for approaches based on other uncertainty formalisms. The workshop focusses on the investigation of reasoning problems and approaches for solving them, including especially tractable ones. For classical DL reasoning problems such as subsumption and satisfiability, algorithms that can handle uncertainty exist, but they are still less well-investigated than in the case of standard DLs without uncertainty. For novel reasoning services, such as query answering, computation of generalizations, modules, or explanations, it is not yet clear how to realize them in DLs that can express uncertainty.

@proceedings{ UniDL-10, editor = {Thomas {Lukasiewicz} and Rafael {Pe{\~n}aloza} and Anni-Yasmin {Turhan}}, month = {July}, note = {UniDL is a IJCAR collocated FLoC workshop. See http://sunsite.informatik.rwth-aachen.de/Publications/CEUR-WS/Vol-613/}, number = {613}, series = {CEUR}, title = {Proceedings of the First International Workshop on Uncertainty in Description Logics}, year = {2010}, }

Rafael Peñaloza:

Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

**Using Sums-of-Products for Non-standard Reasoning**. In A.-H. Dediu, H. Fernau, and C. Martín-Vide, editors,*Proceedings of the 4th International Conference on Language and Automata Theory and Applications (LATA 2010)*, volume 6031 of*Lecture Notes in Computer Science*, pages 488–499. Springer-Verlag, 2010.Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

An important portion of the current research in Description Logics is devoted to the expansion of the reasoning services and the developement of algorithms that can adequatedly perform so-called non-standard reasoning. Applications of non-standard reasoning services cover a wide selection of areas such as access control, agent negotiation, or uncertainty reasoning, to name just a few. In this paper we show that some of these non-standard inferences can be seen as the computation of a sum of products, where ``sum'' and ``product'' are the two operators of a bimonoid. We then show how the main ideas of automata-based axiom-pinpointing, combined with weighted model counting, yield a generic method for computing sums-of-products over arbitrary bimonoids.

@inproceedings{ Pena10, author = {Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 4th International Conference on Language and Automata Theory and Applications ({LATA 2010})}, editor = {A.-H. {Dediu} and H. {Fernau} and C. {Mart{\'i}n-Vide}}, pages = {488--499}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Using Sums-of-Products for Non-standard Reasoning}, volume = {6031}, year = {2010}, }

Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Wie findet man die verantwortliche Axiome? Axiom-Pinpointing in Beschreibungslogiken**. In*Ausgezeichnete Informatikdissertationen 2009*, volume D10 of*Lecture Notes in Informatics*, pages 181–190. Germany, Gesellschaft für Informatik, 2010. In germanAbstract BibTeX Entry PDF File

Axiom-Pinpointing bestimmt die für eine Konsequenz verantwortlichen Axiome einer Ontologie und unterstützt dadurch die Suche und Behebung von Fehlern. In der Dissertation von Rafael Peñaloza, deren Resultate hier zusammengefasst werden, wurde untersucht, unter welchen Bedingungen sich tableau-artige und auf automaten-basierte Schlussfolgerungsverfahren für Beschreibungslogiken stets zu Pinpointing-Verfahren erweitern lassen. Zusätzlich wurde die Komplexität des Pinpointing-Problems erforscht.

@inproceedings{ Pena-GI10, address = {Germany}, author = {Rafael {Pe{\~n}aloza}}, booktitle = {Ausgezeichnete Informatikdissertationen 2009}, note = {In german}, pages = {181--190}, publisher = {Gesellschaft f{\"u}r Informatik}, series = {Lecture Notes in Informatics}, title = {Wie findet man die verantwortliche {A}xiome? {A}xiom-{P}inpointing in {B}eschreibungslogiken}, volume = {D10}, year = {2010}, }

Rafael Peñaloza and Barış Sertkaya:

Abstract BibTeX Entry PDF File

**Complexity of Axiom Pinpointing in the DL-Lite Family**. In Volker Haarslev, David Toman, and Grant Weddell, editors,*Proceedings of the 2010 International Workshop on Description Logics (DL2010)*, volume 573 of*CEUR-WS*, 2010.Abstract BibTeX Entry PDF File

We investigate the computational complexity of axiom pinpointing in the DL-Lite family, which has been very popular due to its success in efficiently accessing large data and answering complex queries. We consider the problem of explaining TBox reasoning. We investigate in detail the complexity of enumerating MinAs in a DL-Lite TBox for a given consequence of this TBox. We show that for DL-Lite_{c}ore^{H}, DL-Lite_{k}rom^{H}and DL-Lite_{h}orn^{N}TBoxes MinAs are efficiently enumerable with polynomial delay, but for DL-Lite_{b}ool they cannot be enumerated in output-polynomial time unless P = NP.

@inproceedings{ PeSe-DL10, author = {Rafael {Pe{\~n}aloza} and Bar\i{}\c{s} {Sertkaya}}, booktitle = {Proceedings of the 2010 International Workshop on Description Logics ({DL2010})}, editor = {Volker {Haarslev} and David {Toman} and Grant {Weddell}}, series = {CEUR-WS}, title = {Complexity of Axiom Pinpointing in the DL-Lite Family}, volume = {573}, year = {2010}, }

Rafael Peñaloza and Barış Sertkaya:

Abstract BibTeX Entry PDF File

**Complexity of Axiom Pinpointing in the DL-Lite Family of Description Logics**. In Helder Coelho, Rudi Studer, and Michael Wooldridge, editors,*Proceedings of the 19th European Conference on Artificial Intelligence (ECAI 2010)*, volume 215 of*Frontiers in Artificial Intelligence and Applications*, pages 29–34. IOS Press, 2010.Abstract BibTeX Entry PDF File

We investigate the complexity of axiom pinpointing for different members of the DL-Lite family of Description Logics. More precisely, we consider the problem of enumerating all minimal subsets of a given DL-Lite knowledge base that have a given consequence. We show that for the DL-Lite_{core}^{H}, DL-Lite_{krom}^{H}and DL-Lite_{horn}^{HN}fragments such minimal subsets are efficiently enumerable with polynomial delay, but for the DL-Lite_{bool}fragment they cannot be enumerated in output polynomial time unless = . We also show that interestingly, for the DL-Lite_{horn}^{HN}fragment such minimal sets can be enumerated in reverse lexicographic order with polynomial delay, but it is not possible in the forward lexicographic order since computing the first one is already -hard.

@inproceedings{ PeSe-ECAI10, author = {Rafael {Pe{\~n}aloza} and Bar\i{}\c{s} {Sertkaya}}, booktitle = {Proceedings of the 19th European Conference on Artificial Intelligence ({ECAI 2010})}, editor = {Helder {Coelho} and Rudi {Studer} and Michael {Wooldridge}}, pages = {29--34}, publisher = {IOS Press}, series = {Frontiers in Artificial Intelligence and Applications}, title = {Complexity of Axiom Pinpointing in the DL-Lite Family of Description Logics}, volume = {215}, year = {2010}, }

Rafael Peñaloza and Barış Sertkaya:

Abstract BibTeX Entry PDF File

**On the Complexity of Axiom Pinpointing in the EL Family of Description Logics**. In Fangzhen Lin, Ulrike Sattler, and Miroslaw Truszczynski, editors,*Proceedings of the Twelfth International Conference on Principles of Knowledge Representation and Reasoning (KR 2010)*. AAAI Press, 2010.Abstract BibTeX Entry PDF File

We investigate the computational complexity of axiom pinpointing, which is the task of finding minimal subsets of a Description Logic knowledge base that have a given consequence. We consider the problems of enumerating such subsets with and without order, and show hardness results that already hold for the propositional Horn fragment, or for the Description Logic . We show complexity results for several other related decision and enumeration problems for these fragments that extend to more expressive logics. In particular we show that hardness of these problems depends not only on expressivity of the fragment but also on the shape of the axioms used.

@inproceedings{ PeSe-KR10, author = {Rafael {Pe{\~n}aloza} and Bar\i{}\c{s} {Sertkaya}}, booktitle = {Proceedings of the Twelfth International Conference on Principles of Knowledge Representation and Reasoning ({KR 2010})}, editor = {Fangzhen {Lin} and Ulrike {Sattler} and Miroslaw {Truszczynski}}, publisher = {AAAI Press}, title = {On the Complexity of Axiom Pinpointing in the EL Family of Description Logics}, year = {2010}, }

Rafael Peñaloza and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File

**Role-depth Bounded Least Common Subsumers by Completion for**\(\mathcal{EL}\)**- and Prob-**\({\mathcal{EL}}\)**-TBoxes**. In V. Haarslev, D. Toman, and G. Weddell, editors,*Proc. of the 2010 Description Logic Workshop (DL'10)*, volume 573 of*CEUR-WS*, 2010.Abstract BibTeX Entry PDF File

The least common subsumer (lcs) w.r.t general EL-TBoxes does not need to exists in general due to cyclic axioms. In this paper we present an algorithm for computing role-depth bounded EL-lcs based on the completion algorithm for . We extend this computation algorithm to a recently introduced probabilistic variant of EL: Prob-EL^{0}1.

@inproceedings{ PenTur-dl10, author = {Rafael {Pe{\~n}aloza} and Anni-Yasmin {Turhan}}, booktitle = {Proc.\ of the 2010 Description Logic Workshop (DL'10)}, editor = {V. {Haarslev} and D. {Toman} and G. {Weddell}}, series = {CEUR-WS}, title = {Role-depth Bounded Least Common Subsumers by Completion for {$\mathcal{EL}$}- and {Prob-${\mathcal{EL}}$}-{TBoxes}}, volume = {573}, year = {2010}, }

Rafael Peñaloza and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File PS File

**Towards Approximative Most Specific Concepts by Completion for EL with Subjective Probabilities**. In Thomas Lukasiewicz, Rafael Peñaloza, and Anni-Yasmin Turhan, editors,*Proceedings of the First International Workshop on Uncertainty in Description Logics (UniDL'10)*, volume 613 of*CEUR-WS*, 2010.Abstract BibTeX Entry PDF File PS File

The most specific concept (msc) w.r.t general EL-TBoxes does not need to exists in general due to cyclic axioms. In this paper we present an algorithm for computing role-depth bounded EL-msc based on the completion algorithm for . We extend this computation algorithm to a recently introduced probabilistic variant of EL: Prob-EL^{0}1.

@inproceedings{ PenTur-unidl10, author = {Rafael {Pe{\~n}aloza} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of the First International Workshop on Uncertainty in Description Logics (UniDL'10)}, editor = {Thomas {Lukasiewicz} and Rafael {Pe{\~n}aloza} and Anni-Yasmin {Turhan}}, series = {CEUR-WS}, title = {Towards Approximative Most Specific Concepts by Completion for EL with Subjective Probabilities}, volume = {613}, year = {2010}, }

Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Reasoning and Explanation in**\(\mathcal EL\)**and in Expressive Description Logics**. In Uwe Aßmann, Andreas Bartho, and Christian Wende, editors,*Reasoning Web*, number 6325 in*LNCS*, pages 1–27. Springer, 2010.Abstract BibTeX Entry PDF File ©Springer-Verlag

Description Logics (DLs) are the formalism underlying the standard web ontology language OWL 2. DLs have formal semantics which are the basis for powerful reasoning services. In this paper, we introduce the basic notions of DLs and the techniques that realize subsumption — the fundamental reasoning service of DL systems. We discuss two reasoning methods for this service: the tableau method for expressive DLs such as ALC and the completion method for the light-weight DL El. We also present methods for generating explanations for computed subsumption relationships in these two DLs.

@incollection{ Tur-RW10, author = {Anni-Yasmin {Turhan}}, booktitle = {Reasoning Web}, editor = {Uwe {A{\"s}mann} and Andreas {Bartho} and Christian {Wende}}, number = {6325}, pages = {1--27}, publisher = {Springer}, series = {LNCS}, title = {Reasoning and Explanation in {$\mathcal EL$} and in Expressive Description Logics}, year = {2010}, }

## 2009

Franz Baader:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Description Logics**. In*Reasoning Web: Semantic Technologies for Information Systems, 5th International Summer School 2009*, volume 5689 of*Lecture Notes in Computer Science*, pages 1–39. Springer–Verlag, 2009.Abstract BibTeX Entry PDF File ©Springer-Verlag

Description Logics (DLs) are a well-investigated family of logic-based knowledge representation formalisms, which can be used to represent the conceptual knowledge of an application domain in a structured and formally well-understood way. They are employed in various application domains, such as natural language processing, configuration, and databases, but their most notable success so far is the adoption of the DL-based language OWL as standard ontology language for the semantic web. This article concentrates on the problem of designing reasoning procedures for DLs. After a short introduction and a brief overview of the research in this area of the last 20 years, it will on the one hand present approaches for reasoning in expressive DLs, which are the foundation for reasoning in the Web ontology language OWL DL. On the other hand, it will consider tractable reasoning in the more light-weight DL EL, which is employed in bio-medical ontologies, and which is the foundation for the OWL 2 profile OWL 2 EL.

@incollection{ Baader09, author = {Franz {Baader}}, booktitle = {Reasoning Web: Semantic Technologies for Information Systems, 5th International Summer School 2009}, pages = {1--39}, publisher = {Springer--Verlag}, series = {Lecture Notes in Computer Science}, title = {Description Logics}, volume = {5689}, year = {2009}, }

Franz Baader, Andreas Bauer, Peter Baumgartner, Anne Cregan, Alfredo Gabaldon, Krystian Ji, Kevin Lee, David Rajaratnam, and Rolf Schwitter:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**A Novel Architecture for Situation Awareness Systems**. In Martin Giese and Arild Waaler, editors,*Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (Tableaux 2009)*, volume 5607 of*Lecture Notes in Computer Science*, pages 77–92. Springer-Verlag, 2009.Abstract BibTeX Entry PDF File ©Springer-Verlag

Situation Awareness (SA) is the problem of comprehending elements of an environment within a volume of time and space. It is a crucial factor in decision-making in dynamic environments. Current SA systems support the collection, filtering and presentation of data from different sources very well, and typically also some form of low-level data fusion and analysis, e.g., recognizing patterns over time. However, a still open research challenge is to build systems that support higher-level information fusion, viz., to integrate domain specific knowledge and automatically draw conclusions that would otherwise remain hidden or would have to be drawn by a human operator. To address this challenge, we have developed a novel system architecture that emphasizes the role of formal logic and automated theorem provers in its main components. Additionally, it features controlled natural language for operator I/O. It offers three logical languages to adequately model different aspects of the domain. This allows to build SA systems in a more declarative way than is possible with current approaches. From an automated reasoning perspective, the main challenges lay in combining (existing) automated reasoning techniques, from low-level data fusion of time-stamped data to semantic analysis and alert generation that is based on linear temporal logic. The system has been implemented and interfaces with Google-Earth to visualize the dynamics of situations and system output. It has been successfully tested on realistic data, but in this paper we focus on the system architecture and in particular on the interplay of the different reasoning components.

@inproceedings{ SAILpaper, author = {Franz {Baader} and Andreas {Bauer} and Peter {Baumgartner} and Anne {Cregan} and Alfredo {Gabaldon} and Krystian {Ji} and Kevin {Lee} and David {Rajaratnam} and Rolf {Schwitter}}, booktitle = {Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (Tableaux 2009)}, editor = {Martin {Giese} and Arild {Waaler}}, pages = {77--92}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {A Novel Architecture for Situation Awareness Systems}, volume = {5607}, year = {2009}, }

Franz Baader, Andreas Bauer, and Marcel Lippmann:

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**Runtime Verification Using a Temporal Description Logic**. In Silvio Ghilardi and Roberto Sebastiani, editors,*Proceedings of the 7th International Symposium on Frontiers of Combining Systems (FroCoS 2009)*, volume 5749 of*Lecture Notes in Computer Science*, pages 149–164. Springer-Verlag, 2009.Abstract BibTeX Entry PDF File ©Springer-Verlag

Formulae of linear temporal logic (LTL) can be used to specify (wanted or unwanted) properties of a dynamical system. In model checking, the system's behaviour is described by a transition system, and one needs to check whether all possible traces of this transition system satisfy the formula. In runtime verification, one observes the actual system behaviour, which at any time point yields a finite prefix of a trace. The task is then to check whether all continuations of this prefix into a trace satisfy (violate) the formula. In this paper, we extend the known approaches to LTL runtime verification in two directions. First, instead of propositional LTL we use ALC-LTL, which can use axioms of the description logic ALC instead of propositional variables to describe properties of single states of the system. Second, instead of assuming that the observed system behaviour provides us with complete information about the states of the system, we consider the case where states may be described in an incomplete way by ALC ABoxes.

@inproceedings{ BaBaLi-FroCoS09, author = {Franz {Baader} and Andreas {Bauer} and Marcel {Lippmann}}, booktitle = {Proceedings of the 7th International Symposium on Frontiers of Combining Systems (FroCoS 2009)}, editor = {Silvio {Ghilardi} and Roberto {Sebastiani}}, pages = {149--164}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Runtime Verification Using a Temporal Description Logic}, volume = {5749}, year = {2009}, }

Franz Baader, Andreas Bauer, and Alwen Tiu:

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**Matching Trace Patterns with Regular Policies**. In A.H. Dediu, A.M. Ionescu, and C. Martin-Vide, editors,*Proceedings of the Third International Conference on Language, and Automata Theory, and Applications (LATA 2009)*, volume 5457 of*Lecture Notes in Artificial Intelligence*, pages 105–116. Springer-Verlag, 2009.Abstract BibTeX Entry PDF File ©Springer-Verlag

We consider policies that are described by regular expressions, finite automata, or formulae of linear temporal logic (LTL). Such policies are assumed to describe situations that are problematic, and thus should be avoided. Given a trace pattern u, i.e., a sequence of action symbols and variables, were the variables stand for unknown (i.e., not observed) sequences of actions, we ask whether u potentially violates a given policy L, i.e., whether the variables in u can be replaced by sequences of actions such that the resulting trace belongs to L. We also consider the dual case where the regular policy L is supposed to describe all the admissible situations. Here, we want to know whether u always adheres to the given policy L, i.e., whether all instances of u belong to L. We determine the complexity of the violation and the adherence problem, depending on whether trace patterns are linear or not, and on whether the policy is assumed to be fixed or not.

@inproceedings{ BaBaTiu09, author = {Franz {Baader} and Andreas {Bauer} and Alwen {Tiu}}, booktitle = {Proceedings of the Third International Conference on Language, and Automata Theory, and Applications {(LATA 2009)}}, editor = {A.H. {Dediu} and A.M. {Ionescu} and C. {Martin-Vide}}, pages = {105--116}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Matching Trace Patterns with Regular Policies}, volume = {5457}, year = {2009}, }

Franz Baader and Felix Distel:

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**Exploring Finite Models in the Description Logic ELgfp**. In Sébastien Ferré and Sebastian Rudolph, editors,*Proceedings of the 7th International Conference on Formal Concept Analysis, (ICFCA 2009)*, volume 5548 of*Lecture Notes in Artificial Intelligence*, pages 146–161. Springer Verlag, 2009.Abstract BibTeX Entry PDF File ©Springer-Verlag

In a previous ICFCA paper we have shown that, in the Description Logics EL and ELgfp, the set of general concept inclusions holding in a finite model always has a finite basis. In this paper, we address the problem of how to compute this basis efficiently, by adapting methods from formal concept analysis.

@inproceedings{ BaDi09, author = {Franz {Baader} and Felix {Distel}}, booktitle = {Proceedings of the 7th International Conference on {F}ormal {C}oncept {A}nalysis, {(ICFCA 2009)}}, editor = {S\'ebastien {Ferr\'e} and Sebastian {Rudolph}}, pages = {146--161}, publisher = {Springer Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Exploring Finite Models in the Description Logic {ELgfp}}, volume = {5548}, year = {2009}, }

Franz Baader, Martin Knechtel, and Rafael Peñaloza:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**A Generic Approach for Large-Scale Ontological Reasoning in the Presence of Access Restrictions to the Ontology's Axioms**. In Abraham Bernstein et al., editor,*Proceedings of the 8th International Semantic Web Conference (ISWC 2009)*, volume 5823 of*Lecture Notes in Computer Science*, pages 49–64, 2009.Abstract BibTeX Entry PDF File ©Springer-Verlag

The framework developed in this paper can deal with scenarios where selected sub-ontologies of a large ontology are offered as views to users, based on criteria like the user's access right, the trust level required by the application, or the level of detail requested by the user. Instead of materializing a large number of different sub-ontologies, we propose to keep just one ontology, but equip each axiom with a label from an appropriate labeling lattice. The access right, required trust level, etc. is then also represented by a label (called user label) from this lattice, and the corresponding sub-ontology is determined by comparing this label with the axiom labels. For large-scale ontologies, certain consequence (like the concept hierarchy) are often precomputed. Instead of precomputing these consequences for every possible sub-ontology, our approach computes just one label for each consequence such that a comparison of the user label with the consequence label determines whether the consequence follows from the corresponding sub-ontology or not. In this paper we determine under which restrictions on the user and axiom labels such consequence labels (called boundaries) always exist, describe different black-box approaches for computing boundaries, and present first experimental results that compare the efficiency of these approaches on large real-world ontologies. Black-box means that, rather than requiring modifications of existing reasoning procedures, these approaches can use such procedures directly as sub-procedures, which allows us to employ existing highly-optimized reasoners.

@inproceedings{ BaKP-ISWC-09, author = {Franz {Baader} and Martin {Knechtel} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 8th International Semantic Web Conference (ISWC 2009)}, editor = {Abraham Bernstein et {al.}}, pages = {49--64}, series = {Lecture Notes in Computer Science}, title = {A Generic Approach for Large-Scale Ontological Reasoning in the Presence of Access Restrictions to the Ontology's Axioms}, volume = {5823}, year = {2009}, }

Franz Baader and Barbara Morawska:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Unification in the Description Logic**\(\mathcal{EL}\). In Ralf Treinen, editor,*Proceedings of the 20th International Conference on Rewriting Techniques and Applications (RTA 2009)*, volume 5595 of*Lecture Notes in Computer Science*, pages 350–364. Springer-Verlag, 2009.Abstract BibTeX Entry PDF File ©Springer-Verlag

The Description Logic EL has recently drawn considerable attention since, on the one hand, important inference problems such as the subsumption problem are polynomial. On the other hand, EL is used to define large biomedical ontologies. Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. The main result of this paper is that unification in EL is decidable. More precisely, EL-unification is NP-complete, and thus has the same complexity as EL-matching. We also show that, w.r.t. the unification type, EL is less well-behaved: it is of type zero, which in particular implies that there are unification problems that have no finite complete set of unifiers.

@inproceedings{ BaMo09, author = {Franz {Baader} and Barbara {Morawska}}, booktitle = {Proceedings of the 20th International Conference on Rewriting Techniques and Applications (RTA 2009)}, editor = {Ralf {Treinen}}, pages = {350--364}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Unification in the Description Logic {$\mathcal{EL}$}}, volume = {5595}, year = {2009}, }

Franz Baader, Stefan Schulz, Kent Spackmann, and Bontawee Suntisrivaraporn:

Abstract BibTeX Entry PDF File

**How Should Parthood Relations be Expressed in SNOMED CT?**. In*Proceedings of 1. Workshop des GI-Arbeitskreises Ontologien in Biomedizin und Lebenswissenschaften (OBML 2009)*, 2009.Abstract BibTeX Entry PDF File

We recall the re-engineering of SNOMED CT's SEP encoding as proposed in a previous paper, and then show that a backward compatible version, which also contains definitions for the auxiliary S- and P-concepts, requires an additional complex role inclusion that destroys the acyclicity property of the set of complex role inclusion. For this reason, the backward compatible reengineered version of SNOMED CT is not expressible in OWL 2, but it is expressible in EL++ and an appropriate extension of SROIQ.

@inproceedings{ OBML09, address = {Leipzig, Germany}, author = {Franz {Baader} and Stefan {Schulz} and Kent {Spackmann} and Bontawee {Suntisrivaraporn}}, booktitle = {Proceedings of 1. Workshop des GI-Arbeitskreises Ontologien in Biomedizin und Lebenswissenschaften (OBML 2009)}, title = {How Should Parthood Relations be Expressed in {SNOMED CT}?}, year = {2009}, }

Franz Baader and Barış Sertkaya:

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**Usability Issues in Description Logic Knowledge Base Completion**. In Sébastien Ferré and Sebastian Rudolph, editors,*Proceedings of the 7th International Conference on Formal Concept Analysis, (ICFCA 2009)*, volume 5548 of*Lecture Notes in Artificial Ingelligence*, pages 1–21. Springer Verlag, 2009.Abstract BibTeX Entry PDF File ©Springer-Verlag

In a previous paper, we have introduced an approach for extending both the terminological and the assertional part of a Description Logic knowledge base by using information provided by the assertional part and by a domain expert. This approach, called knowledge base completion, was based on an extension of attribute exploration to the case of partial contexts. The present paper recalls this approach, and then addresses usability issues that came up during first experiments with a preliminary implementation of the completion algorithm. It turns out that these issues can be addressed by extending the exploration algorithm for partial contexts such that it can deal with implicational background knowledge.

@inproceedings{ BaSe09, author = {Franz {Baader} and Bar\i{}\c{s} {Sertkaya}}, booktitle = {Proceedings of the 7th International Conference on {F}ormal {C}oncept {A}nalysis, {(ICFCA 2009)}}, editor = {S\'ebastien {Ferr\'e} and Sebastian {Rudolph}}, pages = {1--21}, publisher = {Springer Verlag}, series = {Lecture Notes in Artificial Ingelligence}, title = {Usability Issues in Description Logic Knowledge Base Completion}, volume = {5548}, year = {2009}, }

Frithjof Dau and Martin Knechtel:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Access Policy Design Supported by FCA Methods**. In Frithjof Dau and Sebastian Rudolph, editors,*Proceedings of the 17th International Conference on Conceptual Structures, (ICCS 2009)*, volume 5662 of*Lecture Notes in Computer Science*, pages 141–154, 2009.Abstract BibTeX Entry PDF File ©Springer-Verlag

Role Based Access Control (RBAC) is a methodology for providing users in an IT system specific permissions like write or read to users. It abstracts from specific users and binds permissions to user roles. Similarly, one can abstract from specific documents and bind permission to document types. In this paper, we apply Description Logics (DLs) to formalize RBAC. We provide a thorough discussion on different possible interpretations of RBAC matrices and how DLs can be used to capture the RBAC constraints. We show moreover that with DLs, we can express more intended constraints than it can be done in the common RBAC approach, thus proving the benefit of using DLs in the RBAC setting. For deriving additional constraints, we introduce a strict methodology, based on attribute exploration method known from Formal Concept Analysis. The attribute exploration allows to systematically finding unintended implications and to deriving constraints and making them explicit. Finally, we apply our approach to a real-life example.

@inproceedings{ DaKn-ICCS-09, author = {Frithjof {Dau} and Martin {Knechtel}}, booktitle = {Proceedings of the 17th International Conference on {C}onceptual {S}tructures, {(ICCS 2009)}}, editor = {Frithjof {Dau} and Sebastian {Rudolph}}, pages = {141--154}, series = {Lecture Notes in Computer Science}, title = {Access Policy Design Supported by {FCA} Methods}, volume = {5662}, year = {2009}, }

Conrad Drescher, Hongkai Liu, Franz Baader, Steffen Guhlemann, Uwe Petersohn, Peter Steinke, and Michael Thielscher:

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**Putting ABox Updates into Action**. In Silvio Ghilardi and Roberto Sebastiani, editors,*The Seventh International Symposium on Frontiers of Combining Systems (FroCoS-2009)*, volume 5749 of*Lecture Notes in Computer Science*, pages 149–164. Springer-Verlag, 2009.Abstract BibTeX Entry PDF File ©Springer-Verlag

When trying to apply recently developed approaches for updating Description Logic ABoxes in the context of an action programming language, one encounters two problems. First, updates generate so-called Boolean ABoxes, which cannot be handled by traditional Description Logic reasoners. Second, iterated update operations result in very large Boolean ABoxes, which, however, contain a huge amount of redundant information. In this paper, we address both issues from a practical point of view.

@inproceedings{ FroCos-09, author = {Conrad {Drescher} and Hongkai {Liu} and Franz {Baader} and Steffen {Guhlemann} and Uwe {Petersohn} and Peter {Steinke} and Michael {Thielscher}}, booktitle = {The Seventh International Symposium on Frontiers of Combining Systems (FroCoS-2009)}, editor = {Silvio {Ghilardi} and Roberto {Sebastiani}}, pages = {149--164}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Putting ABox Updates into Action}, volume = {5749}, year = {2009}, }

Conrad Drescher, Hongkai Liu, Franz Baader, Peter Steinke, and Michael Thielscher:

Abstract BibTeX Entry PDF File

**Putting ABox Updates into Action**. In*Proceedings of the 8th IJCAI International Workshop on Nonmontonic Reasoning, Action and Change (NRAC-09)*, 2009.Abstract BibTeX Entry PDF File

@inproceedings{ nrac-09, author = {Conrad {Drescher} and Hongkai {Liu} and Franz {Baader} and Peter {Steinke} and Michael {Thielscher}}, booktitle = {Proceedings of the 8th IJCAI International Workshop on Nonmontonic Reasoning, Action and Change (NRAC-09)}, title = {Putting ABox Updates into Action}, year = {2009}, }

Matthias Heinrich, Antje Boehm-Peters, and Martin Knechtel:

Abstract BibTeX Entry PDF File

**A Platform to Automatically Generate and Incorporate Documents into an Ontology-Based Content Repository**. In Uwe M. Borghoff and Boris Chidlovskii, editors,*Proceedings of the 2009 ACM Symposium on Document Engineering (DocEng 2009)*, pages 43–46, 2009.Abstract BibTeX Entry PDF File

In order to access large information pools efficiently data has to be structured and categorized. Recently, applying ontologies to formalize information has become an established approach. In particular, ontology-based search and navigation are promising solutions which are capable to significantly improve state of the art systems (e.g. full-text search engines). However, the ontology roll-out and maintenance are costly tasks. Therefore, we propose a documentation generation platform that automatically derives content and incorporates generated content into an existing ontology. The demanding task of classifying content as concept instances, setting data type and object properties is accomplished by the documentation generation platform. Eventually, our approach results in a semantically enriched content base. Note that no manual effort is required to establish links between content objects and the ontology.

@inproceedings{ HeBK-ACMDocEng-09, author = {Matthias {Heinrich} and Antje {Boehm-Peters} and Martin {Knechtel}}, booktitle = {Proceedings of the 2009 ACM Symposium on Document Engineering (DocEng 2009)}, editor = {Uwe M. {Borghoff} and Boris {Chidlovskii}}, pages = {43--46}, title = {A Platform to Automatically Generate and Incorporate Documents into an Ontology-Based Content Repository}, year = {2009}, }

Kay Kadner, Gerald Huebsch, Martin Knechtel, Thomas Springer, and Christoph Pohl:

Abstract BibTeX Entry

**Multimodality in Mobile Computing and Mobile Devices: Methods for Adaptable Usability**, chapter Platform Support for Multimodality on Mobile Devices, pages 75–105. IGI Global, 2009.Abstract BibTeX Entry

The diversity of todays mobile technology also entails multiple interaction channels offered per device. This chapter surveys the basics of multimodal interactions in a mobility context and introduces a number of concepts for platform support. Synchronization approaches for input fusion and output fission as well as a concept for device federation are discussed with the help of an exemplary multimodal route planning application. An outlook on future trends concludes the chapter.

@inbook{ KHKSP-chapterMM-09, author = {Kay {Kadner} and Gerald {Huebsch} and Martin {Knechtel} and Thomas {Springer} and Christoph {Pohl}}, chapter = {Platform Support for Multimodality on Mobile Devices}, pages = {75--105}, publisher = {IGI Global}, title = {Multimodality in Mobile Computing and Mobile Devices: Methods for Adaptable Usability}, year = {2009}, }

Julian Mendez and Boontawee Suntisrivaraporn:

Abstract BibTeX Entry PDF File

**Reintroducing CEL as an OWL 2 EL Reasoner**. In Bernardo Cuenca Grau, Ian Horrocks, Boris Motik, and Ulrike Sattler, editors,*Proceedings of the 2009 International Workshop on Description Logics (DL2009)*, volume 477 of*CEUR-WS*, 2009.Abstract BibTeX Entry PDF File

The CEL system is known for its scalability of reasoning in the lightweight DL EL++ which has been proved suitable for several ontology applications, most notably from the life science domain. Recently, the DL EL++ has been adopted as the logical underpinning of the OWL 2 EL profile of the new Web Ontology Language which potentially attracts new folks of CEL's users. To seamlessly integrate the reasoner to the OWL user community, we have implemented the OWL API for CEL. This paper describes the challenges, design decision and architecture of this implementation. Additionally, we present experimental results which highlight the scalability of the reasoner, as well as demonstrate a low overhead of our OWL API implementation.

@inproceedings{ MeSu-DL09, author = {Julian {Mendez} and Boontawee {Suntisrivaraporn}}, booktitle = {Proceedings of the 2009 International Workshop on Description Logics ({DL2009})}, editor = {Bernardo Cuenca {Grau} and Ian {Horrocks} and Boris {Motik} and Ulrike {Sattler}}, series = {CEUR-WS}, title = {Reintroducing CEL as an OWL 2 EL Reasoner}, volume = {477}, year = {2009}, }

Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Reasoning With Weighted Ontologies**. In Bernardo Cuenca Grau, Ian Horrocks, Boris Motik, and Ulrike Sattler, editors,*Proceedings of the 2009 International Workshop on Description Logics (DL2009)*, volume 477 of*CEUR-WS*, 2009.Abstract BibTeX Entry PDF File

We study the problem of reasoning over weighted ontologies. We assume that every axiom is labeled with an element of a distributive lattice (called its weight) and try to compute its so-called boundary, with respect to a given property. We show that axiom pinpointing is the most general instance of this problem. Finally, we present three applications of the problem of boundary computation.

@inproceedings{ Pena-DL09, author = {Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 2009 International Workshop on Description Logics ({DL2009})}, editor = {Bernardo Cuenca {Grau} and Ian {Horrocks} and Boris {Motik} and Ulrike {Sattler}}, series = {CEUR-WS}, title = {Reasoning With Weighted Ontologies}, volume = {477}, year = {2009}, }

Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Using Tableaux and Automata for Pinpointing in EL**. In Valentin Goranko, editor,*TABLEAUX 2009 Wokshop on Tableaux versus Automata as Logical Decision Methods (AutoTab'09)*, 2009.Abstract BibTeX Entry PDF File

We show that the subsumption algorithm for the Description Logic EL can be seen both as a tableau-based and an automata-based decision procedure. Each of these views allows an extension into a so-called pinpointing algorithm. We show that the tableau-based extension has a worst-case exponential execution time, while the automata-based extension runs in polynomial time.

@inproceedings{ Pena-AT09, author = {Rafael {Pe{\~n}aloza}}, booktitle = {TABLEAUX 2009 Wokshop on Tableaux versus Automata as Logical Decision Methods ({AutoTab'09})}, editor = {Valentin {Goranko}}, title = {Using Tableaux and Automata for Pinpointing in EL}, year = {2009}, }

Rafael Peñaloza and Barış Sertkaya:

Abstract BibTeX Entry PDF File

**Axiom Pinpointing is Hard**. In Bernardo Cuenca Grau, Ian Horrocks, Boris Motik, and Ulrike Sattler, editors,*Proceedings of the 2009 International Workshop on Description Logics (DL2009)*, volume 477 of*CEUR-WS*, 2009.Abstract BibTeX Entry PDF File

We investigate the complexity of several decision, enumeration and counting problems in axiom pinpointing in Description Logics. We prove hardness results that already hold for the propositional Horn fragment. We show that for this fragment, unless P = NP, all minimal subsets of a given TBox that have a given consequence, i.e. MinAs, cannot be enumerated in a specified lexicographic order with polynomial delay. Moreover, we show that recognizing the set of all MinAs is at least as hard as recognizing the set of all minimal transversals of a given hypergraph, however whether this problem is intractable remains open. We also show that checking the existence of a MinA that does not contain any of the given sets of axioms, as well as checking the existence of a MinA that contains a specified axiom are both NP-hard. In addition we show that counting all MinAs and counting the MinAs that contain a certain axiom are both #P-hard.

@inproceedings{ PeSe09, author = {Rafael {Pe{\~n}aloza} and Bar\i{}\c{s} {Sertkaya}}, booktitle = {Proceedings of the 2009 International Workshop on Description Logics ({DL2009})}, editor = {Bernardo Cuenca {Grau} and Ian {Horrocks} and Boris {Motik} and Ulrike {Sattler}}, series = {CEUR-WS}, title = {Axiom Pinpointing is Hard}, volume = {477}, year = {2009}, }

Stefan Schulz, Boontawee Suntisrivaraporn, Franz Baader, and Martin Boeker:

Abstract BibTeX Entry PDF File

**SNOMED reaching its adolescence: Ontologists' and logicians' health check**.*International Journal of Medical Informatics*, 78(Supplement 1):S86–S94, 2009.Abstract BibTeX Entry PDF File

After a critical review of the present architecture of SNOMED CT, addressing both logical and ontological issues, we present a roadmap toward an overall improvement and recommend the following actions: SNOMED CT's ontology, dictionary, and information model components should be kept separate. SNOMED CT's upper level should be re-arranged according to a standard upper level ontology. SNOMED CT concepts should be assigned to the four disjoint groups: classes, instances, relations, and meta-classes. SNOMED CT's binary relations should be reduced to a set of canonical ones, following existing recommendations. Taxonomies should be cleansed and split into disjoint partitions. The number of full definitions should be increased. Finally, new approaches are proposed for modeling part-whole hierarchies, as well as the integration of qualifier relations into a unified framework. All proposed modifications can be expressed by the computationally tractable description logic EL++.

@article{ SchEtAl-JMI-09, author = {Stefan {Schulz} and Boontawee {Suntisrivaraporn} and Franz {Baader} and Martin {Boeker}}, journal = {International Journal of Medical Informatics}, number = {Supplement 1}, pages = {S86--S94}, publisher = {Elsevier}, title = {{SNOMED} reaching its adolescence: Ontologists' and logicians' health check}, volume = {78}, year = {2009}, }

Barış Sertkaya:

Abstract BibTeX Entry PDF File

**OntoComP System Description**. In Bernardo Cuenca Grau, Ian Horrocks, Boris Motik, and Ulrike Sattler, editors,*Proceedings of the 2009 International Workshop on Description Logics (DL2009)*, volume 477 of*CEUR-WS*, 2009.Abstract BibTeX Entry PDF File

We describe OntoComP, a Protege 4 plugin that supports knowledge engineers in completing DL-based ontologies. More precisely, OntoComP supports a knowledge engineer in checking whether an ontology contains all the relevant information about the application domain, and in extending the ontology appropriately if this is not the case. It acquires complete knowledge about the application domain efficiently by asking successive questions to the knowledge engineer. By using novel techniques from Formal Concept Analysis, it ensures that, on the one hand, the interaction with the knowledge engineer is kept to a minimum, and, on the other hand, the resulting ontology is complete in a certain well-defined sense.

@inproceedings{ Sert09d, author = {Bar\i{}\c{s} {Sertkaya}}, booktitle = {Proceedings of the 2009 International Workshop on Description Logics ({DL2009})}, editor = {Bernardo Cuenca {Grau} and Ian {Horrocks} and Boris {Motik} and Ulrike {Sattler}}, series = {CEUR-WS}, title = {OntoComP System Description}, volume = {477}, year = {2009}, }

Barış Sertkaya:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**OntoComP: A Protege Plugin for Completing OWL Ontologies**. In*Proceedings of the 6th European Semantic Web Conference, (ESWC 2009)*, volume 5554 of*Lecture Notes in Computer Science*, pages 898–902. Springer Verlag, 2009.Abstract BibTeX Entry PDF File ©Springer-Verlag

We describe OntoComP, which is a Protege 4 plugin that supports the ontology engineer in completing OWL ontologies. More precisely, OntoComP supports the ontology engineer in checking whether an ontology contains all the relevant information about the application domain, and in extending the ontology appropriately if this is not the case. It acquires complete knowledge about the application domain efficiently by asking successive questions to the ontology engineer. By using novel techniques from Formal Concept Analysis, it ensures that, on the one hand, the interaction with the ontology engineer is kept to a minimum, and, on the other hand, the resulting ontology is complete in a certain well-defined sense.

@inproceedings{ Sert09b, author = {Bar\i{}\c{s} {Sertkaya}}, booktitle = {Proceedings of the 6th European Semantic Web Conference, {(ESWC 2009)}}, pages = {898--902}, publisher = {Springer Verlag}, series = {Lecture Notes in Computer Science}, title = {OntoComP: A Protege Plugin for Completing OWL Ontologies}, volume = {5554}, year = {2009}, }

Barış Sertkaya:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Some Computational Problems Related to Pseudo-intents**. In Sébastien Ferré and Sebastian Rudolph, editors,*Proceedings of the 7th International Conference on Formal Concept Analysis, (ICFCA 2009)*, volume 5548 of*Lecture Notes in Artificial Intelligence*, pages 130–145. Springer Verlag, 2009.Abstract BibTeX Entry PDF File ©Springer-Verlag

We investigate the computational complexity of several decision, enumeration and counting problems related to pseudo-intents. We show that given a formal context and a subset of its set of pseudo-intents, checking whether this context has an additional pseudo-intent is in coNP, and it is at least as hard as checking whether a given simple hypergraph is not saturated. We also show that recognizing the set of pseudo-intents is also in coNP, and it is at least as hard as identifying the minimal transversals of a given hypergraph. Moreover, we show that if any of these two problems turns out to be coNP-hard, then unless P = NP, pseudo-intents cannot be enumerated in output polynomial time. We also investigate the complexity of finding subsets of a given Duquenne-Guigues Base from which a given implication follows. We show that checking the existence of such a subset within a specified cardinality bound is NP-complete, and counting all such minimal subsets is #P-complete.

@inproceedings{ Sert09, author = {Bar\i{}\c{s} {Sertkaya}}, booktitle = {Proceedings of the 7th International Conference on {F}ormal {C}oncept {A}nalysis, {(ICFCA 2009)}}, editor = {S\'ebastien {Ferr\'e} and Sebastian {Rudolph}}, pages = {130--145}, publisher = {Springer Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Some Computational Problems Related to Pseudo-intents}, volume = {5548}, year = {2009}, }

Barış Sertkaya:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Towards the Complexity of Recognizing Pseudo-intents**. In Frithjof Dau and Sebastian Rudolph, editors,*Proceedings of the 17th International Conference on Conceptual Structures, (ICCS 2009)*, pages 284–292, 2009.Abstract BibTeX Entry PDF File ©Springer-Verlag

Pseudo-intents play a key role in Formal Concept Analysis. They form the premises of the implications in the Duquenne-Guigues Base, which is a minimum cardinality base for the valid implications of a formal context. It has been shown that checking whether a set is a pseudo-intent is in coNP. However, it is still open whether this problem is coNP-hard, or it is solvable in polynomial time. In the current work we prove a first lower bound for this problem by showing that it is at least as hard as TRANSVERSAL HYPERGRAPH, which is the problem of checking whether the edges of a given hypergraph are precisely the minimal transversals of another given hypergraph. This is a prominent open problem in hypergraph theory that is conjectured to form a complexity class properly contained between P and coNP. Our result partially explains why the attempts in the FCA community for finding a polynomial algorithm for recognizing pseudo-intents have failed until now. We also formulate a decision problem, namely FIRST PSEUDO-INTENT, and show that if this problem is not polynomial, then, unless P = NP, pseudo-intents cannot be enumerated with polynomial delay in lexicographic order.

@inproceedings{ Sert09c, author = {Bar\i{}\c{s} {Sertkaya}}, booktitle = {Proceedings of the 17th International Conference on {C}onceptual {S}tructures, {(ICCS 2009)}}, editor = {Frithjof {Dau} and Sebastian {Rudolph}}, pages = {284--292}, title = {Towards the Complexity of Recognizing Pseudo-intents}, volume = {5662}, year = {2009}, }

Thomas Springer and Anni-Yasmin Turhan:

Abstract BibTeX Entry

**Employing Description Logics in Ambient Intelligence for Modeling and Reasoning about Complex Situations**.*Journal of Ambient Intelligence and Smart Environments*, 1(3):235–259, 2009.Abstract BibTeX Entry

Ambient Intelligence systems need to represent information about their environment and recognize relevant situations to perform appropriate actions proactively and autonomously. The context information gathered by these systems comes with imperfections such as incompleteness or incorrectness. These characteristics need to be handled gracefully by the Ambient Intelligence system. Moreover, the represented information must allow for a fast and reliable recognition of the current situation. To solve these problems we propose a method for situation modeling using the Description Logics based ontology language OWL DL and a framework for employing Description Logics reasoning services to recognize the current situation based on context. The benefits from the approach are manifold: the semantics of Description Logics allow for graceful handling of incomplete knowledge. The well-investigated reasoning services do not only allow recognizing the current situation, but also can add to the reliability of the overall system. Moreover optimized reasoning systems are freely available and ready to use. We underpin the feasibility of our approach by providing a case study based on a smart home application conducting an evaluation of different Description Logics reasoners with respect to our application ontology as well as a discussion of Description Logics systems in Ambient Intelligence.

@article{ SpTu-JAISE-09, author = {Thomas {Springer} and Anni-Yasmin {Turhan}}, journal = {Journal of Ambient Intelligence and Smart Environments}, number = {3}, pages = {235--259}, title = {Employing Description Logics in Ambient Intelligence for Modeling and Reasoning about Complex Situations}, volume = {1}, year = {2009}, }

## 2008

Franz Baader, Sebastian Brandt, and Carsten Lutz:

Abstract BibTeX Entry PDF File

**Pushing the EL Envelope Further**. In Kendall Clark and Peter F. Patel-Schneider, editors,*In Proceedings of the OWLED 2008 DC Workshop on OWL: Experiences and Directions*, 2008.Abstract BibTeX Entry PDF File

We extend the description logic EL++ with reflexive roles and range restrictions, and show that subsumption remains tractable if a certain syntactic restriction is adopted. We also show that subsumption becomes PSpace-hard (resp. undecidable) if this restriction is weakened (resp. dropped). Additionally, we prove that tractability is lost when symmetric roles are added: in this case, subsumption becomes ExpTime- hard.

@inproceedings{ BaaderEtAl-OWLED08DC, author = {Franz {Baader} and Sebastian {Brandt} and Carsten {Lutz}}, booktitle = {In Proceedings of the OWLED 2008 DC Workshop on OWL: Experiences and Directions}, editor = {Kendall {Clark} and Peter F. {Patel-Schneider}}, title = {Pushing the EL Envelope Further}, year = {2008}, }

Franz Baader and Felix Distel:

Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

**A Finite Basis for the Set of EL-Implications Holding in a Finite Model**. In Raoul Medina and Sergei Obiedkov, editors,*Proceedings of the 6th International Conference on Formal Concept Analysis, (ICFCA 2008)*, volume 4933 of*Lecture Notes in Artificial Intelligence*, pages 46–61. Springer, 2008.Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

Formal Concept Analysis (FCA) can be used to analyze data given in the form of a formal context. In particular, FCA provides efficient algorithms for computing a minimal basis of the implications holding in the context. In this paper, we extend classical FCA by considering data that are represented by relational structures rather than formal contexts, and by replacing atomic attributes by complex formulae defined in some logic. After generalizing some of the FCA theory to this more general form of contexts, we instantiate the general framework with attributes defined in the Description Logic (DL) EL, and with relational structures over a signature of unary and binary predicates, i.e., models for EL. In this setting, an implication corresponds to a so-called general concept inclusion axiom (GCI) in EL, The main technical result of this paper is that, in EL, for any finite model there is a finite set of implications (GCIs) holding in this model from which all implications (GCIs) holding in the model follow.

@inproceedings{ BaaderDistel08, author = {Franz {Baader} and Felix {Distel}}, booktitle = {Proceedings of the 6th International Conference on Formal Concept Analysis, (ICFCA 2008)}, editor = {Raoul {Medina} and Sergei {Obiedkov}}, pages = {46--61}, publisher = {Springer}, series = {Lecture Notes in Artificial Intelligence}, title = {A Finite Basis for the Set of {EL}-Implications Holding in a Finite Model}, volume = {4933}, year = {2008}, }

Franz Baader, Silvio Ghilardi, and Carsten Lutz:

Abstract BibTeX Entry PDF File

**LTL over Description Logic Axioms**. In*Proceedings of the 11th International Conference on Principles of Knowledge Representation and Reasoning (KR2008)*, 2008.Abstract BibTeX Entry PDF File

Most of the research on temporalized Description Logics (DLs) has concentrated on the case where temporal operators can occur within DL concept descriptions. In this setting, reasoning usually becomes quite hard if rigid roles, i.e., roles whose interpretation does not change over time, are available. In this paper, we consider the case where temporal operators are allowed to occur only in front of DL axioms (i.e., ABox assertions and general concept inclusion axioms), but not inside of concepts descriptions. As the temporal component, we use linear temporal logic (LTL) and in the DL component we consider the basic DL ALC. We show that reasoning in the presence of rigid roles becomes considerably simpler in this setting.

@inproceedings{ BaaGhiLu-KR08, author = {Franz {Baader} and Silvio {Ghilardi} and Carsten {Lutz}}, booktitle = {Proceedings of the 11th International Conference on Principles of Knowledge Representation and Reasoning ({KR2008})}, title = {LTL over Description Logic Axioms}, year = {2008}, }

Franz Baader, Silvio Ghilardi, and Carsten Lutz:

Abstract BibTeX Entry PDF File

**LTL over Description Logic Axioms**. In*Proceedings of the 21st International Workshop on Description Lo gics (DL2008)*, volume 353 of*CEUR-WS*, 2008.Abstract BibTeX Entry PDF File

Most of the research on temporalized Description Logics (DLs) has concentrated on the most general case where temporal operators can occur both within DL concepts and in front of DL axioms. In this setting, reasoning usually becomes quite hard. If rigid roles (i.e., roles whose interpretation does not vary over time) are allowed, then the interesting inference problems (such as satisfiability of concepts) become undecidable. Even if all symbols are interpreted as flexible (i.e., their interpretations can change arbitrarily from one time-point to the next), the complexity of reasoning is doubly exponential, i.e., one exponential higher than the complexity of reasoning in pure DLs such as ALC. In this paper, we consider the case where temporal operators are allowed to occur only in front of axioms (i.e., ABox assertions and general concept inclusion axioms (GCIs)), but not inside concepts. As the temporal component, we use linear temporal logic (LTL) and in the DL component we consider ALC. We show that reasoning becomes simpler in this setting.

@inproceedings{ BaGhiLu-DL08, author = {Franz {Baader} and Silvio {Ghilardi} and Carsten {Lutz}}, booktitle = {Proceedings of the 21st International Workshop on Description Lo\ \ gics ({DL2008})}, series = {CEUR-WS}, title = {LTL over Description Logic Axioms}, volume = {353}, year = {2008}, }

Franz Baader, Jan Hladik, and Rafael Peñaloza:

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**Automata Can Show PSPACE Results for Description Logics**.*Information and Computation, Special Issue: First International Conference on Language and Automata Theory and Applications (LATA'07)*, 206(9–10):1045–1056, 2008.Abstract BibTeX Entry PDF File

In the area of Description Logic (DL), both tableau-based and automata-based algorithms are frequently used to show decidability and complexity results for basic inference problems such as satisfiability of concepts. Whereas tableau-based algorithms usually yield worst-case optimal algorithms in the case of PSPACE-complete logics, it is often very hard to design optimal tableau-based algorithms for EXPTIME-complete DLs. In contrast, the automata-based approach is usually well-suited to prove EXPTIME upper-bounds, but its direct application will usually also yield an EXPTIME-algorithm for a PSPACE-complete logic since the (tree) automaton constructed for a given concept is usually exponentially large. In the present paper, we formulate conditions under which an on-the-fly construction of such an exponentially large automaton can be used to obtain a PSPACE-algorithm. We illustrate the usefulness of this approach by proving a new PSPACE upper-bound for satisfiability of concepts with respect to acyclic terminologies in the DL SI, which extends the basic DL ALC with transitive and inverse roles.

@article{ BaaHlaPen-IC-08, author = {Franz {Baader} and Jan {Hladik} and Rafael {Pe{\~n}aloza}}, journal = {Information and Computation, Special Issue: First International Conference on Language and Automata Theory and Applications ({LATA'07})}, number = {9--10}, pages = {1045--1056}, title = {Automata Can Show {PSPACE} Results for Description Logics}, volume = {206}, year = {2008}, }

Franz Baader, Novak Novakovic, and Boontawee Suntisrivaraporn:

Abstract BibTeX Entry PDF File

**A Proof-Theoretic Subsumption Reasoner for Hybrid**\(\mathcal{EL}\)**-TBoxes**. In*Proceedings of the 2008 International Workshop on Description Logics (DL2008)*, volume 353 of*CEUR-WS*, 2008.Abstract BibTeX Entry PDF File

Hybrid EL-TBoxes combine general concept inclusions (GCIs), which are interpreted with descriptive semantics, with cyclic concept definitions, which are interpreted with greatest fixpoint (gfp) semantics. We introduce a proof-theoretic approach that yields a polynomial-time decision procedure for subsumption in EL w.r.t. hybrid TBoxes, and present preliminary experimental results regarding the performance of the reasoner Hyb that implements this decision procedure.

@inproceedings{ BaaNovSun-DL-08, author = {Franz {Baader} and Novak {Novakovic} and Boontawee {Suntisrivaraporn}}, booktitle = {Proceedings of the 2008 International Workshop on Description Logics ({DL2008})}, series = {CEUR-WS}, title = {A Proof-Theoretic Subsumption Reasoner for Hybrid $\mathcal{EL}$-{TBoxes}}, volume = {353}, year = {2008}, }

Franz Baader and Rafael Peñaloza:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Automata-Based Axiom Pinpointing**. In Alessandro Armando, Peter Baumgartner, and Gilles Dowek, editors,*Proceedings of the 4th International Joint Conference on Automated Reasoning, (IJCAR 2008)*, volume 5195 of*Lecture Notes in Artificial Intelligence*, pages 226–241. Springer, 2008.Abstract BibTeX Entry PDF File ©Springer-Verlag

Axiom pinpointing has been introduced in description logics (DL) to help the user understand the reasons why consequences hold by computing minimal subsets of the knowledge base that have the consequence in question (MinA). Most of the pinpointing algorithms described in the DL literature are obtained as extensions of tableau-based reasoning algorithms for computing consequences from DL knowledge bases. In this paper, we show that automata-based algorithms for reasoning in DLs can also be extended to pinpointing algorithms. The idea is that the tree automaton constructed by the automata-based approach can be transformed into a weighted tree automaton whose so-called behaviour yields a pinpointing formula, i.e., a monotone Boolean formula whose minimal valuations correspond to the MinAs. We also develop an approach for computing the bahaviour of a given weighted tree automaton.

@inproceedings{ BaPe-IJCAR08, author = {Franz {Baader} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 4th International Joint Conference on Automated Reasoning, (IJCAR 2008)}, editor = {Alessandro {Armando} and Peter {Baumgartner} and Gilles {Dowek}}, pages = {226--241}, publisher = {Springer}, series = {Lecture Notes in Artificial Intelligence}, title = {Automata-Based Axiom Pinpointing}, volume = {5195}, year = {2008}, }

Franz Baader and Boontawee Suntisrivaraporn:

Abstract BibTeX Entry PDF File

**Debugging SNOMED CT Using Axiom Pinpointing in the Description Logic**\(\mathcal{EL}^+\). In*Proceedings of the 3rd Knowledge Representation in Medicine (KR-MED'08): Representing and Sharing Knowledge Using SNOMED*, volume 410 of*CEUR-WS*, 2008.Abstract BibTeX Entry PDF File

SNOMED CT is a large-scale medical ontology, which is developed using a variant of the inexpressive Description Logic EL. Description Logic reasoning can not only be used to compute subsumption relationships between SNOMED concepts, but also to pinpoint the reason why a certain subsumption relationship holds by computing the axioms responsible for this relationship. This helps developers and users of SNOMED CT to understand why a given subsumption relationship follows from the ontology, which can be seen as a first step toward removing unwanted subsumption relationships. In this paper, we describe a new method for axiom pinpointing in the Description Logic EL+, which is based on the computation so-called reachability-based modules. Our experiments on SNOMED CT show that the sets of axioms explaining subsumption are usually quite small, and that our method is fast enough to compute such sets on demand.

@inproceedings{ BaaSun-KRMED-08, author = {Franz {Baader} and Boontawee {Suntisrivaraporn}}, booktitle = {Proceedings of the 3rd Knowledge Representation in Medicine (KR-MED'08): Representing and Sharing Knowledge Using SNOMED}, series = {CEUR-WS}, title = {Debugging {SNOMED CT} Using Axiom Pinpointing in the Description Logic $\mathcal{EL}^+$}, volume = {410}, year = {2008}, }

Meghyn Bienvenu:

Abstract BibTeX Entry PDF File

**Complexity of Abduction in the EL Family of Lightweight Description Logics**. In Gerhard Brewka and Jérôme Lang, editors,*Proceedings of the Eleventh International Conference on Principles of Knowledge Representation and Reasoning (KR08)*, pages 220–230. AAAI Press, 2008.Abstract BibTeX Entry PDF File

The complexity of logic-based abduction has been extensively studied for the case in which the background knowledge is represented by a propositional theory, but very little is known about abduction with respect to description logic knowledge bases. The purpose of the current paper is to examine the complexity of logic-based abduction for the EL family of lightweight description logics. We consider several minimality criteria for explanations (set inclusion, cardinality, prioritization, and weight) and three decision problems: deciding whether an explanation exists, deciding whether a given hypothesis appears in some acceptable explanation, and deciding whether a given hypothesis belongs to every acceptable explanation. We determine the complexity of these tasks for general TBoxes and also for EL and EL+ terminologies. We also provide results concerning the complexity of computing abductive explanations.

@inproceedings{ bienvenu-kr08, author = {Meghyn {Bienvenu}}, booktitle = {Proceedings of the Eleventh International Conference on Principles of Knowledge Representation and Reasoning (KR08)}, editor = {Gerhard {Brewka} and J{\'e}r{\^o}me {Lang}}, pages = {220--230}, publisher = {AAAI Press}, title = {Complexity of Abduction in the EL Family of Lightweight Description Logics}, year = {2008}, }

Meghyn Bienvenu:

Abstract BibTeX Entry PDF File

**Prime Implicate Normal Form for**\(\mathcal{ALC}\)**Concepts**. In*Proceedings of the Twenty-Third Conference on Artificial Intelligence (AAAI-08)*, pages 412–417. AAAI Press, 2008.Abstract BibTeX Entry PDF File

In this paper, we present a normal form for concept expressions in the description logic ALC which is based on a recently introduced notion of prime implicate for the modal logic K. We show that concepts in prime implicate normal form enjoy a number of interesting properties. In particular, we prove that subsumption between ALC concepts in prime implicate normal form can be carried out in polynomial time using a simple structural subsumption algorithm reminiscent of those used for less expressive description logics. We provide a sound and complete algorithm for putting concepts into prime implicate normal form, and we investigate the spatial complexity of this transformation, showing there to be an at most doubly-exponential blowup in concept length. At the end of the paper, we compare prime implicate normal form to two other normal forms for ALC, discussing the relative merits of the different approaches.

@inproceedings{ BienvenuAAAI08, author = {Meghyn {Bienvenu}}, booktitle = {Proceedings of the Twenty-Third Conference on Artificial Intelligence (AAAI-08)}, pages = {412--417}, publisher = {AAAI Press}, title = {Prime Implicate Normal Form for {$\mathcal{ALC}$} Concepts}, year = {2008}, }

Birte Glimm, Carsten Lutz, Ian Horrocks, and Ulrike Sattler:

Abstract BibTeX Entry PDF File

**Answering conjunctive queries in the**\(\mathcal{SHIQ}\)**description logic**.*Journal of Artificial Intelligence Research*, 31:150–197, 2008.Abstract BibTeX Entry PDF File

Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, conjunctive query answering over DL knowledge bases is only poorly understood if transitive roles are admitted in the query. In this paper, we consider unions of conjunctive queries over knowledge bases formulated in the prominent DL SHIQ and allow transitive roles in both the query and the knowledge base. We show decidability of query answering in this setting and establish two tight complexity bounds: regarding combined complexity, we prove that there is a deterministic algorithm for query answering that needs time single exponential in the size of the KB and double exponential in the size of the query, which is optimal. Regarding data complexity, we prove containment in co-NP.

@article{ GliHoLuSa-JAIR08, author = {Birte {Glimm} and Carsten {Lutz} and Ian {Horrocks} and Ulrike {Sattler}}, journal = {Journal of Artificial Intelligence Research}, pages = {150--197}, title = {Answering conjunctive queries in the $\mathcal{SHIQ}$ description logic}, volume = {31}, year = {2008}, }

Christoph Haase and Carsten Lutz:

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**Complexity of Subsumption in the EL Family of Description Logics: Acyclic and Cyclic TBoxes**. In Malik Ghallab, Constantine D. Spyropoulos, Nikos Fakotakis, and Nikos Avouris, editors,*Proceedings of the 18th European Conference on Artificial Intelligence (ECAI08)*, volume 178 of*Frontiers in Artificial Intelligence and Applications*, pages 25–29. IOS Press, 2008.Abstract BibTeX Entry PDF File

We perform an exhaustive study of the complexity of subsumption in the EL family of lightweight description logics w.r.t. acyclic and cyclic TBoxes. It turns out that there are interesting members of this family for which subsumption w.r.t. cyclic TBoxes is tractable, whereas it is ExpTime-complete w.r.t. general TBoxes. For other extensions that are intractable w.r.t. general TBoxes, we establish intractability already for acyclic and cyclic TBoxes.

@inproceedings{ Haase-Lutz-ECAI08, author = {Christoph {Haase} and Carsten {Lutz}}, booktitle = {Proceedings of the 18th European Conference on Artificial Intelligence ({ECAI08})}, editor = {Malik {Ghallab} and Constantine D. {Spyropoulos} and Nikos {Fakotakis} and Nikos {Avouris}}, pages = {25--29}, publisher = {IOS Press}, series = {Frontiers in Artificial Intelligence and Applications}, title = {Complexity of Subsumption in the EL Family of Description Logics: Acyclic and Cyclic TBoxes}, volume = {178}, year = {2008}, }

Matthias Heinrich, Antje Boehm-Peters, and Martin Knechtel:

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**MoDDo - a tailored documentation system for model-driven software development**. In*ICWI '08: Proceedings of the IADIS International Conference WWW/Internet*, pages 321–324, 2008.Abstract BibTeX Entry PDF File

In the last decade Model-Driven Software Development (MDSD) has become an established software engineering discipline. The new approach dramatically changed the entire software development lifecycle. However, the documentation process was not adapted and stuck with the old paradigms. In this paper, we propose a model-driven documentation system which is adapted to the MDSD lifecycle and therefore exploits synergies coming along with the alignment of software development and software documentation. Furthermore, the proposed documentation system builds upon the Internet as their major provisioning platform.

@inproceedings{ HeBK-ICWI-08, author = {Matthias {Heinrich} and Antje {Boehm-Peters} and Martin {Knechtel}}, booktitle = {ICWI '08: Proceedings of the IADIS International Conference WWW/Internet}, pages = {321--324}, title = {MoDDo - a tailored documentation system for model-driven software development}, year = {2008}, }

Miki Hermann and Barış Sertkaya:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**On the Complexity of Computing Generators of Closed Sets**. In Raoul Medina and Sergei A. Obiedkov, editors,*Proceedings of the 6th International Conference on Formal Concept Analysis, (ICFCA 2008)*, volume 4933 of*Lecture Notes in Computer Science*, pages 158–168. Springer Verlag, 2008.Abstract BibTeX Entry PDF File ©Springer-Verlag

We investigate the computational complexity of some decision and counting problems related to generators of closed sets fundamental in Formal Concept Analysis. We recall results from the literature about the problem of checking the existence of a generator with a specified cardinality, and about the problem of determining the number of minimal generators. Moreover, we show that the problem of counting minimum cardinality generators is #.coNP-complete. We also present an incremental-polynomial time algorithm from relational database theory that can be used for computing all minimal generators of an implication-closed set.

@inproceedings{ HeSe08, author = {Miki {Hermann} and Bar\i{}\c{s} {Sertkaya}}, booktitle = {Proceedings of the 6th International Conference on {F}ormal {C}oncept {A}nalysis, {(ICFCA 2008)}}, editor = {Raoul {Medina} and Sergei A. {Obiedkov}}, pages = {158--168}, publisher = {Springer Verlag}, series = {Lecture Notes in Computer Science}, title = {On the Complexity of Computing Generators of Closed Sets}, volume = {4933}, year = {2008}, }

Martin Knechtel:

BibTeX Entry PDF File

**Access restriction inside ontologies**. In Rainer Ruggaber, editor,*I-ESA'08: Proceedings of the 1st Internet of Services Doctoral Symposium 2008 at International Conference on Interoperability of Enterprise Systems and Applications*, volume 374 of*CEUR Workshop Proceedings, ISSN 1613-0073*, 2008.BibTeX Entry PDF File

@inproceedings{ Knechtel-IESA-08, address = {Berlin, Germany}, author = {Martin {Knechtel}}, booktitle = {I-ESA'08: Proceedings of the 1st Internet of Services Doctoral Symposium 2008 at International Conference on Interoperability of Enterprise Systems and Applications}, editor = {Rainer {Ruggaber}}, series = {CEUR Workshop Proceedings, ISSN 1613-0073}, title = {Access restriction inside ontologies}, volume = {374}, year = {2008}, }

Martin Knechtel:

BibTeX Entry PDF File

**Access rights and collaborative ontology integration for reuse across security domains**. In Philippe Cudré-Mauroux, editor,*Proceedings of the ESWC 2008 Ph.D. Symposium*, volume 358 of*CEUR Workshop Proceedings, ISSN 1613-0073*, pages 36–40, 2008.BibTeX Entry PDF File

@inproceedings{ Knechtel-ESWC-08, author = {Martin {Knechtel}}, booktitle = {Proceedings of the ESWC 2008 Ph.D. Symposium}, editor = {Philippe {Cudré-Mauroux}}, pages = {36--40}, series = {CEUR Workshop Proceedings, ISSN 1613-0073}, title = {Access rights and collaborative ontology integration for reuse across security domains}, volume = {358}, year = {2008}, }

Martin Knechtel and Jan Hladik:

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**RBAC Authorization Decision with DL Reasoning**. In*ICWI '08: Proceedings of the IADIS International Conference WWW/Internet*, pages 169–176, 2008.Abstract BibTeX Entry PDF File

Access control is crucial also for the Semantic Web. Technologies and Standards from the Semantic Web Community itself provide powerful means to model access control definitions and automatically reason about them. We extend Hierarchical Role Based Access Control by a class hierarchy of the accessed objects and give it the name RBAC-CH. We present a concept to implement this model in a DL knowledge base in the form of an OWL 1.1 ontology. The permissions are defined for user roles on object classes. The concrete permissions of users to objects are then automatically derived by a reasoning service. We present a straightforward ontology model and evaluate it in a running example with a state of the art reasoner. For the RBAC policy enforcement we need to run the reasoner only once and at runtime we only need to read out the inferred knowledge base to decide about authorization.

@inproceedings{ KnHl-ICWI-08, author = {Martin {Knechtel} and Jan {Hladik}}, booktitle = {ICWI '08: Proceedings of the IADIS International Conference WWW/Internet}, pages = {169--176}, title = {{RBAC} Authorization Decision with {DL} Reasoning}, year = {2008}, }

Martin Knechtel, Jan Hladik, and Frithjof Dau:

BibTeX Entry PDF File

**Using OWL DL Reasoning to decide about authorization in RBAC**. In Catherine Dolbear, Alan Ruttenberg, and Ulrike Sattler, editors,*OWLED '08: Proceedings of the OWLED 2008 Workshop on OWL: Experiences and Directions*, volume 432 of*CEUR Workshop Proceedings*, 2008.BibTeX Entry PDF File

@inproceedings{ KnHD-OWLED-08, author = {Martin {Knechtel} and Jan {Hladik} and Frithjof {Dau}}, booktitle = {OWLED '08: Proceedings of the OWLED 2008 Workshop on OWL: Experiences and Directions}, editor = {Catherine {Dolbear} and Alan {Ruttenberg} and Ulrike {Sattler}}, series = {CEUR Workshop Proceedings}, title = {Using {OWL DL} Reasoning to decide about authorization in {RBAC}}, volume = {432}, year = {2008}, }

Martin Knechtel and Daniel Schuster:

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**Semantische Integration und Wiederverwendung von Produktontologien für offene Marktplätze im Web**. In*Proceedings of GeNeMe'08 Workshop*, 2008. In German.BibTeX Entry PDF File

@inproceedings{ KnSc-GeNeMe-08, author = {Martin {Knechtel} and Daniel {Schuster}}, booktitle = {Proceedings of GeNeMe'08 Workshop}, note = {In German.}, title = {{S}emantische {I}ntegration und {W}iederverwendung von {P}roduktontologien für offene {M}arktplätze im {W}eb}, year = {2008}, }

Boris Konev, Carsten Lutz, Dirk Walther, and Frank Wolter:

Abstract BibTeX Entry PDF File

**CEX and MEX: Logical Diff and Semantic Module Extraction in a Fragment of OWL**. In Kendall Clark and Peter F. Patel-Schneider, editors,*In Proceedings of the OWLED 2008 DC Workshop on OWL: Experiences and Directions*, 2008.Abstract BibTeX Entry PDF File

We consider a logical diff operator and semantic module extraction from ontologies. In recent work, we have shown that, for the fragment EL of OWL, these problems can be solved in polynomial time. In this paper, we evaluate our algorithms by experimenting with the prototype implementations CEX and MEX on real-worlds ontologies such as SNOMED. The experiments show the practicability our approach and highlight the benefits of a strictly semantic approach: the diff operation is very fine-grained and the extracted modules are smaller than the ones generated by related approaches.

@inproceedings{ KonevEtAl-OWLED08DC, author = {Boris {Konev} and Carsten {Lutz} and Dirk {Walther} and Frank {Wolter}}, booktitle = {In Proceedings of the OWLED 2008 DC Workshop on OWL: Experiences and Directions}, editor = {Kendall {Clark} and Peter F. {Patel-Schneider}}, title = {CEX and MEX: Logical Diff and Semantic Module Extraction in a Fragment of OWL}, year = {2008}, }

Boris Konev, Carsten Lutz, Dirk Walther, and Frank Wolter:

Abstract BibTeX Entry PDF File

**Formal Properties of Modularisation**. In Alessandro Armando, Peter Baumgartner, and Gilles Dowek, editors,*Proceedings of the 4th International Joint Conference on Automated Reasoning (IJCAR2008)*, number 5195 in*LNCS*, pages 179–193. Springer, 2008.Abstract BibTeX Entry PDF File

Modularity of ontologies is currently an active research field, and many different notions of a module have been proposed. In this paper, we review the fundamental principles of modularity and identify formal properties that a robust notion of modularity should satisfy. We explore these properties in detail in the contexts of description logic and classical predicate logic and put them into the perspective of well-known concepts from logic and modular software specification such as interpolation, forgetting and uniform interpolation. We also discuss reasoning problems related to modularity.

@inproceedings{ KoLuWaWo-ModBook08, author = {Boris {Konev} and Carsten {Lutz} and Dirk {Walther} and Frank {Wolter}}, booktitle = {Proceedings of the 4th International Joint Conference on Automated Reasoning ({IJCAR2008})}, editor = {Alessandro {Armando} and Peter {Baumgartner} and Gilles {Dowek}}, number = {5195}, pages = {179--193}, publisher = {Springer}, series = {LNCS}, title = {Formal Properties of Modularisation}, year = {2008}, }

Boris Konev, Carsten Lutz, Dirk Walther, and Frank Wolter:

Abstract BibTeX Entry PDF File

**Semantic Modularity and Module Extraction in Description Logics**. In Malik Ghallab, Constantine D. Spyropoulos, Nikos Fakotakis, and Nikos Avouris, editors,*Proceedings of the 18th European Conference on Artificial Intelligence (ECAI08)*, volume 178 of*Frontiers in Artificial Intelligence and Applications*, pages 55–59. IOS Press, 2008.Abstract BibTeX Entry PDF File

The aim of this paper is to study semantic notions of modularity in description logic (DL) terminologies and reasoning problems that are relevant for modularity. We define two notions of a module whose independence is formalized in a model-theoretic way. Focusing mainly on the DLs EL and ALC, we the develop algorithms for module extraction, for checking whether a part of a terminology is a module, and for a number of related problems. We also analyse the complexity of these problems, which ranges from tractable to undecidable. Finally, we provide an experimental evaluation of our module extraction algorithms based on the large-scale terminology SNOMED CT.

@inproceedings{ Konev-Lutz-Walther-Wolter-ECAI08, author = {Boris {Konev} and Carsten {Lutz} and Dirk {Walther} and Frank {Wolter}}, booktitle = {Proceedings of the 18th European Conference on Artificial Intelligence ({ECAI08})}, editor = {Malik {Ghallab} and Constantine D. {Spyropoulos} and Nikos {Fakotakis} and Nikos {Avouris}}, pages = {55--59}, publisher = {IOS Press}, series = {Frontiers in Artificial Intelligence and Applications}, title = {Semantic Modularity and Module Extraction in Description Logics}, volume = {178}, year = {2008}, }

Boris Konev, Carsten Lutz, Dirk Walther, and Frank Wolte r:

Abstract BibTeX Entry PDF File

**Logical Difference and Module Extraction with CEX and MEX**. In*Proceedings of the 21st International Workshop on Description Lo gics (DL2008)*, volume 353 of*CEUR-WS*, 2008.Abstract BibTeX Entry PDF File

In this paper, we study the module extraction and logical difference problems for acyclic EL-terminologies. We show that both problems are tractable, present prototype implementations, and evaluate performance on a series of examples. In particular, our implementations can handle large real-world terminologies such as SNOMED-CT.

@inproceedings{ KoLuWaWo-DL08, author = {Boris {Konev} and Carsten {Lutz} and Dirk {Walther} and Frank Wolte\ {r}}, booktitle = {Proceedings of the 21st International Workshop on Description Lo\ \ gics ({DL2008})}, series = {CEUR-WS}, title = {Logical Difference and Module Extraction with CEX and MEX}, volume = {353}, year = {2008}, }

Hongkai Liu, Carsten Lutz, and Maja Milicic:

Abstract BibTeX Entry PDF File

**The Projection Problem for**\(\mathcal{EL}\)**Actions**. In*Proceedings of the 2008 International Workshop on Description Logics (DL2008)*, volume 353 of*CEUR-WS*, 2008.Abstract BibTeX Entry PDF File

In this paper, we investigate the complexity of executability and projection in EL and the extension of EL with atomic negation. In both cases, we allow for negated assertions in the post-conditions of actions. Our results show that, in general, tractability does not transfer from instance checking in EL to executability and projection. Even in EL without TBoxes, the latter problems are co-NP-hard. This is due to two sources of intractability: (1) existential restrictions in the initial ABox together with negated assertions in post-conditions; and (2) conditional post-conditions. We prove a matching co-NP upper bound for EL with atomic negation. We also show that, in the presence of acyclic TBoxes, projection in EL is PSpace-hard and thus not easier than in ALC. Finally, we identify restrictions under which executability and projection in EL w.r.t. acyclic TBoxes can be decided in polynomial time.

@inproceedings{ LiLuMi-DL-08, author = {Hongkai {Liu} and Carsten {Lutz} and Maja {Milicic}}, booktitle = {Proceedings of the 2008 International Workshop on Description Logics ({DL2008})}, series = {CEUR-WS}, title = {The Projection Problem for $\mathcal{EL}$ Actions}, volume = {353}, year = {2008}, }

Carsten Lutz:

Abstract BibTeX Entry PDF File

**The Complexity of Conjunctive Query Answering in Expressive Description Logics**. In Alessandro Armando, Peter Baumgartner, and Gilles Dowek, editors,*Proceedings of the 4th International Joint Conference on Automated Reasoning (IJCAR2008)*, number 5195 in*LNAI*, pages 179–193. Springer, 2008.Abstract BibTeX Entry PDF File

Conjunctive query answering plays a prominent role in applications of description logics (DLs) that involve instance data, but its exact complexity was a long-standing open problem. We determine the complexity of conjunctive query answering in expressive DLs between ALC and SHIQ, and thus settle the problem. In a nutshell, we show that conjunctive query answering is 2ExpTime-complete in the presence of inverse roles, and only ExpTime-complete without them.

@inproceedings{ Lutz-IJCAR08, author = {Carsten {Lutz}}, booktitle = {Proceedings of the 4th International Joint Conference on Automated Reasoning ({IJCAR2008})}, editor = {Alessandro {Armando} and Peter {Baumgartner} and Gilles {Dowek}}, number = {5195}, pages = {179--193}, publisher = {Springer}, series = {LNAI}, title = {The Complexity of Conjunctive Query Answering in Expressive Description Logics}, year = {2008}, }

Carsten Lutz:

Abstract BibTeX Entry PDF File

**Two Upper Bounds for Conjunctive Query Answering in SHIQ**. In*Proceedings of the 21st International Workshop on Description Logics (DL2008)*, volume 353 of*CEUR-WS*, 2008.Abstract BibTeX Entry PDF File

We have shown recently that, in extensions of ALC that involve inverse roles, conjunctive query answering is harder than satisfiability: it is 2-ExpTime-complete in general and NExpTime-hard if queries are connected and contain at least one answer variable. In this paper, we show that, in SHIQ without inverse roles (and without transitive roles in the query), conjunctive query answering is only ExpTime-complete and thus not harder than satisfiability. We also show that the mentioned NExpTime-lower bound is tight.

@inproceedings{ Lutz-DL08, author = {Carsten {Lutz}}, booktitle = {Proceedings of the 21st International Workshop on Description Logics ({DL2008})}, series = {CEUR-WS}, title = {Two Upper Bounds for Conjunctive Query Answering in SHIQ}, volume = {353}, year = {2008}, }

Carsten Lutz, Frank Wolter, and Michael Zakharyaschev:

Abstract BibTeX Entry PDF File

**Temporal Description Logics: A Survey**. In*Proceedings of the Fifteenth International Symposium on Temporal Representation and Reasoning*. IEEE Computer Society Press, 2008.Abstract BibTeX Entry PDF File

We survey temporal description logics that are based on standard temporal logics such as LTL and CTL. In particular, we concentrate on the computational complexity of the satisfiability problem and algorithms for deciding it.

@inproceedings{ LuWoZa-Time08, author = {Carsten {Lutz} and Frank {Wolter} and Michael {Zakharyaschev}}, booktitle = {Proceedings of the Fifteenth International Symposium on Temporal Representation and Reasoning}, publisher = {IEEE Computer Society Press}, title = {Temporal Description Logics: A Survey}, year = {2008}, }

Rafael Peñaloza:

Abstract BibTeX Entry PDF File

**Automata-based Pinpointing for DLs**. In*Proceedings of the 2008 International Workshop on Description Logics (DL2008)*, volume 353 of*CEUR-WS*, 2008.Abstract BibTeX Entry PDF File

The task of pinpointing the relevant subsets of axioms for a given property has acquired relevancy in the last years. In this paper we show how automata-based decision procedures can be adapted to produce a so-called pinpointing formula. The relevance of this method is method is shown by giving an (optimal) algorithm that computes pinpointing formulas for unsatisfiability of SI concepts w.r.t. general TBoxes.

@inproceedings{ Pen-DL08, author = {Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 2008 International Workshop on Description Logics ({DL2008})}, series = {CEUR-WS}, title = {Automata-based Pinpointing for DLs}, volume = {353}, year = {2008}, }

Stefan Schulz, Kornél Markó, and Boontawee Suntisrivaraporn:

Abstract BibTeX Entry PDF File

**Formal representation of complex SNOMED CT expressions**.*BMC Medical Informatics and Decision Making*, 8(1):S9, 2008.Abstract BibTeX Entry PDF File

Background: Definitory expressions about clinical procedures, findings and diseases constitute a major benefit of a formally founded clinical reference terminology which is ontologically sound and suited for formal reasoning. SNOMED CT claims to support formal reasoning by description-logic based concept definitions. Methods: On the basis of formal ontology criteria we analyze complex SNOMED CT concepts, such as "Concussion of Brain with(out) Loss of Consciousness", using alternatively full first order logics and the description logic EL. Results: Typical complex SNOMED CT concepts, including negations or not, can be expressed in full first-order logics. Negations cannot be properly expressed in the description logic EL underlying SNOMED CT. All concepts concepts the meaning of which implies a temporal scope may be subject to diverging interpretations, which are often unclear in SNOMED CT as their contextual determinants are not made explicit. Conclusion: The description of complex medical occurrents is ambiguous, as the same situations can be described as (i) a complex occurrent C that has A and B as temporal parts, (ii) a simple occurrent A' defined as a kind of A followed by some B, or (iii) a simple occurrent B' defined as a kind of B preceded by some A. As negative statements in SNOMED CT cannot be exactly represented without a (computationally costly) extension of the set of logical constructors, a solution can be the reification of negative statments (e.g., "Period with no Loss of Consciousness"), or the use of the SNOMED CT context model. However, the interpretation of SNOMED CT context model concepts as description logics axioms is not recommended, because this may entail unintended models.

@article{ SchMarSun-BMC-08, author = {Stefan {Schulz} and Korn{\'e}l {Mark{\'o}} and Boontawee {Suntisrivaraporn}}, journal = {BMC Medical Informatics and Decision Making}, number = {1}, pages = {S9}, title = {Formal representation of complex {SNOMED CT} expressions}, volume = {8}, year = {2008}, }

Barış Sertkaya:

Abstract BibTeX Entry PDF File

**Explaining User Errors in Description Logic Knowledge Base Completion**. In*Informal Proceedings of the 2008 International Workshop on Complexity, Expressibility, and Decidability in Automated Reasoning (CEDAR'08)*, 2008.Abstract BibTeX Entry PDF File

In our previous work we have developed a method for completing a Description Logic knowledge base w.r.t. a fixed interpretation by asking questions to a domain expert. Our experiments showed that during this process the domain expert sometimes gives wrong answers to the questions, which cause the resultant knowledge base to have unwanted consequences. In the present work we consider the problem of explaining the reasons of such unwanted consequences in knowledge base completion. We show that in this setting the problem of deciding the existence of an explanation within a specified cardinality bound is NP-complete, and the problem of counting explanations that are minimal w.r.t. set inclusion is #P-complete. We also provide an algorithm that computes one minimal explanation by performing at most polynomially many subsumption tests.

@inproceedings{ Sert08b, author = {Bar\i{}\c{s} {Sertkaya}}, booktitle = {Informal Proceedings of the 2008 International Workshop on Complexity, Expressibility, and Decidability in Automated Reasoning ({CEDAR'08})}, title = {Explaining User Errors in Description Logic Knowledge Base Completion}, year = {2008}, }

Barış Sertkaya:

Abstract BibTeX Entry PDF File

**Explaining User Errors in Knowledge Base Completion**. In*Proceedings of the 2008 International Workshop on Description Logics (DL2008)*, volume 353 of*CEUR-WS*, 2008.Abstract BibTeX Entry PDF File

Knowledge base completion is a method for extending both the terminological and assertional part of a Description Logic knowledge base by using information provided by a domain expert. It ensures that the extended knowledge base is complete w.r.t. a fixed interpretation in a certain, well-defined sense. Here we consider the problem of explaining user errors in knowledge base completion. We show that for this setting, the problem of deciding the existence of an explanation within a specified cardinality bound is NP-complete, and the problem of counting explanations that are minimal w.r.t. set inclusion is #P-complete. We also provide an algorithm that computes one minimal explanation by performing at most polynomially many subsumption tests.

@inproceedings{ Sert08, author = {Bar\i{}\c{s} {Sertkaya}}, booktitle = {Proceedings of the 2008 International Workshop on Description Logics ({DL2008})}, series = {CEUR-WS}, title = {Explaining User Errors in Knowledge Base Completion}, volume = {353}, year = {2008}, }

Boontawee Suntisrivaraporn:

Abstract BibTeX Entry PDF File

**Empirical evaluation of reasoning in lightweight DLs on life science ontologies**. In*Proceedings of the 2nd Mahasarakham International Workshop on AI (MIWAI'08)*, 2008.Abstract BibTeX Entry PDF File

Description Logics (DLs) belong to a successful family of knowledge representation formalisms with two key assets: formally well-dned semantics which allows to represent knowledge in an unambiguous way and automated reasoning which allows to infer implicit knowledge from the one given explicitly. One of the most prominent applications of DLs is their use as ontology languages, especially for the life science domain. This paper investigates several life science ontologies and summarizes their common characteristics. It suggests that the use of lightweight DLs in the EL family, in which reasoning is tractable, is bencial both in terms of expressivity and of scalability. The claim is supported by extensive empirical evaluation of various DL reasoning services on large-scale life science ontologies, including an overview comparison of state-ofthe-art DL reasoners.

@inproceedings{ Sun-MIWAI-08, author = {Boontawee {Suntisrivaraporn}}, booktitle = {Proceedings of the 2nd Mahasarakham International Workshop on AI (MIWAI'08)}, title = {Empirical evaluation of reasoning in lightweight {DLs} on life science ontologies}, year = {2008}, }

Boontawee Suntisrivaraporn:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Module Extraction and Incremental Classification: A Pragmatic Approach for**\(\mathcal{EL}^+\)**Ontologies**. In Sean Bechhofer, Manfred Hauswirth, Joerg Hoffmann, and Manolis Koubarakis, editors,*Proceedings of the 5th European Semantic Web Conference (ESWC'08)*, volume 5021 of*Lecture Notes in Computer Science*, pages 230–244. Springer-Verlag, 2008.Abstract BibTeX Entry PDF File ©Springer-Verlag

The description logic EL+ has recently proved practically useful in the life science domain with presence of several large-scale biomedical ontologies such as SNOMED CT. To deal with ontologies of this scale, standard reasoning of classification is essential but not sufficient. The ability to extract relevant fragments from a large ontology and to incrementally classify it has become more crucial to support ontology design, maintenance and re-use. In this paper, we propose a pragmatic approach to module extraction and incremental classification for EL+ ontologies and report on empirical evaluations of our algorithms which have been implemented as an extension of the CEL reasoner.

@inproceedings{ Sun-ESWC-08, author = {Boontawee {Suntisrivaraporn}}, booktitle = {Proceedings of the 5th European Semantic Web Conference ({ESWC'08})}, editor = {Sean {Bechhofer} and Manfred {Hauswirth} and Joerg {Hoffmann} and Manolis {Koubarakis}}, pages = {230--244}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Module Extraction and Incremental Classification: A Pragmatic Approach for $\mathcal{EL}^+$ Ontologies}, volume = {5021}, year = {2008}, }

Boontawee Suntisrivaraporn, Guilin Qi, Qiu Ji, and Peter Haase:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**A Modularization-based Approach to Finding All Justifications for OWL DL Entailments**. In John Domingue and Chutiporn Anutariya, editors,*Proceedings of the 3th Asian Semantic Web Conference (ASWC'08)*, volume 5367 of*Lecture Notes in Computer Science*, pages 1–15. Springer-Verlag, 2008.Abstract BibTeX Entry PDF File ©Springer-Verlag

Finding the justifications for an entailment (i.e., minimal sets of axioms responsible for it) is a prominent reasoning service in ontology engineering, as justifications facilitate important tasks like debugging inconsistencies or undesired subsumption. Though several algorithms for finding all justifications exist, issues concerning efficiency and scalability remain a challenge due to the sheer size of real-life ontologies. In this paper, we propose a novel method for finding all justifications in OWL DL ontologies by limiting the search space to smaller modules. To this end, we show that so-called locality-based modules cover all axioms in the justifications. We present empirical results that demonstrate an improvement of several orders of magnitude in efficiency and scalability of finding all justifications in OWL DL ontologies.

@inproceedings{ SunEtAl-ASWC-08, author = {Boontawee {Suntisrivaraporn} and Guilin {Qi} and Qiu {Ji} and Peter {Haase}}, booktitle = {Proceedings of the 3th Asian Semantic Web Conference ({ASWC'08})}, editor = {John {Domingue} and Chutiporn {Anutariya}}, pages = {1--15}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {A Modularization-based Approach to Finding All Justifications for OWL DL Entailments}, volume = {5367}, year = {2008}, }

## 2007

A. Artale, R. Kontchakov, C. Lutz, F. Wolter, and M. Zakharyaschev:

Abstract BibTeX Entry PDF File

**Temporalising Tractable Description Logics**. In*Proceedings of the Fourteenth International Symposium on Temporal Representation and Reasoning*. IEEE Computer Society Press, 2007.Abstract BibTeX Entry PDF File

It is known that for temporal languages, such as first-order LTL, reasoning about constant (time-independent) relations is almost always undecidable. This applies to temporal description logics as well: constant binary relations together with general concept subsumptions in combinations of LTL and the basic description logic ALC cause undecidability. In this paper, we explore temporal extensions of two recently introduced families of "weak" description logics known as DL-Lite and EL. Our results are twofold: temporalisations of even rather expressive variants of DL-Lite turn out to be decidable, while the temporalisation of EL with general concept subsumptions and constant relations is undecidable.

@inproceedings{ ArKoLuWoZa-TIME-07, author = {A. {Artale} and R. {Kontchakov} and C. {Lutz} and F. {Wolter} and M. {Zakharyaschev}}, booktitle = {Proceedings of the Fourteenth International Symposium on Temporal Representation and Reasoning}, publisher = {IEEE Computer Society Press}, title = {Temporalising Tractable Description Logics}, year = {2007}, }

Alessandro Artale, Carsten Lutz, and David Toman:

Abstract BibTeX Entry PDF File

**A Description Logic of Change**. In Manuela Veloso, editor,*Proceedings of the Twentieth International Joint Conference on Artificial Intelligence (IJCAI'07)*, pages 218–223. AAAI Press, 2007.Abstract BibTeX Entry PDF File

We combine the modal logic S5 with the description logic (DL) ALCQI. The resulting multi-dimensional DL S5-ALCQI supports reasoning about change by allowing to express that concepts and roles change over time. It cannot, however, discriminate between changes in the past and in the future. Our main technical result is that satisfiability of S5-ALCQI concepts with respect to general TBoxes (including GCIs) is decidable and 2-ExpTime-complete. In contrast, reasoning in temporal DLs that are able to discriminate between past and future is inherently undecidable. We argue that our logic is sufficient for reasoning about temporal conceptual models with time-stamping constraints.

@inproceedings{ ArLuTo-07, author = {Alessandro {Artale} and Carsten {Lutz} and David {Toman}}, booktitle = {Proceedings of the Twentieth International Joint Conference on Artificial Intelligence (IJCAI'07)}, editor = {Manuela {Veloso}}, pages = {218--223}, publisher = {AAAI Press}, title = {A Description Logic of Change}, year = {2007}, }

F. Baader, editor:

Abstract BibTeX Entry

**18th International Conference on Rewriting Techniques and Applications (RTA 2007)**. Springer-Verlag, 2007.Abstract BibTeX Entry

This volume contains the papers presented at the 18th International Conference on Rewriting Techniques and Applications (RTA'07), which was held on June 26–28, 2007, on the Paris campus of the Conservatoire National des Arts et Metiers (CNAM) in Paris, France.

@book{ BaaderRTA07, editor = {F. {Baader}}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {18th International Conference on Rewriting Techniques and Applications {(RTA 2007)}}, volume = {4533}, year = {2007}, }

F. Baader and S. Ghilardi:

Abstract BibTeX Entry PDF File

**Connecting Many-Sorted Theories**.*The Journal of Symbolic Logic*, 72(2):535–583, 2007.Abstract BibTeX Entry PDF File

Basically, the connection of two many-sorted theories is obtained by taking their disjoint union, and then connecting the two parts through connection functions that must behave like homomorphisms on the shared signature. We determine conditions under which decidability of the validity of universal formulae in the component theories transfers to their connection. In addition, we consider variants of the basic connection scheme. Our results can be seen as a generalization of the so-called E-connection approach for combining modal logics to an algebraic setting.

@article{ BaaGi-JSL-07, author = {F. {Baader} and S. {Ghilardi}}, journal = {The Journal of Symbolic Logic}, number = {2}, pages = {535--583}, title = {Connecting Many-Sorted Theories}, volume = {72}, year = {2007}, }

F. Baader, J. Hladik, and R. Peñaloza:

Abstract BibTeX Entry PDF File

**Blocking Automata for PSPACE DLs**. In D. Calvanese, E. Franconi, and S. Tessaris, editors,*Proceedings of the 2007 International Workshop on Description Logics*,*CEUR-WS*, 2007.Abstract BibTeX Entry PDF File

In Description Logics (DLs), both tableau-based and automata-based algorithms are frequently used to show decidability and complexity results for basic inference problems such as concept satisfiability. Whereas tableau-based algorithms usually yield worst-case optimal algorithms in the case of PSPACE-complete logics, it is often very hard to design optimal tableau-based algorithms for EXPTIME-complete DLs. In contrast, the automata-based approach is usually well-suited to prove EXPTIME upper-bounds, but its direct application will usually also yield an EXPTIME-algorithm for a PSPACE-complete logic since the (tree) automaton constructed for a given concept is usually exponentially large. In the present paper, we formulate conditions under which an on-the-fly construction of such an exponentially large automaton can be used to obtain a PSPACE-algorithm. We illustrate the usefulness of this approach by proving a new PSPACE upper-bound for satisfiability of concepts w.r.t. acyclic terminologies in the DL SI.

@inproceedings{ BaaHlaPen-DL-07, author = {F. {Baader} and J. {Hladik} and R. {Pe{\~n}aloza}}, booktitle = {Proceedings of the 2007 International Workshop on Description Logics}, editor = {D. {Calvanese} and E. {Franconi} and S. {Tessaris}}, series = {CEUR-WS}, title = {Blocking Automata for {PSPACE} {DLs}}, year = {2007}, }

F. Baader, J. Hladik, and R. Peñaloza:

Abstract BibTeX Entry PDF File PS File

**SI! Automata Can Show PSPACE Results for Description Logics**. In C. Martin-Vide, editor,*Proceedings of the First International Conference on Language and Automata Theory and Applications (LATA'07)*, 2007.Abstract BibTeX Entry PDF File PS File

In Description Logics (DLs), both tableau-based and automata-based algorithms are frequently used to show decidability and complexity results for basic inference problems such as satisfiability of concepts. Whereas tableau-based algorithms usually yield worst-case optimal algorithms in the case of PSPACE-complete logics, it is often very hard to design optimal tableau-based algorithms for EXPTIME-complete DLs. In contrast, the automata-based approach is usually well-suited to prove EXPTIME upper-bounds, but its direct application will usually also yield an EXPTIME-algorithm for a PSPACE-complete logic since the (tree) automaton constructed for a given concept is usually exponentially large. In the present paper, we formulate conditions under which an on-the-fly construction of such an exponentially large automaton can be used to obtain a PSPACE-algorithm. We illustrate the usefulness of this approach by proving a new PSPACE upper-bound for satisfiability of concepts w.r.t. acyclic terminologies in the DL SI, which extends the basic DL ALC with transitive and inverse roles.

@inproceedings{ BaaHlaPen-LATA-07, author = {F. {Baader} and J. {Hladik} and R. {Pe{\~n}aloza}}, booktitle = {Proceedings of the First International Conference on Language and Automata Theory and Applications ({LATA'07})}, editor = {C. {Martin-Vide}}, title = {{SI}! Automata Can Show {PSPACE} Results for Description Logics}, year = {2007}, }

F. Baader, I. Horrocks, and U. Sattler:

Abstract BibTeX Entry

**Description Logics**. In Frank van Harmelen, Vladimir Lifschitz, and Bruce Porter, editors,*Handbook of Knowledge Representation*, pages 135–179. Elsevier, 2007.Abstract BibTeX Entry

In this chapter we will introduce description logics, a family of logic-based knowledge representation languages that can be used to represent the terminological knowledge of an application domain in a structured way. We will first review their provenance and history, and show how the field has developed. We will then introduce the basic description logic ALC in some detail, including definitions of syntax, semantics and basic reasoning services, and describe important extensions such as inverse roles, number restrictions, and concrete domains. Next, we will discuss the relationship between description logics and other formalisms, in particular first order and modal logics; the most commonly used reasoning techniques, in particular tableaux, resolution and automata based techniques; and the computational complexity of basic reasoning problems. After reviewing some of the most prominent applications of description logics, in particular ontology language applications, we will conclude with an overview of other aspects of description logic research, and with pointers to the relevant literature.

@incollection{ BaHS07, author = {F. {Baader} and I. {Horrocks} and U. {Sattler}}, booktitle = {Handbook of Knowledge Representation}, editor = {Frank van {Harmelen} and Vladimir {Lifschitz} and Bruce {Porter}}, pages = {135--179}, publisher = {Elsevier}, title = {Description Logics}, year = {2007}, }

Franz Baader, Bernhard Ganter, Ulrike Sattler, and Baris Sertkaya:

Abstract BibTeX Entry PDF File

**Completing Description Logic Knowledge Bases using Formal Concept Analysis**. In Christine Golbreich, Aditya Kalyanpur, and Bijan Parsia, editors,*Proceedings of the Third International Workshop OWL: Experiences and Directions (OWLED 2007)*. CEUR-WS, 2007.Abstract BibTeX Entry PDF File

We propose an approach for extending both the terminological and the assertional part of a Description Logic knowledge base by using information provided by the knowledge base and by a domain expert. The use of techniques from Formal Concept Analysis ensures that, on the one hand, the interaction with the expert is kept to a minimum, and, on the other hand, we can show that the extended knowledge base is complete in a certain, well-defined sense.

@inproceedings{ BGSS07b, author = {Franz {Baader} and Bernhard {Ganter} and Ulrike {Sattler} and Baris {Sertkaya}}, booktitle = {Proceedings of the Third International Workshop OWL: Experiences and Directions {(OWLED 2007)}}, editor = {Christine {Golbreich} and Aditya {Kalyanpur} and Bijan {Parsia}}, publisher = {CEUR-WS}, title = {Completing Description Logic Knowledge Bases using Formal Concept Analysis}, volume = {258}, year = {2007}, }

Franz Baader, Bernhard Ganter, Ulrike Sattler, and Baris Sertkaya:

Abstract BibTeX Entry PDF File

**Completing Description Logic Knowledge Bases using Formal Concept Analysis**. In*Proceedings of the Twentieth International Joint Conference on Artificial Intelligence (IJCAI-07)*. AAAI Press, 2007.Abstract BibTeX Entry PDF File

@inproceedings{ BGSS07, author = {Franz {Baader} and Bernhard {Ganter} and Ulrike {Sattler} and Baris {Sertkaya}}, booktitle = {Proceedings of the Twentieth International Joint Conference on Artificial Intelligence {(IJCAI-07)}}, publisher = {AAAI Press}, title = {Completing Description Logic Knowledge Bases using Formal Concept Analysis}, year = {2007}, }

Franz Baader, Carsten Lutz, and Boontawee Suntisrivaraporn:

Abstract BibTeX Entry PDF File PS File

**Is Tractable Reasoning in Extensions of the Description Logic**\(\mathcal{EL}\)**Useful in Practice?**. In*Journal of Logic, Language and Information, Special Issue on Method for Modality (M4M)*, 2007. To appearAbstract BibTeX Entry PDF File PS File

Extensions of the description logic EL have recently been proposed as lightweight ontology languages. The most important feature of these extensions is that, despite including powerful expressive means such as general concept inclusion axioms, reasoning can be carried out in polynomial time. In this paper, we consider one of these extensions, EL+, and introduce a refinement of the known polynomial-time classification algorithm for this logic. This refined algorithm was implemented in our <b>CEL</b> reasoner. We describe the results of several experiments with <b>CEL</b> on large ontologies from practice, which show that even a relatively straightforward implementation of the described algorithm outperforms highly optimized, state-of-the-art tableau reasoners for expressive description logics.

@inproceedings{ BaaLutSun-JoLLI-07, author = {Franz {Baader} and Carsten {Lutz} and Boontawee {Suntisrivaraporn}}, booktitle = {Journal of Logic, Language and Information, Special Issue on Method for Modality (M4M)}, note = {To appear}, title = {Is Tractable Reasoning in Extensions of the Description Logic $\mathcal{EL}$ Useful in Practice?}, year = {2007}, }

Franz Baader and Rafael Peñaloza:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Axiom Pinpointing in General Tableaux**. In N. Olivetti, editor,*Proceedings of the 16th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods TABLEAUX 2007*, volume 4548 of*Lecture Notes in Computer Science*, pages 11–27. Aix-en-Provence, France, Springer-Verlag, 2007.Abstract BibTeX Entry PDF File ©Springer-Verlag

Axiom pinpointing has been introduced in description logics to help the user to understand the reasons why consequences hold and to remove unwanted consequences by computing minimal (maximal) subsets of the knowledge base that have (do not have) the consequence in question. The pinpointing algorithms described in the DL literature are obtained as extensions of the standard tableau-based reasoning algorithms for computing consequences from DL knowledge bases. Although these extensions are based on similar ideas, they are all introduced for a particular tableau-based algorithm for a particular DL. The purpose of this paper is to develop a general approach for extending a tableau-based algorithm to a pinpointing algorithm. This approach is based on a general definition of "tableaux algorithms," which captures many of the known tableau-based algorithms employed in DLs, but also other kinds of reasoning procedures.

@inproceedings{ BaaderPenaloza-Tableaux-07, address = {Aix-en-Provence, France}, author = {Franz {Baader} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 16th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods {TABLEAUX 2007}}, editor = {N. {Olivetti}}, pages = {11--27}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Axiom Pinpointing in General Tableaux}, volume = {4548}, year = {2007}, }

Franz Baader, Rafael Peñaloza, and Boontawee Suntisrivaraporn:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Pinpointing in the Description Logic**\(\mathcal{EL}\). In*Proceedings of the 30th German Conference on Artificial Intelligence (KI2007)*, volume 4667 of*Lecture Notes in Artificial Intelligence*, pages 52–67. Osnabrück, Germany, Springer-Verlag, 2007.Abstract BibTeX Entry PDF File ©Springer-Verlag

Axiom pinpointing has been introduced in description logics (DLs) to help the user understand the reasons why consequences hold by computing minimal subsets of the knowledge base that have the consequence in question. Until now, the pinpointing approach has only been applied to the DL ALC and some of its extensions. This paper considers axiom pinpointing in the less expressive DL EL+, for which subsumption can be decided in polynomial time. More precisely, we consider an extension of the pinpointing problem where the knowledge base is divided into a <i>static</i> part, which is always present, and a <i>refutable</i> part, of which subsets are taken. We describe an extension of the subsumption algorithm for EL+ that can be used to compute all minimal subsets of (the refutable part of) a given TBox that imply a certain subsumption relationship. The worst-case complexity of this algorithm turns out to be exponential. This is not surprising since we can show that a given TBox may have exponentially many such minimal subsets. However, we can also show that the problem is not even output polynomial, i.e., unless P=NP, there cannot be an algorithm computing all such minimal sets that is polynomial in the size of its input <i>and output</i>. In addition, we show that finding out whether there is such a minimal subset within a given cardinality bound is an NP-complete problem. In contrast to these negative results, we also show that one such minimal subset can be computed in polynomial time. Finally, we provide some encouraging experimental results regarding the performance of a practical algorithm that computes one (small, but not necessarily minimal) subset that has a given subsumption relation as consequence.

@inproceedings{ BaaPenSun-KI-07, address = {Osnabr\"uck, Germany}, author = {Franz {Baader} and Rafael {Pe{\~n}aloza} and Boontawee {Suntisrivaraporn}}, booktitle = {Proceedings of the 30th German Conference on Artificial Intelligence ({KI2007})}, pages = {52--67}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Pinpointing in the Description Logic $\mathcal{EL}$}, volume = {4667}, year = {2007}, }

Franz Baader, Rafael Peñaloza, and Boontawee Suntisrivaraporn:

Abstract BibTeX Entry PDF File

**Pinpointing in the Description Logic**\(\mathcal{EL}\). In*Proceedings of the 2007 International Workshop on Description Logics (DL2007)*,*CEUR-WS*, 2007.Abstract BibTeX Entry PDF File

Axiom pinpointing has been introduced in description logics (DLs) to help the user to understand the reasons why consequences hold by computing minimal subsets of the knowledge base that have the consequence in question. Until now, the pinpointing approach has only been applied to the DL ALC and some of its extensions. This paper considers axiom pinpointing in the DL EL, for which subsumption can be decided in polynomial time. We describe an extension of the subsumption algorithm for EL that can be used to compute all minimal subsets of a given TBox that imply a certain subsumption relationship. We also show that an EL TBox may have exponentially many such minimal subsets and that even finding out whether there is such a minimal subset within a given cardinality bound is an NP-complete problem. In contrast to these negative results, we also show that one such minimal set can be computed in polynomial time. Finally, we provide some encouraging experimental results regarding the performance of a practical algorithm that computes one (not necessarily minimal) set that has a given subsumption relation as consequence.

@inproceedings{ BaaPenSun-DL-07, author = {Franz {Baader} and Rafael {Pe{\~n}aloza} and Boontawee {Suntisrivaraporn}}, booktitle = {Proceedings of the 2007 International Workshop on Description Logics ({DL2007})}, series = {CEUR-WS}, title = {Pinpointing in the Description Logic $\mathcal{EL}$}, year = {2007}, }

Franz Baader, Barış Sertkaya, and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File PS File

**Computing the Least Common Subsumer w.r.t. a Background Terminology**.*Journal of Applied Logic*, 5(3):392–420, 2007.Abstract BibTeX Entry PDF File PS File

Methods for computing the least common subsumer (lcs) are usually restricted to rather inexpressive Description Logics (DLs) whereas existing knowledge bases are written in very expressive DLs. In order to allow the user to re-use concepts defined in such terminologies and still support the definition of new concepts by computing the lcs, we extend the notion of the lcs of concept descriptions to the notion of the lcs w.r.t. a background terminology. We will show both theoretical results on the existence of the least common subsumer in this setting, and describe a practical approach—based on a method from formal concept analysis—for computing good common subsumers, which may, however, not be the least ones. We will also describe results obtained in a first evaluation of this practical approach.

@article{ BaaderSertkayaTurhan-JAL-07, author = {Franz {Baader} and Bar\i{}\c{s} {Sertkaya} and Anni-Yasmin {Turhan}}, journal = {Journal of Applied Logic}, number = {3}, pages = {392--420}, publisher = {Elsevier Science Publishers (North-Holland), Amsterdam}, title = {Computing the Least Common Subsumer w.r.t.~a Background Terminology}, volume = {5}, year = {2007}, }

Balder ten Cate and Carsten Lutz:

Abstract BibTeX Entry PDF File

**Query Containment in Very Expressive XPath dialects**. In Leonid Libkin, editor,*26th ACM Symposium on Principles of Database Systems (PODS'07)*, pages 73–82. ACM Press, 2007.Abstract BibTeX Entry PDF File

Query containment has been studied extensively for fragments of XPath 1.0. For instance, the problem is known to be EXPTIMEcomplete for CoreXPath, the navigational core of XPath 1.0. Much less is known about query containment in (fragments of) the richer language XPath 2.0. In this paper, we consider extensions of CoreXPath with the following operators, which are all part of XPath 2.0 (except the last): path intersection, path equality, path complementation, for-loops, and transitive closure. For each combination of these operators, we determine the complexity of query containment, both with and without DTDs. It turns out to range from EXPTIME (for extensions with path equality) and 2-EXPTIME (for extensions with path intersection) to non-elementary (for extensions with path complementation or for-loops). In almost all cases, adding transitive closure on top has no further impact on the complexity. We also investigate the effect of dropping the upward and/or sibling axes, and show that this sometimes leads to a reduction in complexity. Since the languages we study include negation and conjunction in filters, our complexity results can equivalently be stated in terms of satisfiability. We also analyze the above languages in terms of succinctness.

@inproceedings{ tenCate-Lutz-07, author = {Balder ten {Cate} and Carsten {Lutz}}, booktitle = {26th {ACM} Symposium on Principles of Database Systems (PODS'07)}, editor = {Leonid {Libkin}}, pages = {73--82}, publisher = {ACM Press}, title = {Query Containment in Very Expressive {XPath} dialects}, year = {2007}, }

Birte Glimm, Carsten Lutz, Ian Horrocks, and Ulrike Sattler:

Abstract BibTeX Entry PDF File

**Answering conjunctive queries in the**\(\mathcal{SHIQ}\)**description logic**. In Manuela Veloso, editor,*Proceedings of the Twentieth International Joint Conference on Artificial Intelligence (IJCAI'07)*, pages 299–404. AAAI Press, 2007.Abstract BibTeX Entry PDF File

Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, it was an open problem whether conjunctive query answering over DL knowledge bases is decidable if transitive roles are admitted in the query. In this paper, we consider conjunctive queries over knowledge bases formulated in the popular DL SHIQ and allow transitive roles in both the query and the knowledge base. We show that query answering is decidable and establish the following complexity bounds: regarding combined complexity, we devise a deterministic algorithm for query answering that needs time single exponential in the size of the KB and double exponential in the size of the query. Regarding data complexity, we prove co-NP-completeness.

@inproceedings{ GliHoLuSa-07, author = {Birte {Glimm} and Carsten {Lutz} and Ian {Horrocks} and Ulrike {Sattler}}, booktitle = {Proceedings of the Twentieth International Joint Conference on Artificial Intelligence (IJCAI'07)}, editor = {Manuela {Veloso}}, pages = {299--404}, publisher = {AAAI Press}, title = {Answering conjunctive queries in the $\mathcal{SHIQ}$ description logic}, year = {2007}, }

Stefan Göller, Markus Lohrey, and Carsten Lutz:

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**PDL with Intersection and Converse is 2EXP-complete**. In Helmut Seidl, editor,*Proceedings of the Tenth International Conference on Foundations of Software Science and Computation Structures (FoSSaCS'07)*, volume 4423 of*Lecture Notes in Computer Science*, pages 198–212. Springer-Verlag, 2007.Abstract BibTeX Entry PDF File

We study the complexity of satisfiability in the expressive extension ICPDL of PDL (Propositional Dynamic Logic), which admits intersection and converse as program operations. Our main result is containment in 2EXP, which improves the previously known non-elementary upper bound and implies 2EXP-completeness due to an existing lower bound for PDL with intersection. The proof proceeds by showing that every satisfiable ICPDL formula has a model of tree-width at most two and then giving a reduction to the (non)-emptiness problem for alternating two-way automata on infinite trees. In this way, we also reprove in an elegant way Danecki's difficult result that satisfiability for PDL with intersection is in 2EXP.

@inproceedings{ GoeLoLu-07, author = {Stefan {G\"oller} and Markus {Lohrey} and Carsten {Lutz}}, booktitle = {Proceedings of the Tenth International Conference on Foundations of Software Science and Computation Structures ({FoSSaCS'07})}, editor = {Helmut {Seidl}}, pages = {198--212}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {{PDL} with Intersection and Converse is {2EXP}-complete}, volume = {4423}, year = {2007}, }

A. Krisnadhi and C. Lutz:

Abstract BibTeX Entry PDF File

**Data Complexity in the**\(\mathcal{EL}\)**family of DLs**. In*Proceedings of the 2007 International Workshop on Description Logics (DL2007)*,*CEUR-WS*, 2007.Abstract BibTeX Entry PDF File

We study the data complexity of instance checking and conjunctive query answering in the EL family of DLs, with a particular emphasis on the boundary of tractability. We identify a large number of intractable extensions of EL, but also show that in ELIf, the extension of EL with inverse roles and global functionality, conjunctive query answering is tractable regarding data complexity. In contrast, instance checking in EL extended with only inverse roles or global functionality is ExpTime-complete regarding combined complexity.

@inproceedings{ Krisnadhi-Lutz-DL-07, author = {A. {Krisnadhi} and C. {Lutz}}, booktitle = {Proceedings of the 2007 International Workshop on Description Logics ({DL2007})}, series = {CEUR-WS}, title = {Data Complexity in the $\mathcal{EL}$ family of DLs}, year = {2007}, }

Adila Krisnadhi and Carsten Lutz:

Abstract BibTeX Entry PDF File

**Data Complexity in the**\(\mathcal{EL}\)**family of Description Logics**. In Nachum Dershowitz and Andrei Voronkov, editors,*Proceedings of the 14th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR2007)*, volume 4790 of*Lecture Notes in Artificial Intelligence*, pages 333–347. Springer-Verlag, 2007.Abstract BibTeX Entry PDF File

We study the data complexity of instance checking and conjunctive query answering in the EL family of description logics, with a particular emphasis on the boundary of tractability. We identify a large number of intractable extensions of EL, but also show that in ELI^{f}, the extension of EL with inverse roles and global functionality, conjunctive query answering is tractable regarding data complexity. In contrast, already instance checking in EL extended with only inverse roles or global functionality is ExpTime-complete regarding combined complexity.

@inproceedings{ Krisnadhi-Lutz-LPAR-07, author = {Adila {Krisnadhi} and Carsten {Lutz}}, booktitle = {Proceedings of the 14th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning ({LPAR2007})}, editor = {Nachum {Dershowitz} and Andrei {Voronkov}}, pages = {333--347}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Data Complexity in the $\mathcal{EL}$ family of Description Logics}, volume = {4790}, year = {2007}, }

C. Löding, C. Lutz, and O. Serre:

Abstract BibTeX Entry PDF File

**Propositional Dynamic Logic with Recursive Programs**.*Journal of Logic and Algebraic Programming*, 73:51–69, 2007.Abstract BibTeX Entry PDF File

We extend the propositional dynamic logic PDL of Fischer and Ladner with a restricted kind of recursive programs using the formalism of visibly pushdown automata (Alur, Madhusudan 2004). We show that the satisfiability problem for this extension remains decidable, generalising known decidability results for extensions of PDL by non-regular programs. Our decision procedure establishes a 2- ExpTime upper complexity bound, and we prove a matching lower bound that applies already to rather weak extensions of PDL with non-regular programs. Thus, we also show that such extensions tend to be more complex than standard PDL.

@article{ LoeLuSe-JLAP-07, author = {C. {L\"oding} and C. {Lutz} and O. {Serre}}, journal = {Journal of Logic and Algebraic Programming}, pages = {51--69}, title = {Propositional Dynamic Logic with Recursive Programs}, volume = {73}, year = {2007}, }

C. Lutz:

Abstract BibTeX Entry PDF File

**Inverse Roles Make Conjunctive Queries Hard**. In*Proceedings of the 2007 International Workshop on Description Logics (DL2007)*,*CEUR-WS*, 2007.Abstract BibTeX Entry PDF File

Conjunctive query answering is an important DL reasoning task. Although this task is by now quite well-understood, tight complexity bounds for conjunctive query answering in expressive DLs have never been obtained: all known algorithms run in deterministic double exponential time, but the existing lower bound is only an ExpTime one. In this paper, we prove that conjunctive query answering in ALCI is 2-ExpTime-hard (and thus complete), and that it becomes NExpTime-complete under some reasonable assumptions.

@inproceedings{ Lutz-DL-07, author = {C. {Lutz}}, booktitle = {Proceedings of the 2007 International Workshop on Description Logics ({DL2007})}, series = {CEUR-WS}, title = {Inverse Roles Make Conjunctive Queries Hard}, year = {2007}, }

C. Lutz and M. Milicic:

Abstract BibTeX Entry PDF File

**A Tableau Algorithm for DLs with Concrete Domains and GCIs**.*Journal of Automated Reasoning*, 38(1–3):227–259, 2007.Abstract BibTeX Entry PDF File

To use description logics (DLs) in an application, it is crucial to identify a DL that is sufficiently expressive to represent the relevant notions of the application domain, but for which reasoning is still decidable. Two means of expressivity that are required by many modern applications of DLs are concrete domains and general TBoxes. The former are used for decidablening concepts based on concrete qualities of their instances such as the weight, age, duration, and spatial extension. The purpose of the latter is to capture background knowledge by stating that the extension of a concept is included in the extension of another concept. Unfortunately, it is wellknown that combining concrete domains with general TBoxes often leads to DLs for which reasoning is undecidable. In this paper, we identify a general property of concrete domains that is sucient for proving decidability of DLs with both concrete domains and general TBoxes. We exhibit some useful concrete domains, most notably a spatial one based on the RCC-8 relations, which have this property. Then, we present a tableau algorithm for reasoning in DLs equipped with concrete domains and general TBoxes.

@article{ LuMi-Jar-07, author = {C. {Lutz} and M. {Milicic}}, journal = {Journal of Automated Reasoning}, number = {1--3}, pages = {227--259}, title = {A Tableau Algorithm for {DL}s with Concrete Domains and {GCI}s}, volume = {38}, year = {2007}, }

Carsten Lutz, Dirk Walther, and Frank Wolter:

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**Conservative Extensions in Expressive Description Logics**. In Manuela Veloso, editor,*Proceedings of the Twentieth International Joint Conference on Artificial Intelligence (IJCAI'07)*, pages 453–458. AAAI Press, 2007.Abstract BibTeX Entry PDF File

The notion of a conservative extension plays a central role in ontology design and integration: it can be used to formalize ontology refinements, safe mergings of two ontologies, and independent modules inside an ontology. Regarding reasoning support, the most basic task is to decide whether one ontology is a conservative extension of another. It has recently been proved that this problem is decidable and 2ExpTime-complete if ontologies are formulated in the basic description logic ALC. We consider more expressive description logics and begin to map out the boundary between logics for which conservativity is decidable and those for which it is not. We prove that conservative extensions are 2ExpTime-complete in ALCQI, but undecidable in ALCQIO. We also show that if conservative extensions are defined model-theoretically rather than in terms of the consequence relation, they are undecidable already in ALC.

@inproceedings{ LuWaWo-07, author = {Carsten {Lutz} and Dirk {Walther} and Frank {Wolter}}, booktitle = {Proceedings of the Twentieth International Joint Conference on Artificial Intelligence (IJCAI'07)}, editor = {Manuela {Veloso}}, pages = {453--458}, publisher = {AAAI Press}, title = {Conservative Extensions in Expressive Description Logics}, year = {2007}, }

Carsten Lutz and Frank Wolter:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Conservative Extensions in the Lightweight Description Logic**\(\mathcal{EL}\). In Frank Pfenning, editor,*Proceedings of the 21th Conference on Automated Deduction (CADE-21)*, volume 4603 of*Lecture Notes in Artificial Intelligence*, pages 84–99. Springer-Verlag, 2007.Abstract BibTeX Entry PDF File ©Springer-Verlag

We bring together two recent trends in description logic (DL): lightweight DLs in which the subsumption problem is tractable and conservative extensions as a central tool for formalizing notions of ontology design such as refinement and modularity. Our aim is to investigate conservative extensions as an automated reasoning problem for the basic tractable DL EL. The main result is that deciding (deductive) conservative extensions is ExpTime-complete, thus more difficult than subsumption in EL, but not more difficult than subsumption in expressive DLs. We also show that if conservative extensions are defined model-theoretically, the associated decision problem for EL is undecidable.

@inproceedings{ Lutz-Wolter-CADE-07, author = {Carsten {Lutz} and Frank {Wolter}}, booktitle = {Proceedings of the 21th Conference on Automated Deduction (CADE-21)}, editor = {Frank {Pfenning}}, pages = {84--99}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Conservative Extensions in the Lightweight Description Logic $\mathcal{EL}$}, volume = {4603}, year = {2007}, }

Maja Milicic:

Abstract BibTeX Entry PDF File

**Complexity of Planning in Action Formalisms Based on Description Logics**. In*Proceedings of the 14th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2007)*,*Lecture Notes in Artificial Intelligence*. Springer-Verlag, 2007.Abstract BibTeX Entry PDF File

In this paper, we continue the recently started work on integrating action formalisms with description logics (DLs), by investigating planning in the context of DLs. We prove that the plan existence problem is decidable for actions described in fragments of ALCQIO. More precisely, we show that its computational complexity coincides with the one of projection for DLs between ALC and ALCQIO if operators contain only unconditional post-conditions. If we allow for conditional post-conditions, the plan existence problem is shown to be in 2-ExpSpace.

@inproceedings{ Milicic-LPAR07, author = {Maja {Milicic}}, booktitle = {Proceedings of the 14th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning ({LPAR 2007})}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Complexity of Planning in Action Formalisms Based on Description Logics}, year = {2007}, }

Maja Milicic:

Abstract BibTeX Entry PDF File

**Planning in Action Formalisms based on DLs: First Results**. In*Proceedings of the 2007 International Workshop on Description Logics (DL2007)*,*CEUR-WS*, 2007.Abstract BibTeX Entry PDF File

In this paper, we continue the recently started work on integrating action formalisms with description logics (DLs), by investigating planning in the context of DLs. We prove that the plan existence problem is decidable for actions described in fragments of ALCQIO. More precisely, we show that, if post-conditions of operators are unconditional, its computational complexity coincides with the one of projection for DLs between ALC and ALCQIO.

@inproceedings{ Milicic-DL07, author = {Maja {Milicic}}, booktitle = {Proceedings of the 2007 International Workshop on Description Logics ({DL2007})}, series = {CEUR-WS}, title = {Planning in Action Formalisms based on {DL}s: First Results}, year = {2007}, }

Stefan Schulz, Boontawee Suntisrivaraporn, and Franz Baader:

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**SNOMED CT's Problem List: Ontologists' and Logicians' Therapy Suggestions**. In , editor,*Proceedings of The Medinfo 2007 Congress*, volume of*Studies in Health Technology and Informatics (SHTI-series)*, page . IOS Press, 2007.Abstract BibTeX Entry PDF File

After a critical review of the present architecture of SNOMED CT, addressing both logical and ontological issues, we present a roadmap towards an overall improvement of this terminology. In particular, we recommend the following actions: Upper level categories should be re-arranged according to a standard upper level ontology. Meta-class like concepts should be identified and removed from the taxonomy. SNOMED concepts denoting (non instantiable) individual entities (e.g. geographical regions) should be kept separate from those concepts that denote (instantiable) types. SNOMED binary relations should be reduced to a set of canonical ones, following existing recommendations. Taxonomies should be cleansed and split into disjoint partitions. The number of full definitions should be increased. Finally, we propose a new approach to modeling part-whole hierarchies, as well as the integration of qualifier relations into the description logic framework.

@inproceedings{ SchSunBaa-Medinfo-07, author = {Stefan {Schulz} and Boontawee {Suntisrivaraporn} and Franz {Baader}}, booktitle = {Proceedings of The Medinfo 2007 Congress}, editor = {}, pages = {}, publisher = {IOS Press}, series = {Studies in Health Technology and Informatics (SHTI-series)}, title = {{SNOMED CT}'s Problem List: Ontologists' and Logicians' Therapy Suggestions}, volume = {}, year = {2007}, }

Boontawee Suntisrivaraporn, Franz Baader, Stefan Schulz, and Kent Spackman:

Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

**Replacing SEP-Triplets in SNOMED CT using Tractable Description Logic Operators**. In Jim Hunter Riccardo Bellazzi, Ameen Abu-Hanna, editor,*Proceedings of the 11th Conference on Artificial Intelligence in Medicine (AIME'07)*, volume of*Lecture Notes in Computer Science*, page . Springer-Verlag, 2007.Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

Reification of parthood relations according to the SEP-triplet encoding pattern has been employed in the clinical terminology SNOMED CT to simulate transitivity of the part-of relation via transitivity of the is-a relation and to inherit properties along part-of links. In this paper we argue that using a more expressive representation language, which allows for a direct representation of the relevant properties of the part-of relation, makes modelling less error prone while having no adverse effect on the efficiency of reasoning.

@inproceedings{ SunBaaSchSpa-AIME-07, author = {Boontawee {Suntisrivaraporn} and Franz {Baader} and Stefan {Schulz} and Kent {Spackman}}, booktitle = {Proceedings of the 11th Conference on Artificial Intelligence in Medicine {(AIME'07})}, editor = {Jim Hunter {Riccardo Bellazzi, Ameen Abu-Hanna}}, pages = {}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Replacing SEP-Triplets in SNOMED CT using Tractable Description Logic Operators}, volume = {}, year = {2007}, }

A.-Y. Turhan and Y. Bong:

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**Speeding up Approximation with Nicer Concepts**. In D. Calvanese, E. Franconi, V. Haarslev, D. Lembo, B. Motik, S. Tessaris, and A.-Y. Turhan, editors,*Proc. of the 2007 Description Logic Workshop (DL 2007)*, 2007.Abstract BibTeX Entry PDF File PS File

Concept approximation is an inference service for Description Logics that provides ``translations'' of concept descriptions from one DL to a less expressive DL. In [4] a method for optimizing the computation of ALC-ALE-approximations of ALC-concept descriptions was introduced. The idea is to characterize a certain class of concept descriptions for which conjuncts can be approximated independently. In this paper we provide relaxed conditions for this class of ALC-concept descriptions, extend this notion to number restrictions and report on a first implementation of this method for ALCN-ALEN-approximation.

@inproceedings{ TurBo-DL07, author = {A.-Y. {Turhan} and Y. {Bong}}, booktitle = {Proc.\ of the 2007 Description Logic Workshop (DL 2007)}, editor = {D. {Calvanese} and E. {Franconi} and V. {Haarslev} and D. {Lembo} and B. {Motik} and S. {Tessaris} and A.-Y. {Turhan}}, title = {Speeding up Approximation with Nicer Concepts}, year = {2007}, }

## 2006

F. Baader and R. Küsters:

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**Nonstandard Inferences in Description Logics: The Story So Far**. In D.M. Gabbay, S.S. Goncharov, and M. Zakharyaschev, editors,*Mathematical Problems from Applied Logic I*, volume 4 of*International Mathematical Series*, pages 1–75. Springer-Verlag, 2006.Abstract BibTeX Entry PDF File

Description logics (DLs) are a successful family of logic-based knowledge representation formalisms that can be used to represent the terminological knowledge of an application domain in a structured and formally well-founded way. DL systems provide their users with inference procedures that allow to reason about the represented knowledge. Standard inference problems (such as the subsumption and the instance problem) are now well-understood. Their computational properties (such as decidability and complexity) have been investigated in detail, and modern DL systems are equipped with highly optimized implementations of these inference procedures, which - in spite of their high worst-case complexity - perform quite well in practice. In applications of DL systems it has turned out that building and maintaining large DL knowledge bases can be further facilitated by procedures for other, non-standard inference problem, such as computing the least common subsumer and the most specific concept, and rewriting and matching of concepts. While the research concerning these non-standard inferences is not as mature as the one for the standard inferences, it has now reached a point where it makes sense to motivate these inferences within a uniform application framework, give an overview of the results obtained so far, describe the remaining open problems, and give perspectives for future research in this direction.

@incollection{ BaaderKuesters-IMAT-06, author = {F. {Baader} and R. {K{\"u}sters}}, booktitle = {Mathematical Problems from Applied Logic {I}}, editor = {D.M. {Gabbay} and S.S. {Goncharov} and M. {Zakharyaschev}}, pages = {1--75}, publisher = {Springer-Verlag}, series = {International Mathematical Series}, title = {Nonstandard Inferences in Description Logics: The Story So Far}, volume = {4}, year = {2006}, }

F. Baader and C. Lutz:

Abstract BibTeX Entry PDF File PS File

**Description Logic**. In Patrick Blackburn, Johan van Benthem, and Frank Wolter, editors,*The Handbook of Modal Logic*, pages 757–820. Elsevier, 2006.Abstract BibTeX Entry PDF File PS File

Description logics are a family of knowledge representation languages that were developed independently of modal logics, but later turned out to be closely related to them. This chapter introduces description logics and briefly recalls the connections between description and modal logics, but then concentrates on means of expressivity and reasoning problems that are important for description logics, but not in the focus of research in modal logics.

@incollection{ BaaderLutz-MLHandbook-06, author = {F. {Baader} and C. {Lutz}}, booktitle = {The Handbook of Modal Logic}, editor = {Patrick {Blackburn} and Johan van {Benthem} and Frank {Wolter}}, pages = {757--820}, publisher = {Elsevier}, title = {Description Logic}, year = {2006}, }

F. Baader, C. Lutz, and B. Suntisrivaraporn:

Abstract BibTeX Entry PDF File PS File

**Efficient Reasoning in**\(\mathcal{EL}^+\). In*Proceedings of the 2006 International Workshop on Description Logics (DL2006)*,*CEUR-WS*, 2006.Abstract BibTeX Entry PDF File PS File

@inproceedings{ BaaLutSun-DL-06, author = {F. {Baader} and C. {Lutz} and B. {Suntisrivaraporn}}, booktitle = {Proceedings of the 2006 International Workshop on Description Logics ({DL2006})}, series = {CEUR-WS}, title = {Efficient Reasoning in $\mathcal{EL}^+$}, year = {2006}, }

F. Baader, C. Lutz, and B. Suntisrivaraporn:

Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

**CEL—A Polynomial-time Reasoner for Life Science Ontologies**. In U. Furbach and N. Shankar, editors,*Proceedings of the 3rd International Joint Conference on Automated Reasoning (IJCAR'06)*, volume 4130 of*Lecture Notes in Artificial Intelligence*, pages 287–291. Springer-Verlag, 2006.Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

CEL (Classifier for EL) is a reasoner for the small description logic EL+ which can be used to compute the subsumption hierarchy induced by EL+ ontologies. The most distinguishing feature of CEL is that, unlike other modern DL reasoners, it is based on a polynomial-time subsumption algorithm, which allows it to process very large ontologies in reasonable time. In spite of its restricted expressive power, EL+ is well-suited for formulating life science ontologies.

@inproceedings{ BaaLutSun-IJCAR-06, author = {F. {Baader} and C. {Lutz} and B. {Suntisrivaraporn}}, booktitle = {Proceedings of the 3rd International Joint Conference on Automated Reasoning ({IJCAR'06})}, editor = {U. {Furbach} and N. {Shankar}}, pages = {287--291}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {{\textsf{CEL}}---A Polynomial-time Reasoner for Life Science Ontologies}, volume = {4130}, year = {2006}, }

F. Baader and A. Okhotin:

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**Complexity of Language Equations With One-Sided Concatenation and All Boolean Operations**. In Jordi Levy, editor,*Proceedings of the 20th International Workshop on Unification, UNIF'06*, pages 59–73, 2006.Abstract BibTeX Entry PDF File

Language equations are equations where both the constants occurring in the equations and the solutions are formal languages. They have first been introduced in formal language theory, but are now also considered in other areas of computer science. In particular, they can be seen as unification problems in the algebra of languages whose operations are the Boolean operations and concatenation. They are also closely related to monadic set constraints. In the present paper, we restrict the attention to language equations with one-sided concatenation, but in contrast to previous work on these equations, we allow not just union but all Boolean operations to be used when formulating them. In addition, we are not just interested in deciding solvability of such equations, but also in deciding other properties of the set of solutions, like its cardinality (finite, infinite, uncountable) and whether it contains least/greatest solutions. We show that all these decision problems are ExpTime-complete.

@inproceedings{ Baader-Okhotin-UNIF-06, author = {F. {Baader} and A. {Okhotin}}, booktitle = {Proceedings of the 20th International Workshop on Unification, {UNIF'06}}, editor = {Jordi {Levy}}, pages = {59--73}, title = {Complexity of Language Equations With One-Sided Concatenation and All {B}oolean Operations}, year = {2006}, }

Franz Baader, Silvio Ghilardi, and Cesare Tinelli:

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**A new combination procedure for the word problem that generalizes fusion decidability results in modal logics**.*Information and Computation*, 204(10):1413–1452, 2006.Abstract BibTeX Entry PDF File

Previous results for combining decision procedures for the word problem in the non-disjoint case do not apply to equational theories induced by modal logics—which are not disjoint for sharing the theory of Boolean algebras. Conversely, decidability results for the fusion of modal logics are strongly tailored towards the special theories at hand, and thus do not generalize to other types of equational theories. In this paper, we present a new approach for combining decision procedures for the word problem in the non-disjoint case that applies to equational theories induced by modal logics, but is not restricted to them. The known fusion decidability results for modal logics are instances of our approach. However, even for equational theories induced by modal logics our results are more general since they are not restricted to so-called normal modal logics.

@article{ BaaGT-IC-06, author = {Franz {Baader} and Silvio {Ghilardi} and Cesare {Tinelli}}, journal = {Information and Computation}, number = {10}, pages = {1413--1452}, title = {A new combination procedure for the word problem that generalizes fusion decidability results in modal logics}, volume = {204}, year = {2006}, }

P. Bonatti, C. Lutz, A. Murano, and M. Vardi:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**The Complexity of Enriched**\(\mu\)**-Calculi**. In Michele Bugliesi, Bart Preneel, Vladimiro Sassone, and Ingo Wegener, editors,*Proccedings of the 33rd International Colloquium on Automata, Languages and Programming, Part II (ICALP'06)*, volume 4052 of*Lecture Notes in Computer Science*, pages 540–551. Springer-Verlag, 2006.Abstract BibTeX Entry PDF File ©Springer-Verlag

The fully enriched mu-calculus is the extension of the propositional mu-calculus with inverse programs, graded modalities, and nominals. While satisfiability in several expressive fragments of the fully enriched mu-calculus is known to be decidable and ExpTime-complete, it has recently been proved that the full calculus is undecidable. In this paper, we study the fragments of the fully enriched mu-calculus that are obtained by dropping at least one of the additional constructs. We show that, in all fragments obtained in this way, satisfiability is decidable and ExpTime-complete. Thus, we identify a family of decidable logics that are maximal (and incomparable) in expressive power. Our results are obtained by introducing two new automata models, showing that their emptyness problems are ExpTime-complete, and then reducing satisfiability in the relevant logics to this problem. The automata models we introduce are two-way graded alternating parity automata over infinite trees (2GAPT) and fully enriched automata (FEA) over infinite forests. The former are a common generalization of two incomparable automata models from the literature. The latter extend alternating automata in a similar way as the fully enriched mu-calculus extends the standard mu-calculus.

@inproceedings{ BoLuMuVa-ICALP06, author = {P. {Bonatti} and C. {Lutz} and A. {Murano} and M. {Vardi}}, booktitle = {Proccedings of the 33rd International Colloquium on Automata, Languages and Programming, Part {II} ({ICALP'06})}, editor = {Michele {Bugliesi} and Bart {Preneel} and Vladimiro {Sassone} and Ingo {Wegener}}, pages = {540--551}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {The Complexity of Enriched $\mu$-Calculi}, volume = {4052}, year = {2006}, }

P. Bonatti, C. Lutz, and F. Wolter:

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**Expressive Non-Monotonic Description Logics Based on Circumscription**. In Patrick Doherty, John Mylopoulos, and Christopher Welty, editors,*Proceedings of the Tenth International Conference on Principles of Knowledge Representation and Reasoning (KR'06)*, pages 400–410. AAAI Press, 2006.Abstract BibTeX Entry PDF File

We show that circumscription can be used to extend description logics (DLs) with non-monotonic features in a straightforward and transparent way. In particular, we consider extensions with circumscription of the expressive DLs ALCIO and ALCQO and prove that reasoning in these logics is decidable under a simple restriction: only concept names can be circumscribed, and role names vary freely during circumscription. We pinpoint the exact computational complexity of reasoning as complete for NP^{N}Exp and NExp^{N}P, depending on whether or not the number of minimized and fixed predicates is assumed to be bounded by a constant. We also show that we cannot allow role names to be fixed during minimization rather than having them vary: this modification renders reasoning undecidable already in the basic DL ALC. Finally, we argue that non-monotonic DLs based on circumscription are an appropriate tool for modelling defeasible inheritance. In particular, we can avoid the restriction of non-monotonic reasoning to domain elements that are named by an individual constant, as adopted by other non-monotonic DLs.

@inproceedings{ BonattiLutzWolter-KR06, author = {P. {Bonatti} and C. {Lutz} and F. {Wolter}}, booktitle = {Proceedings of the Tenth International Conference on Principles of Knowledge Representation and Reasoning (KR'06)}, editor = {Patrick {Doherty} and John {Mylopoulos} and Christopher {Welty}}, pages = {400--410}, publisher = {AAAI Press}, title = {Expressive Non-Monotonic Description Logics Based on Circumscription}, year = {2006}, }

S. Ghilardi, C. Lutz, and F. Wolter:

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**Did I Damage my Ontology? A Case for Conservative Extensions in Description Logics**. In Patrick Doherty, John Mylopoulos, and Christopher Welty, editors,*Proceedings of the Tenth International Conference on Principles of Knowledge Representation and Reasoning (KR'06)*, pages 187–197. AAAI Press, 2006.Abstract BibTeX Entry PDF File

In computer science, ontologies are dynamic entities: to adapt them to new and evolving applications, it is necessary to frequently perform modifications such as the extension with new axioms and merging with other ontologies. We argue that, after performing such modifications, it is important to know whether the resulting ontology is a conservative extension of the original one. If this is not the case, then there may be unexpected consequences when using the modified ontology in place of the original one in applications. In this paper, we propose and investigate new reasoning problems based on the notion of conservative extension, assuming that ontologies are formulated as TBoxes in the description logic ALC. We show that the fundamental such reasoning problems are decidable and 2ExpTime-complete. Additionally, we perform a finer-grained analysis that distinguishes between the size of the original ontology and the size of the additional axioms. In particular, we show that there are algorithms whose runtime is "only" exponential in the size of the original ontology, but double exponential in the size of the added axioms. If the size of the new axioms is small compared to the size of the ontology, these algorithms are thus not significantly more complex than the standard reasoning services implemented in modern description logic reasoners. If the extension of an ontology is not conservative, our algorithm is capable of computing a concept that witnesses non-conservativeness. We show that the computed concepts are of (worst-case) minimal size.

@inproceedings{ GhilardiLutzWolter-KR06, author = {S. {Ghilardi} and C. {Lutz} and F. {Wolter}}, booktitle = {Proceedings of the Tenth International Conference on Principles of Knowledge Representation and Reasoning (KR'06)}, editor = {Patrick {Doherty} and John {Mylopoulos} and Christopher {Welty}}, pages = {187--197}, publisher = {AAAI Press}, title = {Did {I} Damage my Ontology? A Case for Conservative Extensions in Description Logics}, year = {2006}, }

S. Ghilardi, C. Lutz, F. Wolter, and M. Zakharyaschev:

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**Conservative Extensions in Modal Logics**. In Guido Governatori, Ian Hodkinson, and Yde Venema, editors,*Advances in Modal Logics Volume 6*, pages 187–207. College Publications, 2006.Abstract BibTeX Entry PDF File

Every modal logic L gives rise to the consequence relation that relates formulas phi and psi iff is true in a world of an L-model whenever phi is true in that world. We consider the following algorithmic problem for L. Given two modal formulas phi1 and phi2, decide whether their conjunction is a conservative extension of phi1 in the sense that whenever psi is a consequence of the conjunction of phi1 and phi2 and psi does not contain propositional variables not occurring in phi1, then psi is already a consequence of phi1.. We first prove that the conservativeness problem is co-NExpTime-hard for all modal logics of unbounded width (which have rooted frames with more than N successors of the root, for any N smaller than omega. Then we show that this problem is (i) co-NExpTime-complete for S5 and K, (ii) in for S4 and (iii) -complete for GL.3 (the logic of finite strict linear orders). The proofs for S5 and K use the fact that these logics have uniform interpolants of exponential size.

@inproceedings{ GhiLuWoZa-06, author = {S. {Ghilardi} and C. {Lutz} and F. {Wolter} and M. {Zakharyaschev}}, booktitle = {Advances in Modal Logics Volume 6}, editor = {Guido {Governatori} and Ian {Hodkinson} and Yde {Venema}}, pages = {187--207}, publisher = {College Publications}, title = {Conservative Extensions in Modal Logics}, year = {2006}, }

Jan Hladik and Rafael Peñaloza:

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**PSPACE Automata for Description Logics**. In B. Parsia, U. Sattler, and D. Toman, editors,*Proceedings of the 2006 International Workshop on Description Logics (DL'06)*, volume 189 of*CEUR-WS*, 2006.Abstract BibTeX Entry PDF File

Tree automata are often used for satisfiability testing in the area of description logics, which usually yields EXPTIME complexity results. We examine conditions under which this result can be improved, and we define two classes of automata, called segmentable and weakly-segmentable, for which emptiness can be decided using space logarithmic in the size of the automaton (and thus polynomial in the size of the input). The usefulness of segmentable automata is demonstrated by reproving the known PSPACE result for satisfiability of ALC concepts with respect to acyclic TBoxes.

@inproceedings{ HlaPen-DL-06, author = {Jan {Hladik} and Rafael {Pe{\~n}aloza}}, booktitle = {Proceedings of the 2006 International Workshop on Description Logics ({DL'06})}, editor = {B. {Parsia} and U. {Sattler} and D. {Toman}}, series = {{CEUR-WS}}, title = {{PSPACE} Automata for Description Logics}, volume = {189}, year = {2006}, }

H. Liu, C. Lutz, M. Milicic, and F. Wolter:

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**Description Logic Actions with general TBoxes: a Pragmatic Approach**. In*Proceedings of the 2006 International Workshop on Description Logics (DL2006)*, 2006.Abstract BibTeX Entry PDF File

We recently proposed action formalisms based on description logics (DLs) as decidable fragments of well-established action theories such as the Situation Calculus and the Fluent Calculus. One short-coming of our initial proposal is that the considered formalisms admit only acyclic TBoxes, but not GCIs. In this paper, we define DL action formalisms that admit GCIs, propose a pragmatic approach to addressing the ramification problem that is introduced in this way, show that our formalim is decidable and investigate its computational complexity.

@inproceedings{ LiLuMiWo-DL-06, author = {H. {Liu} and C. {Lutz} and M. {Milicic} and F. {Wolter}}, booktitle = {Proceedings of the 2006 International Workshop on Description Logics ({DL2006})}, title = {Description Logic Actions with general {T}{B}oxes: a Pragmatic Approach}, year = {2006}, }

H. Liu, C. Lutz, M. Milicic, and F. Wolter:

Abstract BibTeX Entry PDF File

**Reasoning about Actions using Description Logics with general TBoxes**. In Michael Fisher, Wiebe van der Hoek, Boris Konev, and Alexei Lisitsa, editors,*Proceedings of the 10th European Conference on Logics in Artificial Intelligence (JELIA 2006)*, volume 4160 of*Lecture Notes in Artificial Intelligence*, pages 266–279. Springer-Verlag, 2006.Abstract BibTeX Entry PDF File

Action formalisms based on description logics (DLs) have recently been introduced as decidable fragments of well-established action theories such as the Situation Calculus and the Fluent Calculus. However, existing DL action formalisms fail to include general TBoxes, which are the standard tool for formalising ontologies in modern description logics. We define a DL action formalism that admits general TBoxes, propose an approach to addressing the ramification problem that is introduced in this way, show that our formalism is decidable and perform a detailed investigation of its computational complexity.

@inproceedings{ LiLuMiWo-JELIA-06, author = {H. {Liu} and C. {Lutz} and M. {Milicic} and F. {Wolter}}, booktitle = {Proceedings of the 10th European Conference on Logics in Artificial Intelligence {(JELIA 2006)}}, editor = {Michael {Fisher} and Wiebe van der {Hoek} and Boris {Konev} and Alexei {Lisitsa}}, pages = {266--279}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Reasoning about Actions using Description Logics with general {TBoxes}}, volume = {4160}, year = {2006}, }

H. Liu, C. Lutz, M. Milicic, and F. Wolter:

Abstract BibTeX Entry PDF File

**Updating Description Logic ABoxes**. In Patrick Doherty, John Mylopoulos, and Christopher Welty, editors,*Proceedings of the Tenth International Conference on Principles of Knowledge Representation and Reasoning (KR'06)*, pages 46–56. AAAI Press, 2006.Abstract BibTeX Entry PDF File

Description logic (DL) ABoxes are a tool for describing the state of affairs in an application domain. In this paper, we consider the problem of updating ABoxes when the state changes. We assume that changes are described at an atomic level, i.e., in terms of possibly negated ABox assertions that involve only atomic concepts and roles. We analyze such basic ABox updates in several standard DLs by investigating whether the updated ABox can be expressed in these DLs and, if so, whether it is computable and what is its size. It turns out that DLs have to include nominals and the "@" constructor of hybrid logic (or, equivalently, admit Boolean ABoxes) for updated ABoxes to be expressible. We devise algorithms to compute updated ABoxes in several expressive DLs and show that an exponential blowup in the size of the whole input (original ABox + update information) cannot be avoided unless every PTIME problem is LOGTIME-parallelizable. We also exhibit ways to avoid an exponential blowup in the size of the original ABox, which is usually large compared to the update information.

@inproceedings{ LiLuMiWo-KR-06, author = {H. {Liu} and C. {Lutz} and M. {Milicic} and F. {Wolter}}, booktitle = {Proceedings of the Tenth International Conference on Principles of Knowledge Representation and Reasoning (KR'06)}, editor = {Patrick {Doherty} and John {Mylopoulos} and Christopher {Welty}}, pages = {46--56}, publisher = {AAAI Press}, title = {Updating Description Logic {ABoxes}}, year = {2006}, }

C. Lutz:

Abstract BibTeX Entry PDF File

**Complexity and Succinctness of Public Announcement Logic**. In Peter Stone and Gerhard Weiss, editors,*Proceedings of the Fifth International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS'06)*, pages 137–144. Association for Computing Machinery (ACM), 2006.Abstract BibTeX Entry PDF File

There is a recent trend of extending epistemic logic (EL) with dynamic operators that allow to express the evolution of knowledge and belief induced by knowledge-changing actions. The most basic such extension is public announcement logic (PAL), which is obtained from EL by adding an operator for truthful public announcements. In this paper, we consider the computational complexity of PAL and show that it coincides with that of EL. This holds in the single- and multi-agent case, and also in the presence of common knowledge operators. We also prove that there are properties that can be expressed exponentially more succinct in PAL than in EL. This shows that, despite the known fact that PAL and EL have the same expressive power, there is a benefit in adding the public announcement operator to EL: it exponentially increases the succinctness of formulas without having negative effects on computational complexity.

@inproceedings{ Lutz-AAMAS-06, author = {C. {Lutz}}, booktitle = {Proceedings of the Fifth International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS'06)}, editor = {Peter {Stone} and Gerhard {Weiss}}, pages = {137--144}, publisher = {Association for Computing Machinery (ACM)}, title = {Complexity and Succinctness of Public Announcement Logic}, year = {2006}, }

C. Lutz and M. Milicic:

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**A Tableau Algorithm for Description Logics with Concrete Domains and General TBoxes**.*Journal of Automated Reasoning. Special Issue on on Automated Reasoning with Analytic Tableaux and Related Methods*, 2006. To appear.Abstract BibTeX Entry PDF File

To use description logics (DLs) in an application, it is crucial to identify a DL that is sufficiently expressive to represent the relevant notions of the application domain, but for which reasoning is still decidable. Two means of expressivity that are required by many modern applications of DLs are concrete domains and general TBoxes. The former are used for defining concepts based on concrete qualities of their instances such as the weight, age, duration, and spatial extension. The purpose of the latter is to capture background knowledge by stating that the extension of a concept is included in the extension of another concept. Unfortunately, it is well- known that combining concrete domains with general TBoxes often leads to DLs for which reasoning is undecidable. In this paper, we identify a general property of concrete domains that is sufficient for proving decidability of DLs with both concrete domains and general TBoxes. We exhibit some useful concrete domains, most notably a spatial one based on the RCC-8 relations, which have this property. Then, we present a tableau algorithm for reasoning in DLs equipped with concrete domains and general TBoxes.

@article{ LutzMilicic-JAR06, author = {C. {Lutz} and M. {Milicic}}, journal = {Journal of Automated Reasoning. Special Issue on on Automated Reasoning with Analytic Tableaux and Related Methods}, note = {To appear.}, publisher = {Springer}, title = {A Tableau Algorithm for Description Logics with Concrete Domains and General TBoxes}, year = {2006}, }

C. Lutz, D. Walther, and F. Wolter:

Abstract BibTeX Entry PDF File PS File

**Quantitative Temporal Logics: PSpace and below**.*Information and Computation*, 205(1):99–123, 2006.Abstract BibTeX Entry PDF File PS File

In many cases, the addition of metric operators to qualitative temporal logics (TLs) increases the complexity of satisfiability by at least one exponential: while common qualitative TLs are complete for NP or PSpace, their metric extensions are often ExpSpace-complete or even undecidable. In this paper, we exhibit several metric extensions of qualitative TLs of the real line that are at most PSpace-complete, and analyze the transition from NP to PSpace for such logics. Our first result is that the logic obtained by extending since-until logic of the real line with the operators `sometime within n time units in the past/future' is still PSpace-complete. In contrast to existing results, we also capture the case where n is coded in binary and the finite variability assumption is not made. To establish containment in PSpace, we use a novel reduction technique that can also be used to prove tight upper complexity bounds for many other metric TLs in which the numerical parameters to metric operators are coded in binary. We then consider metric TLs of the reals that do not offer any qualitative temporal operators. In such languages, the complexity turns out to depend on whether binary or unary coding of parameters is assumed: satisfiability is still PSpace-complete under binary coding, but only NP-complete under unary coding.

@article{ LuWaWo-IandC-06, author = {C. {Lutz} and D. {Walther} and F. {Wolter}}, journal = {Information and Computation}, number = {1}, pages = {99--123}, title = {Quantitative Temporal Logics: {{\sc PSpace}} and below}, volume = {205}, year = {2006}, }

C. Lutz and F. Wolter:

Abstract BibTeX Entry PDF File PS File

**Modal Logics of Topological Relations**.*Logical Methods in Computer Science*, 2(2), 2006.Abstract BibTeX Entry PDF File PS File

Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham's modal logic of time intervals based on the Allen relations, we introduce a family of modal logics equipped with eight modal operators that are interpreted by the Egenhofer-Franzosa (or RCC8) relations between regions in topological spaces such as the real plane. We investigate the expressive power and computational complexity of logics obtained in this way. It turns out that our modal logics have the same expressive power as the two-variable fragment of first-order logic, but are exponentially less succinct. The complexity ranges from (undecidable and) recursively enumerable to Pi_{1}^{1}-hard, where the recursively enumerable logics are obtained by considering substructures of structures induced by topological spaces. As our undecidability results also capture logics based on the real line, they improve upon undecidability results for interval temporal logics by Halpern and Shoham. We also analyze modal logics based on the five RCC5 relations, with similar results regarding the expressive power, but weaker results regarding the complexity.

@article{ Lutz-Wolter-LMCS-06, author = {C. {Lutz} and F. {Wolter}}, journal = {Logical Methods in Computer Science}, number = {2}, title = {Modal Logics of Topological Relations}, volume = {2}, year = {2006}, }

Carsten Lutz, Franz Baader, Enrico Franconi, Domenico Lembo, Ralf Möller, Riccardo Rosati, Ulrike Sattler, Boontawee Suntisrivaraporn, and Sergio Tessaris:

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**Reasoning Support for Ontology Design**. In Bernardo Cuenca Grau, Pascal Hitzler, Connor Shankey, and Evan Wallace, editors,*In Proceedings of the second international workshop OWL: Experiences and Directions*, November 2006.Abstract BibTeX Entry PDF File

The design of comprehensive ontologies is a serious challenge. Therefore, it is necessary to support the ontology designer by providing him with design methodologies, ontology editors, and automated reasoning tools that explicate the consequences of his design decisions. Currently, reasoning tools are largely limited to the reasoning services (i) computing the subsumption hierarchy of the classes in an ontology and (ii) determining the consistency of these classes. In this paper, we survey the most important tasks that arise in ontology design and discuss how they can be supported by automated reasoning tools. In particular, we show that it is beneficial to go beyond the usual reasoning services (i) and (ii).

@inproceedings{ LutzEtAl-OWLED06, author = {Carsten {Lutz} and Franz {Baader} and Enrico {Franconi} and Domenico {Lembo} and Ralf {M{\"o}ller} and Riccardo {Rosati} and Ulrike {Sattler} and Boontawee {Suntisrivaraporn} and Sergio {Tessaris}}, booktitle = {In Proceedings of the second international workshop OWL: Experiences and Directions}, editor = {Bernardo Cuenca {Grau} and Pascal {Hitzler} and Connor {Shankey} and Evan {Wallace}}, month = {November}, title = {Reasoning Support for Ontology Design}, year = {2006}, }

Barış Sertkaya:

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**Computing the hierarchy of conjunctions of concept names and their negations in a Description Logic knowledge base using Formal Concept Analysis (ICFCA 2006)**. In Bernhard Ganter and Leonard Kwuida, editors,*Contributions to ICFCA 2006*, pages 73–86. Dresden, Germany, Verlag Allgemeine Wissenschaft, 2006.Abstract BibTeX Entry PDF File PS File

In a series of previous work, we have presented how attribute exploration can be used in the bottom-up construction of DL knowledge bases to compute a concept lattice that is isomorphic to the subsumption hierarchy of all conjunctions of concept names occurring in a knowledge base, and the negations of these concept names. This work is a continuation in the line of the previous work, that makes a step towards more efficient computation of the mentioned hierarchy. Its specific accomplishment is reducing the number of questions asked to the expert and the number of objects produced during the computation of this hierarchy, thus speeding up the computation. Despite its simple nature, the approach speeds up the computation of this hierarchy drastically.

@inproceedings{ SertkayaICFCA06, address = {Dresden, Germany}, author = {Bar\i{}\c{s} {Sertkaya}}, booktitle = {Contributions to ICFCA 2006}, editor = {Bernhard {Ganter} and Leonard {Kwuida}}, pages = {73--86}, publisher = {Verlag Allgemeine Wissenschaft}, title = {Computing the hierarchy of conjunctions of concept names and their negations in a Description Logic knowledge base using Formal Concept Analysis ({ICFCA 2006})}, year = {2006}, }

Anni-Yasmin Turhan, Sean Bechhofer, Alissa Kaplunova, Thorsten Liebig, Marko Luther, Ralf Möller, Olaf Noppens, Peter Patel-Schneider, Boontawee Suntisrivaraporn, and Timo Weithöner:

Abstract BibTeX Entry PDF File PS File

**DIG 2.0 – Towards a Flexible Interface for Description Logic Reasoners**. In Bernardo Cuenca Grau, Pascal Hitzler, Connor Shankey, and Evan Wallace, editors,*In Proceedings of the second international workshop OWL: Experiences and Directions*, November 2006.Abstract BibTeX Entry PDF File PS File

The DIG Interface provides an implementation-neutral mechanism for accessing Description Logic reasoner functionality. At a high level the interface can be realised as XML messages sent to the reasoner over HTTP connections, with the reasoner responding as appropriate. Key changes in the current version (DIG 2.0) include support for OWL 1.1 and well-defined mechanisms for extensions to the basic interface.

@inproceedings{ TurhanEtAl-OWLED06, author = {Anni-Yasmin {Turhan} and Sean {Bechhofer} and Alissa {Kaplunova} and Thorsten {Liebig} and Marko {Luther} and Ralf {M{\"o}ller} and Olaf {Noppens} and Peter {Patel-Schneider} and Boontawee {Suntisrivaraporn} and Timo {Weith{\"o}ner}}, booktitle = {In Proceedings of the second international workshop OWL: Experiences and Directions}, editor = {Bernardo Cuenca {Grau} and Pascal {Hitzler} and Connor {Shankey} and Evan {Wallace}}, month = {November}, title = {DIG 2.0 -- Towards a Flexible Interface for Description Logic Reasoners}, year = {2006}, }

Anni-Yasmin Turhan, Thomas Springer, and Michael Berger:

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**Pushing Doors for Modeling Contexts with OWL DL –a Case Study**. In Jadwiga Indulska and Daniela Nicklas, editors,*Proceedings of the Workshop on Context Modeling and Reasoning (CoMoRea'06)*. IEEE Computer Society, March 2006.Abstract BibTeX Entry PDF File PS File

In this paper we present an integrated view for modeling and reasoning for context applications using OWL DL. In our case study, we describe a task driven approach to model typical situations as context concepts in an OWL DL ontology. At run-time OWL individuals form situation descriptions and by use of realization we recognise a certain context. We demonstrate the feasibility of our approach by performance measurements of available highly optimised Description Logics (DL) reasoners for OWL DL.

@inproceedings{ TuSpBe-CoMoRea05, author = {Anni-Yasmin {Turhan} and Thomas {Springer} and Michael {Berger}}, booktitle = {Proceedings of the Workshop on Context Modeling and Reasoning (CoMoRea'06)}, editor = {Jadwiga {Indulska} and Daniela {Nicklas}}, month = {March}, publisher = {IEEE Computer Society}, title = {Pushing Doors for Modeling Contexts with \mbox{OWL DL} --a Case Study}, year = {2006}, }

D. Walther, C. Lutz, F. Wolter, and M. Wooldridge:

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**ATL is Indeed ExpTime-complete**.*Journal of Logic and Computation*, 16(6):765–787, 2006.Abstract BibTeX Entry PDF File

The Alternating-time Temporal Logic (ATL) of Alur, Henzinger, and Kupferman is being increasingly widely applied in the specification and verification of open distributed systems and game-like multi-agent systems. In this paper, we investigate the computational complexity of the satisfiability problem for ATL. For the case where the set of agents is fixed in advance, this problem was settled at ExpTime-complete in a result of van Drimmelen. If the set of agents is not fixed in advance, then van Drimmelen's construction yields a 2ExpTime upper bound. In this paper, we focus on the latter case and define three natural variations of the satisfiability problem. Although none of these variations fixes the set of agents in advance, we are able to prove containment in ExpTime for all of them by means of a type elimination construction-thus improving the existing 2ExpTime upper bound to a tight ExpTime one.

@article{ WaLuWoWo-06b, author = {D. {Walther} and C. {Lutz} and F. {Wolter} and M. {Wooldridge}}, journal = {Journal of Logic and Computation}, number = {6}, pages = {765--787}, title = {{ATL} is Indeed {\sc ExpTime}-complete}, volume = {16}, year = {2006}, }

## 2005

F. Baader, S. Brandt, and C. Lutz:

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**Pushing the**\(\mathcal{EL}\)**Envelope**. In*Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence IJCAI-05*. Edinburgh, UK, Morgan-Kaufmann Publishers, 2005.Abstract BibTeX Entry PDF File

Recently, it has been shown that the small description logic (DL) EL, which allows for conjunction and existential restrictions, has better algorithmic properties than its counterpart FL0, which allows for conjunction and value restrictions. Whereas the subsumption problem in FL0 becomes already intractable in the presence of acyclic TBoxes, it remains tractable in EL even with general concept inclusion axioms (GCIs). On the one hand, we extend the positive result for EL by identifying a set of expressive means that can be added to EL without sacrificing tractability. On the other hand, we show that basically all other additions of typical DL constructors to EL with GCIs make subsumption intractable, and in most cases even ExpTime-complete. In addition, we show that subsumption in FL0 with GCIs is ExpTime-complete.

@inproceedings{ BaaderBrandtLutz-IJCAI-05, address = {Edinburgh, UK}, author = {F. {Baader} and S. {Brandt} and C. {Lutz}}, booktitle = {Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence {IJCAI-05}}, publisher = {Morgan-Kaufmann Publishers}, title = {Pushing the $\mathcal{EL}$ Envelope}, year = {2005}, }

F. Baader and S. Ghilardi:

Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

**Connecting Many-Sorted Structures and Theories through Adjoint Functions**. In*Proceedings of the 5th International Workshop on Frontiers of Combining Systems (FroCoS'05)*, volume 3717 of*Lecture Notes in Artificial Intelligence*. Vienna (Austria), Springer-Verlag, 2005.Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

In a previous paper, we have introduced a general approach for connecting two many-sorted theories through connection functions that behave like homomorphisms on the shared signature, and have shown that, under appropriate algebraic conditions, decidability of the validity of universal formulae in the component theories transfers to their connection. This work generalizes decidability transfer results for so-called E-connections of modal logics. However, in this general algebraic setting, only the most basic type of E-connections could be handled. In the present paper, we overcome this restriction by looking at pairs of connection functions that are adjoint pairs for partial orders defined in the component theories.

@inproceedings{ BaaderGhilardiFroCoS05, address = {Vienna (Austria)}, author = {F. {Baader} and S. {Ghilardi}}, booktitle = {Proceedings of the 5th International Workshop on Frontiers of Combining Systems (FroCoS'05)}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Connecting Many-Sorted Structures and Theories through Adjoint Functions}, volume = {3717}, year = {2005}, }

F. Baader and S. Ghilardi:

Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

**Connecting Many-Sorted Theories**. In*Proceedings of the 20th International Conference on Automated Deduction (CADE-05)*, volume 3632 of*Lecture Notes in Artificial Intelligence*, pages 278–294. Tallinn (Estonia), Springer-Verlag, 2005.Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

Basically, the connection of two many-sorted theories is obtained by taking their disjoint union, and then connecting the two parts through connection functions that must behave like homomorphisms on the shared signature. We determine conditions under which decidability of the validity of universal formulae in the component theories transfers to their connection. In addition, we consider variants of the basic connection scheme.

@inproceedings{ BaaderGhilardiCADE05, address = {Tallinn (Estonia)}, author = {F. {Baader} and S. {Ghilardi}}, booktitle = {Proceedings of the 20th International Conference on Automated Deduction (CADE-05)}, pages = {278--294}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Connecting Many-Sorted Theories}, volume = {3632}, year = {2005}, }

F. Baader, I. Horrocks, and U. Sattler:

Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

**Description Logics as Ontology Languages for the Semantic Web**. In D. Hutter and W. Stephan, editors,*Mechanizing Mathematical Reasoning: Essays in Honor of Jörg H. Siekmann on the Occasion of His 60th Birthday*, volume 2605 of*Lecture Notes in Artificial Intelligence*, pages 228–248. Springer-Verlag, 2005.Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

The vision of a Semantic Web has recently drawn considerable attention, both from academia and industry. Description logics are often named as one of the tools that can support the Semantic Web and thus help to make this vision reality. In this paper, we describe what description logics are and what they can do for the Semantic Web. Descriptions logics are very useful for defining, integrating, and maintaining ontologies, which provide the SemanticWeb with a common understanding of the basic semantic concepts used to annotate Web pages. We also argue that, without the last decade of basic research in this area, description logics could not play such an important role in this domain.

@incollection{ BaSaJS60, author = {F. {Baader} and I. {Horrocks} and U. {Sattler}}, booktitle = {Mechanizing Mathematical Reasoning: Essays in Honor of J{\"o}rg H. Siekmann on the Occasion of His 60th Birthday}, editor = {D. {Hutter} and W. {Stephan}}, pages = {228--248}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Description Logics as Ontology Languages for the Semantic Web}, volume = {2605}, year = {2005}, }

F. Baader, C. Lutz, M. Milicic, U. Sattler, and F. Wolter:

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**A Description Logic Based Approach to Reasoning about Web Services**. In*Proceedings of the WWW 2005 Workshop on Web Service Semantics (WSS2005)*, 2005.Abstract BibTeX Entry PDF File

Motivated by the need for semantically well-founded and algorithmically managable formalisms for describing the functionality of Web services, we introduce an action formalism that is based on description logics (DLs), but is also firmly grounded on research in the reasoning about action community. Our main contribution is an analysis of how the choice of the DL influences the complexity of standard reasoning tasks such as projection and executability, which are important for Web service discovery and composition.

@inproceedings{ BaLuMiSaWo-WSS-2005, address = {Chiba City, Japan}, author = {F. {Baader} and C. {Lutz} and M. {Milicic} and U. {Sattler} and F. {Wolter}}, booktitle = {Proceedings of the WWW 2005 Workshop on Web Service Semantics ({WSS2005})}, title = {A Description Logic Based Approach to Reasoning about Web Services}, year = {2005}, }

F. Baader, C. Lutz, M. Milicic, U. Sattler, and F. Wolter:

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**Integrating Description Logics and Action Formalisms: First Results**. In*Proceedings of the 2005 International Workshop on Description Logics (DL2005)*, number 147 in*CEUR-WS*, 2005.Abstract BibTeX Entry PDF File

We propose an action formalism that is based on description logics (DLs) and may be viewed as an instance of the Situation Calculus (SitCalc). In particular, description logic concepts can be used for describing the state of the world, and the pre- and post-conditions of actions. The main advantage of such a combination is that, on the one hand, the expressive power for describing world states and conditions is higher than in other decidable fragments of the SitCalc, which are usually propositional. On the other hand, in contrast to the full SitCalc, effective reasoning is still possible. In this paper, we perform a detailed investigation of how the choice of the DL influences the complexity of the standard reasoning tasks executability and projection in the corresponding action formalism. We also discuss semantic and computational problems in natural extensions of our framework.

@inproceedings{ BaaderEtAlDL05b, author = {F. {Baader} and C. {Lutz} and M. {Milicic} and U. {Sattler} and F. {Wolter}}, booktitle = {Proceedings of the 2005 International Workshop on Description Logics ({DL2005})}, number = {147}, series = {CEUR-WS}, title = {Integrating Description Logics and Action Formalisms: First Results}, year = {2005}, }

F. Baader, C. Lutz, M. Milicic, U. Sattler, and F. Wolter:

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**Integrating Description Logics and Action Formalisms: First Results**. In*Proceedings of the Twentieth National Conference on Artificial Intelligence (AAAI-05)*, 2005.Abstract BibTeX Entry PDF File

@inproceedings{ BaLuMiSaWo-AAAI-2005, address = {Pittsburgh, PA, USA}, author = {F. {Baader} and C. {Lutz} and M. {Milicic} and U. {Sattler} and F. {Wolter}}, booktitle = {Proceedings of the Twentieth National Conference on Artificial Intelligence ({AAAI-05})}, title = {Integrating Description Logics and Action Formalisms: First Results}, year = {2005}, }

F. Baader, C. Lutz, and B. Suntisrivaraporn:

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**Is Tractable Reasoning in Extensions of the Description Logic**\(\mathcal{EL}\)**Useful in Practice?**. In*Proceedings of the Methods for Modalities Workshop (M4M-05)*, 2005.Abstract BibTeX Entry PDF File PS File

Extensions of the description logic EL have recently been proposed as lightweight ontology languages. The most important feature of these extensions is that, despite including powerful expressive means such as general concept inclusion axioms, reasoning can be carried out in polynomial time. In this paper, we consider one of these extensions, EL+, and introduce a refinement of the known polynomial-time classification algorithm for this logic, which was implemented in our CEL reasoner. We describe the results of several experiments with CEL on large ontologies from practice, which show that even a relatively straightforward implementation of the described algorithm outperforms highly optimized, state-of-the-art tableau reasoners for expressive description logics.

@inproceedings{ BaaLutSun-M4M-05, address = {Berlin, Germany}, author = {F. {Baader} and C. {Lutz} and B. {Suntisrivaraporn}}, booktitle = {Proceedings of the Methods for Modalities Workshop (M4M-05)}, title = {Is Tractable Reasoning in Extensions of the Description Logic $\mathcal{EL}$ Useful in Practice?}, year = {2005}, }

F. Baader and A. Voronkonv, editors:

Abstract BibTeX Entry

**11th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning LPAR 2004**. Montevideo, Uruguay, Springer-Verlag, 2005.Abstract BibTeX Entry

This volume contains the papers presented at the 11th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR), held from March 14 to 18, 2005, in Montevideo, Uruguay, together with the 5th International Workshop on the Implementation of Logics (organised by Stephan Schulz and Boris Konev) and the Workshop on Analytic Proof Systems (organised by Matthias Baaz).

@book{ BaaderLPAR2004, address = {Montevideo, Uruguay}, editor = {F. {Baader} and A. {Voronkonv}}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {11th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning {LPAR 2004}}, volume = {3452}, year = {2005}, }

Franz Baader, Carsten Lutz, Eldar Karabaev, and Manfred Theißen:

Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

**A New**\(n\)**-ary Existential Quantifier in Description Logics**. In*Proceedings of the 28th Annual German Conference on Artificial Intelligence, KI 2005*, volume 3698 of*Lecture Notes in Artificial Intelligence*, pages 18–33. Springer-Verlag, 2005.Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

Motivated by a chemical process engineering application, we introduce a new concept constructor in Description Logics (DLs), an n-ary variant of the existential restriction constructor, which generalizes both the usual existential restrictions and so-called qualified number restrictions. We show that the new constructor can be expressed in ALCQ, the extension of the basic DL ALC by qualified number restrictions. However, this representation results in an exponential blow-up. By giving direct algorithms for ALC extended with the new constructor, we can show that the complexity of reasoning in this new DL is actually not harder than the one of reasoning in ALCQ. Moreover, in our chemical process engineering application, a restricted DL that provides only the new constructor together with conjunction, and satisfies an additional restriction on the occurrence of roles names, is sufficient. For this DL, the subsumption problem is polynomial.

@inproceedings{ BaaderEtAlKI05, author = {Franz {Baader} and Carsten {Lutz} and Eldar {Karabaev} and Manfred {Thei{\ss}en}}, booktitle = {Proceedings of the 28th Annual German Conference on Artificial Intelligence, {KI 2005}}, pages = {18--33}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {A New $n$-ary Existential Quantifier in Description Logics}, volume = {3698}, year = {2005}, }

Franz Baader, Carsten Lutz, Eldar Karabaev, and Manfred Theißen:

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**A New**\(n\)**-ary Existential Quantifier in Description Logics**. In*Proceedings of the 2005 International Workshop on Description Logics (DL2005)*, number 147 in*CEUR-WS*, 2005.Abstract BibTeX Entry PDF File PS File

@inproceedings{ BaaderEtAlDL05, author = {Franz {Baader} and Carsten {Lutz} and Eldar {Karabaev} and Manfred {Thei{\ss}en}}, booktitle = {Proceedings of the 2005 International Workshop on Description Logics ({DL2005})}, number = {147}, series = {CEUR-WS}, title = {A New $n$-ary Existential Quantifier in Description Logics}, year = {2005}, }

Sebastian Brandt and Jörg Model:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**Subsumption in**\(\cal EL\)**w.r.t. hybrid TBoxes**. In*Proceedings of the 28th Annual German Conference on Artificial Intelligence, KI 2005*,*Lecture Notes in Artificial Intelligence*. Springer-Verlag, 2005.Abstract BibTeX Entry PDF File ©Springer-Verlag

In the area of Description Logic (DL) based knowledge representation, two desirable features of DL systems have as yet been incompatible: firstly, the support of general TBoxes containing general concept inclusion (GCI) axioms, and secondly, non-standard inference services facilitating knowledge engineering tasks, such as build-up and maintenance of terminologies (TBoxes). In order to make non-standard inferences available without sacrificing the convenience of GCIs, the present paper proposes hybrid TBoxes consisting of a pair of a general TBox F interpreted by descriptive semantics, and a (possibly) cyclic TBox T interpreted by fixpoint semantics. F serves as a foundation of T in the sense that the GCIs in F define relationships between concepts used as atomic concept names in the definitions in T. % Our main technical result is a polynomial time subsumption algorithm for hybrid EL-TBoxes based on a polynomial reduction to subsumption w.r.t. cyclic EL-TBoxes with fixpoint semantics. By virtue of this reduction, all non-standard inferences already available for cyclic EL-TBoxes become available for hybrid ones.

@inproceedings{ BrandtModel-KI2005, author = {Sebastian {Brandt} and J{\"o}rg {Model}}, booktitle = {Proceedings of the 28th Annual German Conference on Artificial Intelligence, {KI 2005}}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {Subsumption in {$\cal EL$} w.r.t.\ hybrid TBoxes}, year = {2005}, }

J. Hladik:

Abstract BibTeX Entry PDF File

**A Generator for Description Logic Formulas**. In I. Horrocks, U. Sattler, and F. Wolter, editors,*Proceedings of DL 2005*. CEUR-WS, 2005. Available from ceur-ws.orgAbstract BibTeX Entry PDF File

We introduce a schema for generating random formulas for different description logics, which extends an existing pattern for modal logics. Using the DL reasoners FaCT and RACER, we test the difficulty of these formulas, and it turns out that the properties that make a formula in an expressive DL hard are quite different from those known for ALC formulas.

@inproceedings{ Hladik-DL-2005, author = {J. {Hladik}}, booktitle = {Proceedings of DL 2005}, editor = {I. {Horrocks} and U. {Sattler} and F. {Wolter}}, note = {Available from \texttt{ceur-ws.org}}, publisher = {CEUR-WS}, title = {A Generator for Description Logic Formulas}, year = {2005}, }

M. Lange and C. Lutz:

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**2-ExpTime lower bounds for Propositional Dynamic Logics with intersection**.*Journal of Symbolic Logic*, 70(5):1072–1086, 2005.Abstract BibTeX Entry PDF File PS File

In 1984, Danecki proved that satisfiability in IPDL, i.e., Propositional Dynamic Logic (PDL) extended with an intersection operator on programs, is decidable in deterministic double exponential time. Since then, the exact complexity of IPDL has remained an open problem: the best known lower bound was the ExpTime one stemming from plain PDL until, in 2004, the first author established ExpSpace-hardness. In this paper, we finally close the gap and prove that IPDL is hard for 2-ExpTime, thus 2-ExpTime-complete. We then sharpen our lower bound, showing that it even applies to IPDL without the test operator interpreted on tree structures.

@article{ LangeLutzJSL05, author = {M. {Lange} and C. {Lutz}}, journal = {Journal of Symbolic Logic}, number = {5}, pages = {1072--1086}, title = {2-ExpTime lower bounds for Propositional Dynamic Logics with intersection}, volume = {70}, year = {2005}, }

C. Lutz:

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**PDL with Intersection and Converse is Decidable**. In*Annual Conference of the European Association for Computer Science Logic CSL'05*,*LNCS*. Springer Verlag, 2005.Abstract BibTeX Entry PDF File PS File

In its many guises and variations, propositional dynamic logic (PDL) plays an important role in various areas of computer science such as databases, artificial intelligence, and computer linguistics. One relevant and powerful variation is ICPDL, the extension of PDL with intersection and converse. Although ICPDL has several interesting applications, its computational properties have never been investigated. In this paper, we prove that ICPDL is decidable by developing a translation to the monadic second order logic of infinite trees. Our result has applications in information logic, description logic, and epistemic logic. In particular, we solve a long-standing open problem in information logic. Another virtue of our approach is that it provides a decidability proof that is more transparent than existing ones for PDL with intersection (but without converse).

@inproceedings{ Lutz-CSL-01, author = {C. {Lutz}}, booktitle = {Annual Conference of the European Association for Computer Science Logic CSL'05}, publisher = {Springer Verlag}, series = {LNCS}, title = {PDL with Intersection and Converse is Decidable}, year = {2005}, }

C. Lutz, C. Areces, I. Horrocks, and U. Sattler:

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**Keys, Nominals, and Concrete Domains**.*Journal of Artificial Intelligence Research*, 23:667–726, 2005.Abstract BibTeX Entry PDF File PS File

Many description logics (DLs) combine knowledge representation on an abstract, logical level with an interface to "concrete" domains like numbers and strings with built-in predicates such as <, +, and prefix-of. These hybrid DLs have turned out to be useful in several application areas, such as reasoning about conceptual database models. We propose to further extend such DLs with key constraints that allow the expression of statements like "US citizens are uniquely identified by their social security number". Based on this idea, we introduce a number of natural description logics and perform a detailed analysis of their decidability and computational complexity. It turns out that naive extensions with key constraints easily lead to undecidability, whereas more careful extensions yield NExpTime-complete DLs for a variety of useful concrete domains.

@article{ LuArHoSaJAIR05, author = {C. {Lutz} and C. {Areces} and I. {Horrocks} and U. {Sattler}}, journal = {Journal of Artificial Intelligence Research}, pages = {667--726}, title = {Keys, Nominals, and Concrete Domains}, volume = {23}, year = {2005}, }

C. Lutz and M. Milicic:

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**A Tableau Algorithm for DLs with Concrete Domains and GCIs**. In*Proceedings of the 2005 International Workshop on Description Logics (DL2005)*, number 147 in*CEUR-WS*, 2005.Abstract BibTeX Entry PDF File

We identify a general property of concrete domains that is sufficient for proving decidability of DLs equipped with them and GCIs. We show that some useful concrete domains, such as a temporal one based on the Allen relations and a spatial one based on the RCC-8 relations, have this property. Then, we present a tableau algorithm for reasoning in DLs equipped with such concrete domains.

@inproceedings{ LutzMilicic-DL-2005, author = {C. {Lutz} and M. {Milicic}}, booktitle = {Proceedings of the 2005 International Workshop on Description Logics ({DL2005})}, number = {147}, series = {CEUR-WS}, title = {A Tableau Algorithm for DLs with Concrete Domains and GCIs}, year = {2005}, }

C. Lutz and M. Milicic:

Abstract BibTeX Entry PDF File ©Springer-Verlag

**A Tableau Algorithm for Description Logics with Concrete Domains and GCIs**. In*Proceedings of the 14th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods TABLEAUX 2005*,*LNAI*. Koblenz, Germany, Springer, 2005.Abstract BibTeX Entry PDF File ©Springer-Verlag

In description logics (DLs), concrete domains are used for defining concepts based on concrete qualities of their instances such as the weight, age, duration, and spatial extension. So-called general concept inclusions (GCIs) play an important role for capturing background knowledge. It is well-known that, when combining concrete domains with GCIs, reasoning easily becomes undecidable. In this paper, we identify a general property of concrete domains that is sufficient for proving decidability of DLs with both concrete domains and GCIs. We exhibit some useful concrete domains, most notably a spatial one based on the RCC-8 relations, which have this property. Then, we present a tableau algorithm for reasoning in DLs equipped with concrete domains and GCIs.

@inproceedings{ LutzMilicic-Tableaux2005, address = {Koblenz, Germany}, author = {C. {Lutz} and M. {Milicic}}, booktitle = {Proceedings of the 14th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods {TABLEAUX 2005}}, publisher = {Springer}, series = {LNAI}, title = {A Tableau Algorithm for Description Logics with Concrete Domains and GCIs}, year = {2005}, }

C. Lutz, U. Sattler, and L. Tendera:

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**The Complexity of Finite Model Reasoning in Description Logics**.*Information and Computation*, 199:132–171, 2005.Abstract BibTeX Entry PDF File PS File

We analyse the complexity of finite model reasoning in the description logic ALCQI, i.e. ALC augmented with qualifying number restrictions, inverse roles, and general TBoxes. It turns out that all relevant reasoning tasks such as concept satisfiability and ABox consistency are Exptime-complete, regardless of whether the numbers in number restrictions are coded unarily or binarily. Thus, finite model reasoning with ALCQI is not harder than standard reasoning with ALCQI.

@article{ Lutz-et-al-IANDC-05, author = {C. {Lutz} and U. {Sattler} and L. {Tendera}}, journal = {Information and Computation}, pages = {132--171}, title = {The Complexity of Finite Model Reasoning in Description Logics}, volume = {199}, year = {2005}, }

C. Lutz and D. Walther:

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**PDL with Negation of Atomic Programs**.*Journal of Applied Non-Classical Logic*, 15(2):189–214, 2005.Abstract BibTeX Entry PDF File PS File

Propositional dynamic logic (PDL) is one of the most successful variants of modal logic. To make it even more useful for applications, many extensions of PDL have been considered in the literature. A very natural and useful such extension is with negation of programs. Unfortunately, as long known, reasoning with the resulting logic is undecidable. In this paper, we consider the extension of PDL with negation of atomic programs, only. We argue that this logic is still useful, e.g. in the context of description logics, and prove that satisfiability is decidable and ExpTime-complete using an approach based on Buechi tree automata.

@article{ LutzWaltherJANCL05, author = {C. {Lutz} and D. {Walther}}, journal = {Journal of Applied Non-Classical Logic}, number = {2}, pages = {189--214}, title = {PDL with Negation of Atomic Programs}, volume = {15}, year = {2005}, }

C. Lutz, D. Walther, and F. Wolter:

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**Quantitative Temporal Logics: PSpace and below**. In*Proceedings of the Twelfth International Symposium on Temporal Representation and Reasoning*. Burlington, VT, USA, IEEE Computer Society Press, 2005.Abstract BibTeX Entry PDF File

Often, the addition of metric operators to qualitative temporal logics leads to an increase of the complexity of satisfiability by at least one exponential. In this paper, we exhibit a number of metric extensions of qualitative temporal logics of the real line that do not lead to an increase in computational complexity. We show that the language obtained by extending since/until logic of the real line with the operators `sometime within n time units', n coded in binary, is PSpace-complete even without the finite variability assumption. Without qualitative temporal operators the complexity of this language turns out to depend on whether binary or unary coding of parameters is assumed: it is still PSpace-hard under binary coding but in NP under unary coding.

@inproceedings{ LutzWaltherWolter-TIME-05, address = {Burlington, VT, USA}, author = {C. {Lutz} and D. {Walther} and F. {Wolter}}, booktitle = {Proceedings of the Twelfth International Symposium on Temporal Representation and Reasoning}, publisher = {IEEE Computer Society Press}, title = {Quantitative Temporal Logics: {\sc PSpace} and below}, year = {2005}, }

Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File PS File

**Pushing the SONIC border — SONIC 1.0**. In Reinhold Letz, editor,*FTP 2005 — Fifth International Workshop on First-Order Theorem Proving*. Technical Report University of Koblenz, 2005. http://www.uni-koblenz.de/fb4/publikationen/gelbereihe/RR-13-2005.pdfAbstract BibTeX Entry PDF File PS File

This paper reports on extensions of the Description Logics non-standard inference system SONIC. The recent contributions to the system are two-fold. Firstly, SONIC is extended by two new of non-standard inferences, namely, implementations of the good common subsumer w.r.t. a background terminology and a heuristics for computing a minimal rewriting. Secondly, SONIC is available as a plugin for the well-known ontology editor Protege.

@incollection{ Turhan-ftp-05, author = {Anni-Yasmin {Turhan}}, booktitle = {FTP 2005 --- Fifth International Workshop on First-Order Theorem Proving}, editor = {Reinhold {Letz}}, note = {http://www.uni-koblenz.de/fb4/publikationen/gelbereihe/RR-13-2005.pdf}, publisher = {Technical Report University of Koblenz}, title = {Pushing the {SONIC} border --- {SONIC} 1.0}, type = {Fachberichte Informatik}, year = {2005}, }

## 2004

A. Artale and C. Lutz:

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**A Correspondence between Temporal Description Logics**.*Journal of Applied Non-Classical Logic*, 14(1–2):209–233, 2004.Abstract BibTeX Entry PDF File PS File

In this paper, we investigate the relationship between two decidable interval-based temporal description logics that have been proposed in the literature, TL-ALCF and ALCF(A). Although many aspects of these two logics are quite similar, the two logics suggest two rather different paradigms for representing temporal conceptual knowledge. In this paper, we exhibit a reduction from TL-ALCF concepts to ALCF(A) concepts that serves two purposes: first, it nicely illustrates the relationship between the two knowledge representation paradigms; and second, it provides a tight PSpace upper bound for TL-ALCF concept satisfiabiliy, whose complexity was previously unknown.

@article{ ArtaleLutzJANCL04, author = {A. {Artale} and C. {Lutz}}, journal = {Journal of Applied Non-Classical Logic}, number = {1--2}, pages = {209--233}, title = {A Correspondence between Temporal Description Logics}, volume = {14}, year = {2004}, }

F. Baader:

Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

**A Graph-Theoretic Generalization of the Least Common Subsumer and the Most Specific Concept in the Description Logic**\(\mathcal{EL}\). In J. Hromkovic and M. Nagl, editors,*Proceedings of the 30th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2004)*, volume 3353 of*Lecture Notes in Computer Science*, pages 177–188. Bad Honnef, Germany, Springer-Verlag, 2004.Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

In two previous papers we have investigates the problem of computing the least common subsumer (lcs) and the most specific concept (msc) for the description logic EL in the presence of terminological cycles that are interpreted with descriptive semantics, which is the usual first-order semantics for description logics. In this setting, neither the lcs nor the msc needs to exist. We were able to characterize the cases in which the lcs/msc exists, but it was not clear whether this characterization yields decidability of the existence problem. In the present paper, we develop a common graph-theoretic generalization of these characterizations, and show that the resulting property is indeed decidable, thus yielding decidability of the existence of the lcs and the msc. This is achieved by expressing the property in monadic second-order logic on infinite trees. We also show that, if it exists, then the lcs/msc can be computed in polynomial time.

@inproceedings{ BaaderWG04, address = {Bad Honnef, Germany}, author = {F. {Baader}}, booktitle = {Proceedings of the 30th International Workshop on Graph-Theoretic Concepts in Computer Science {(WG 2004)}}, editor = {J. {Hromkovic} and M. {Nagl}}, pages = {177--188}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {A Graph-Theoretic Generalization of the Least Common Subsumer and the Most Specific Concept in the Description Logic $\mathcal{EL}$}, volume = {3353}, year = {2004}, }

F. Baader, S. Ghilardi, and C. Tinelli:

Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

**A New Combination Procedure for the Word Problem that Generalizes Fusion Decidability Results in Modal Logics**. In D. Basin and M. Rusinowitch, editors,*Proceedings of the 2nd International Joint Conference on Automated Reasoning (IJCAR'04)*, volume 3097 of*Lecture Notes in Artificial Intelligence*, pages 183–197. Springer-Verlag, 2004.Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

Previous results for combining decision procedures for the word problem in the non-disjoint case do not apply to equational theories induced by modal logics—whose combination is not disjoint since they share the theory of Boolean algebras. Conversely, decidability results for the fusion of modal logics are strongly tailored towards the special theories at hand, and thus do not generalize to other equational theories. In this paper, we present a new approach for combining decision procedures for the word problem in the non-disjoint case that applies to equational theories induced by modal logics, but is not restricted to them. The known fusion decidability results for modal logics are instances of our approach. However, even for equational theories induced by modal logics our results are more general since they are not restricted to so-called normal modal logics.

@inproceedings{ BaaderEtAlIJCAR04, author = {F. {Baader} and S. {Ghilardi} and C. {Tinelli}}, booktitle = {Proceedings of the 2nd International Joint Conference on Automated Reasoning ({IJCAR'04})}, editor = {D. {Basin} and M. {Rusinowitch}}, pages = {183--197}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {A New Combination Procedure for the Word Problem that Generalizes Fusion Decidability Results in Modal Logics}, volume = {3097}, year = {2004}, }

F. Baader, I. Horrocks, and U. Sattler:

Abstract BibTeX Entry

**Description Logics**. In S. Staab and R. Studer, editors,*Handbook on Ontologies*,*International Handbooks in Information Systems*, pages 3–28. Berlin, Germany, Springer–Verlag, 2004.Abstract BibTeX Entry

In this chapter, we explain what description logics are and why they make good ontology languages. In particular, we introduce the description logic SHIQ, which has formed the basis of several well-known ontology languages, including OWL.We argue that, without the last decade of basic research in description logics, this family of knowledge representation languages could not have played such an important role in this context. Description logic reasoning can be used both during the design phase, in order to improve the quality of ontologies, and in the deployment phase, in order to exploit the rich structure of ontologies and ontology based information. We discuss the extensions to SHIQ that are required for languages such as OWL and, finally, we sketch how novel reasoning services can support building DL knowledge bases.

@incollection{ BaHoSaOntologyHB, address = {Berlin, Germany}, author = {F. {Baader} and I. {Horrocks} and U. {Sattler}}, booktitle = {Handbook on Ontologies}, editor = {S. {Staab} and R. {Studer}}, pages = {3--28}, publisher = {Springer--Verlag}, series = {International Handbooks in Information Systems}, title = {Description Logics}, year = {2004}, }

F. Baader and B. Sertkaya:

Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

**Applying Formal Concept Analysis to Description Logics**. In P. Eklund, editor,*Proceedings of the 2nd International Conference on Formal Concept Analysis (ICFCA 2004)*, volume 2961 of*Lecture Notes in Artificial Intelligence*, pages 261–286. Springer, 2004.Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

Given a finite set S := C1, ..., Cn of description logic concepts, we are interested in computing the subsumption hierarchy of all least common subsumers of subsets of S as well as the hierarchy of all conjunctions of subsets of S. These hierarchies can be used to support the bottom-up construction of description logic knowledge bases. The point is to compute the first hierarchy without having to compute the least common subsumer for all subsets of S, and the second hierarchy without having to check all possible pairs of such conjunctions explicitly for subsumption. We will show that methods from formal concept analysis developed for computing concept lattices can be employed for this purpose.

@inproceedings{ BaaderSertkayaICFCA04, author = {F. {Baader} and B. {Sertkaya}}, booktitle = {Proceedings of the 2nd International Conference on Formal Concept Analysis ({ICFCA 2004})}, editor = {P. {Eklund}}, pages = {261--286}, publisher = {Springer}, series = {Lecture Notes in Artificial Intelligence}, title = {Applying Formal Concept Analysis to Description Logics}, volume = {2961}, year = {2004}, }

F. Baader, B. Sertkaya, and A.-Y. Turhan:

Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

**Computing the Least Common Subsumer w.r.t. a Background Terminology**. In José Júlio Alferes and João Alexandre Leite, editors,*Proceedings of the 9th European Conference on Logics in Artificial Intelligence (JELIA 2004)*, volume 3229 of*Lecture Notes in Computer Science*, pages 400–412. Lisbon, Portugal, Springer-Verlag, 2004.Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

Methods for computing the least common subsumer (lcs) are usually restricted to rather inexpressive Description Logics (DLs) whereas existing knowledge bases are written in very expressive DLs. In order to allow the user to re-use concepts defined in such terminologies and still support the definition of new concepts by computing the lcs, we extend the notion of the lcs of concept descriptions to the notion of the lcs w.r.t. a background terminology. We will both show a theoretical result on the existence of the least common subsumer in this setting, and describe a practical approach (based on a method from formal concept analysis) for computing good common subsumers, which may, however, not be the least ones.

@inproceedings{ BaaderSertkayaTurhan04, address = {Lisbon, Portugal}, author = {F. {Baader} and B. {Sertkaya} and A.-Y. {Turhan}}, booktitle = {Proceedings of the 9th European Conference on Logics in Artificial Intelligence {(JELIA 2004)}}, editor = {Jos{\'e} J{\'u}lio {Alferes} and Jo{\~a}o Alexandre {Leite}}, pages = {400--412}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, title = {Computing the Least Common Subsumer w.r.t.\ a Background Terminology}, volume = {3229}, year = {2004}, }

Franz Baader, Baris Sertkaya, and Anni-Yasmin Turhan:

Abstract BibTeX Entry PDF File PS File

**Computing the Least Common Subsumer w.r.t. a Background Terminology**. In*Proceedings of the 2004 International Workshop on Description Logics (DL2004)*,*CEUR-WS*, 2004.Abstract BibTeX Entry PDF File PS File

Methods for computing the least common subsumer (lcs) are usually restricted to rather inexpressive DLs whereas existing knowledge bases are written in very expressive DLs. In order to allow the user to re-use concepts defined in such terminologies and still support the definition of new concepts by computing the lcs, we extend the notion of the lcs of concept descriptions to the notion of the lcs w.r.t. a background terminology.

@inproceedings{ BaaderSertkayaTurhanDL2004, author = {Franz {Baader} and Baris {Sertkaya} and Anni-Yasmin {Turhan}}, booktitle = {Proceedings of the 2004 International Workshop on Description Logics ({DL2004})}, series = {CEUR-WS}, title = {Computing the Least Common Subsumer w.r.t. a Background Terminology}, year = {2004}, }

Sebastian Brandt:

Abstract BibTeX Entry PDF File

**On Subsumption and Instance Problem in**\(\mathcal{E\!LH}\)**w.r.t. General TBoxes**. In*Proceedings of the 2004 International Workshop on Description Logics (DL2004)*,*CEUR-WS*, 2004.Abstract BibTeX Entry PDF File

Recently, it was shown for the DL EL that subsumption and instance problem w.r.t. cyclic terminologies can be decided in polynomial time. In this paper, we show that both problems remain tractable even when admitting general concept inclusion axioms and simple role inclusion axioms.

@inproceedings{ Brandt-DL-2004, author = {Sebastian {Brandt}}, booktitle = {Proceedings of the 2004 International Workshop on Description Logics ({DL2004})}, series = {CEUR-WS}, title = {On Subsumption and Instance Problem in $\mathcal{E\!LH}$ w.r.t. General TBoxes}, year = {2004}, }

Sebastian Brandt:

Abstract BibTeX Entry PDF File

**Polynomial Time Reasoning in a Description Logic with Existential Restrictions, GCI Axioms, and—What Else?**. In R. López de Mantáras and L. Saitta, editors,*Proceedings of the 16th European Conference on Artificial Intelligence (ECAI-2004)*, pages 298–302. IOS Press, 2004.Abstract BibTeX Entry PDF File

In the area of Description Logic (DL) based knowledge representation, research on reasoning w.r.t. general terminologies has mainly focused on very expressive DLs. Recently, though, it was shown for the DL EL, providing only the constructors conjunction and existential restriction, that the subsumption problem w.r.t. cyclic terminologies can be decided in polynomial time, a surprisingly low upper bound. In this paper, we show that even admitting general concept inclusion (GCI) axioms and role hierarchies in EL terminologies preserves the polynomial time upper bound for subsumption. We also show that subsumption becomes co-NP hard when adding one of the constructors number restriction, disjunction, and `allsome', an operator used in the DL K-Rep. An interesting implication of the first result is that reasoning over the widely used medical terminology SNOMED is possible in polynomial time.

@inproceedings{ Brandt-ECAI-2004, author = {Sebastian {Brandt}}, booktitle = {Proceedings of the 16th European Conference on Artificial Intelligence (ECAI-2004)}, editor = {R. L{\'o}pez de {Mant{\'a}ras} and L. {Saitta}}, pages = {298--302}, publisher = {IOS Press}, title = {Polynomial Time Reasoning in a Description Logic with Existential Restrictions, {GCI} Axioms, and---What Else?}, year = {2004}, }

Sebastian Brandt and Hongkai Liu:

Abstract BibTeX Entry PDF File

**Implementing Matching in**\({\mathcal ALN}\). In*Proceedings of the KI-2004 Workshop on Applications of Description Logics (KI-ADL'04)*,*CEUR-WS*, September 2004.Abstract BibTeX Entry PDF File

Although matching in Description Logics (DLs) is theoretically well-investigated, an implementation of a matching algorithm exists only for the DL ALE. The present paper presents an implementation of an existing polynomial time matching algorithm for the DL ALN. Benchmarks using randomly generated matching problems indicate a relatively good performance even on large matching problems. Nevertheless, striking differences are revealed by direct comparison between the ALN- and the ALE-algorithm w.r.t. FL(-)-matching problems.

@inproceedings{ BrandtLiu-KIADL-04, address = {Ulm, Germany}, author = {Sebastian {Brandt} and Hongkai {Liu}}, booktitle = {Proceedings of the KI-2004 Workshop on Applications of Description Logics {(KI-ADL'04)}}, month = {September}, series = {CEUR-WS}, title = {Implementing Matching in {${\mathcal ALN}$}}, year = {2004}, }

Mitchell A. Harris and Edward R. Reingold:

Abstract BibTeX Entry PDF File

**Line Drawing, Leap Years, and Euclid**.*ACM Computing Surveys*, 36:68–80, 2004.Abstract BibTeX Entry PDF File

Bresenham's algorithm minimizes error in drawing lines on integer grid points; leap year calculations, surprisingly, are a generalization. We compare the two calculations, explicate the pattern, and discuss the connection of the leap year/line pattern with integer division and Euclid's algorithm for computing the greatest common divisor.

@article{ Harris-ACMCS2004, author = {Mitchell A. {Harris} and Edward R. {Reingold}}, journal = {ACM Computing Surveys}, pages = {68--80}, title = {Line {D}rawing, {L}eap {Y}ears, and {E}uclid}, volume = {36}, year = {2004}, }

T. Hinze and M. Sturm:

Abstract BibTeX Entry PDF File

**Rechnen mit DNA - Eine Einführung in Theorie und Praxis**. ISBN 3-486-27530-5, R. Oldenbourg Wissenschaftsverlag München, 2004.Abstract BibTeX Entry PDF File

Das Buch bietet eine umfassende und systematische Einführung in das interdisziplinär geprägte Wissensgebiet des DNA-Computing einschließlich seiner mathematischen wie auch molekularbiologischen Grundlagen. Im Zentrum des DNA-Computing stehen biologische Rechner, bei denen organische Moleküle als Speichermedium dienen und Rechenoperationen durch geeignete molekularbiologische und biochemische Prozesse im Reagenzglas ausgeführt werden. Algorithmen, die DNA-basiert konstruiert sind, nutzen eine massive Datenparallelität, die es ermöglicht, mit DNA-Computern Leistungsparameter zu erreichen, die einen Vergleich zu bekannter elektronischer Rechentechnik herausfordern. Bereits heute existiert eine Vielzahl interessanter praktischer Anwendungsfelder, deren Kommerzialisierung schon begonnen hat. Neben der Vermittlung von Basiswissen zum DNA-Computing werden Modelle, Methoden und Techniken vorgestellt, die eine Realisierung im Labor vorbereiten. Einen Schwerpunkt bildet die labornahe Simulation von Prozessen des DNA-Computing.

@book{ HinzeSturm-04, address = {ISBN 3-486-27530-5}, author = {T. {Hinze} and M. {Sturm}}, publisher = {R. Oldenbourg Wissenschaftsverlag M\"unchen}, title = {Rechnen mit DNA - Eine Einf\"uhrung in Theorie und Praxis}, year = {2004}, }

J. Hladik:

Abstract BibTeX Entry PDF File PS File

**A Tableau System for the Description Logic SHIO**. In Ulrike Sattler, editor,*Contributions to the Doctoral Programme of IJCAR 2004*. CEUR, 2004. Available from ceur-ws.orgAbstract BibTeX Entry PDF File PS File

Tableau systems are a framework for tableau algorithms which tries to combine the advantages of tableau and automata algorithms, in particular efficiency in practice and worst-case complexity. In this paper, we present a tableau system for the expressive description logic SHIO and prove that the satisfiability problem for SHIO concepts is EXPTIME-complete. The succinctness of the proofs illustrates the usefulness of the tableau system framework.

@inproceedings{ Hladik-IJCAR-04, author = {J. {Hladik}}, booktitle = {Contributions to the Doctoral Programme of {IJCAR} 2004}, editor = {Ulrike {Sattler}}, note = {Available from \texttt{ceur-ws.org}}, publisher = {CEUR}, title = {A Tableau System for the Description Logic {SHIO}}, year = {2004}, }

J. Hladik:

Abstract BibTeX Entry PDF File

**Spinoza's Ontology**. In G. Büchel, B. Klein, and T. Roth-Berghofer, editors,*Proceedings of the 1st Workshop on Philosophy and Informatics (WSPI 2004)*, number RR-04-02 in*DFKI Research Reports*, 2004.Abstract BibTeX Entry PDF File

We examine the possibility of applying knowledge representation and automated reasoning in the context of philosophical ontology. For this purpose, we use the axioms and propositions in the first book of Spinoza's Ethics as knowledge base and a tableau-based satisfiability tester as reasoner. We are able to reconstruct most of Spinoza's system with formal logic, but this requires additional axioms which are assumed implicitly by Spinoza. This study illustrates how tools developed in computer science can be of practical use for philosophy.

@inproceedings{ Hladik-WSPI-04, author = {J. {Hladik}}, booktitle = {Proceedings of the 1st Workshop on Philosophy and Informatics (WSPI 2004)}, editor = {G. {B\"uchel} and B. {Klein} and T. {Roth-Berghofer}}, number = {RR-04-02}, series = {DFKI Research Reports}, title = {Spinoza's Ontology}, year = {2004}, }

J. Hladik and J. Model:

Abstract BibTeX Entry PDF File

**Tableau Systems for SHIO and SHIQ**. In V. Haarslev and R. Möller, editors,*Proceedings of the 2004 International Workshop on Description Logics (DL 2004)*. CEUR, 2004. Available from ceur-ws.orgAbstract BibTeX Entry PDF File

Tableau systems are a framework for tableau algorithms which tries to combine the advantages of tableau and automata algorithms, in particular efficiency in practice and worst-case complexity. In this paper, we present tableau systems for two expressive description logics, firstly the well-known SHIQ, and secondly SHIO, which has not been examined so far. The succinctness of the proofs illustrates the usefulness of the tableau system framework. As a corollary, we obtain that satisfiability of SHIO concepts is EXPTIME-complete.

@inproceedings{ HladikModel-DL-04, author = {J. {Hladik} and J. {Model}}, booktitle = {Proceedings of the 2004 International Workshop on Description Logics (DL 2004)}, editor = {V. {Haarslev} and R. {M\"oller}}, note = {Available from \texttt{ceur-ws.org}}, publisher = {CEUR}, title = {Tableau Systems for {SHIO} and {SHIQ}}, year = {2004}, }

E. Karabaev and C. Lutz:

Abstract BibTeX Entry PDF File PS File

**Mona as a DL Reasoner**. In*Proceedings of the 2004 International Workshop on Description Logics (DL2004)*,*CEUR-WS*, 2004.Abstract BibTeX Entry PDF File PS File

We show how the Mona tool for reasoning in the monadic second order theories WS1S and WS2S can be used to obtain decision procedures for description logics. The performance of this approach is evaluated and compared to the dedicated DL reasoners FaCT and RACER.

@inproceedings{ KarabaevLutz-DL2004, author = {E. {Karabaev} and C. {Lutz}}, booktitle = {Proceedings of the 2004 International Workshop on Description Logics ({DL2004})}, series = {CEUR-WS}, title = {Mona as a DL Reasoner}, year = {2004}, }

R. Kontchakov, C. Lutz, F. Wolter, and M. Zakharyaschev:

Abstract BibTeX Entry PDF File PS File

**Temporal Tableaux**.*Studia Logica*, 76(1):91–134, 2004.Abstract BibTeX Entry PDF File PS File

As a remedy for the bad computational behaviour of first-order temporal logic (FOTL), it has recently been proposed to restrict the application of temporal operators to formulas with at most one free variable thereby obtaining so-called monodic fragments of FOTL. In this paper, we are concerned with constructing tableau algorithms for monodic fragments based on decidable fragments of first-order logic like the two-variable fragment or the guarded fragment. We present a general framework that shows how existing decision procedures for first-order fragments can be used for constructing a tableau algorithm for the corresponding monodic fragment of FOTL. Some example instantiations of the framework are presented.

@article{ KoLuWoZa-04, author = {R. {Kontchakov} and C. {Lutz} and F. {Wolter} and M. {Zakharyaschev}}, journal = {Studia Logica}, number = {1}, pages = {91--134}, title = {Temporal Tableaux}, volume = {76}, year = {2004}, }

O. Kutz, C. Lutz, F. Wolter, and M. Zakharyaschev:

Abstract BibTeX Entry PDF File PS File

**E-Connections of Abstract Description Systems**.*Artificial Intelligence*, 156(1):1–73, 2004.Abstract BibTeX Entry PDF File PS File

Combining knowledge representation and reasoning formalisms is an important and challenging task. It is important because non-trivial AI applications often comprise different aspects of the world, thus requiring suitable combinations of available formalisms modeling each of these aspects. It is challenging because the computational behavior of the resulting hybrids is often much worse than the behavior of their components. In this paper, we propose a new combination method which is computationally robust in the sense that the combination of decidable formalisms is again decidable, and which, nonetheless, allows non-trivial interactions between the combined components. The new method, called E-connection, is defined in terms of abstract description systems (ADSs), a common generalization of description logics, many logics of time and space, as well as modal and epistemic logics. The basic idea of E-connections is that the interpretation domains of n combined systems are disjoint, and that these domains are connected by means of n-ary `link relations.' We define several natural variants of E-connections and study in-depth the transfer of decidability from the component systems to their E-connections.

@article{ KuLuWoZa-AI-03, author = {O. {Kutz} and C. {Lutz} and F. {Wolter} and M. {Zakharyaschev}}, journal = {Artificial Intelligence}, number = {1}, pages = {1--73}, title = {E-Connections of Abstract Description Systems}, volume = {156}, year = {2004}, }

C. Lutz:

Abstract BibTeX Entry PDF File PS File

**Combining Interval-based Temporal Reasoning with General TBoxes**.*Artificial Intelligence*, 152(2):235–274, 2004.Abstract BibTeX Entry PDF File PS File

While classical Description Logics (DLs) concentrate on the representation of static conceptual knowledge, recently there is a growing interest in DLs that, additionally, allow to capture the temporal aspects of conceptual knowledge. Such temporal DLs are based either on time points or on time intervals as the temporal primitive. Whereas point-based temporal DLs are well-investigated, this is not the case for interval-based temporal DLs: all known logics either suffer from rather limited expressive power or have undecidable reasoning problems. In particular, there exists no decidable interval-based temporal DL that provides for general TBoxes-one of the most important expressive means in modern description logics. In this paper, for the first time we define an interval-temporal DL that is equipped with general TBoxes and for which reasoning is decidable (and, more precisely, ExpTime-complete).

@article{ Lutz-AI-04, author = {C. {Lutz}}, journal = {Artificial Intelligence}, number = {2}, pages = {235--274}, title = {Combining Interval-based Temporal Reasoning with General TBoxes}, volume = {152}, year = {2004}, }

C. Lutz and M. Milicic:

Abstract BibTeX Entry PDF File PS File

**Description Logics with Concrete Domains and Functional Dependencies**. In*Proceedings of the 16th European Conference on Artificial Intelligence (ECAI-2004)*, 2004.Abstract BibTeX Entry PDF File PS File

Description Logics (DLs) with concrete domains are a useful tool in many applications. To further enhance the expressive power of such DLs, it has been proposed to add database-style key constraints. Up to now, however, only uniqueness constraints have been considered in this context, thus neglecting the second fundamental family of key constraints: functional dependencies. In this paper, we consider the basic DL with concrete domains , extend it with functional dependencies, and analyze the impact of this extension on the decidability and complexity of reasoning. Though intuitively the expressivity of functional dependencies seems weaker than that of uniqueness constraints, we are able to show that the former have a similarly severe impact on the computational properties: reasoning is undecidable in the general case, and -complete in some slightly restricted variants of our logic.

@inproceedings{ LutzMilicic-ECAI-2004, author = {C. {Lutz} and M. {Milicic}}, booktitle = {Proceedings of the 16th European Conference on Artificial Intelligence (ECAI-2004)}, title = {Description Logics with Concrete Domains and Functional Dependencies}, year = {2004}, }

C. Lutz and D. Walther:

Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

**PDL with Negation of Atomic Programs**. In*Proceedings of the 2nd International Joint Conference on Automated Reasoning IJCAR'04*,*Lecture Notes in Artificial Intelligence*. Springer Verlag, 2004.Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

Propositional dynamic logic (PDL) is one of the most successful variants of modal logic. To make it even more useful for applications, many extensions of PDL have been considered in the literature. A very natural and useful such extension is with negation of programs. Unfortunately, it is long known that reasoning with the resulting logic is undecidable. In this paper, we consider the extension of PDL with negation of atomic programs, only. We argue that this logic is still useful, e.g. in the context of description logics, and prove that satisfiability is decidable and ExpTime-complete using an approach based on Buechi tree automata.

@inproceedings{ LutzWaltherIJCAR04, author = {C. {Lutz} and D. {Walther}}, booktitle = {Proceedings of the 2nd International Joint Conference on Automated Reasoning {IJCAR'04}}, publisher = {Springer Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {PDL with Negation of Atomic Programs}, year = {2004}, }

C. Lutz and F. Wolter:

Abstract BibTeX Entry PDF File PS File

**Modal Logics of Topological Relations**. In*Proceedings of Advances in Modal Logics 2004*, 2004.Abstract BibTeX Entry PDF File PS File

We introduce a family of modal logics that are interpreted in domains consisting of regions in topological spaces, in particular the real plane. The underlying modal language has 8 operators interpreted by the RCC8 (or Egenhofer-Franzosa)-relations between regions. The following results on the expressive power and computational complexity of the resulting modal systems are obtained: they are expressively complete for the two-variable fragment of first-order logic, and are usually undecidable and often not even recursively enumerable. This also holds if we interpret our language in the class of all (finite) substructures of full region spaces. If interpreted in region spaces consisting of intervals in the real line, our results significantly extend undecidability results of Halpern and Shoham in that we prove the undecidability of interval temporal logic over the class of all substructures of all full interval structures. We also analyze modal logics based on the set of RCC5-relations which are more coarse than the RCC8 relations.

@inproceedings{ Lutz-Wolter-AiML-04, author = {C. {Lutz} and F. {Wolter}}, booktitle = {Proceedings of Advances in Modal Logics 2004}, title = {Modal Logics of Topological Relations}, year = {2004}, }

Carsten Lutz:

Abstract BibTeX Entry

**NExpTime-complete Description Logics with Concrete Domains**.*ACM Transactions on Computational Logic*, 5(4):669–705, 2004.Abstract BibTeX Entry

Concrete domains are an extension of Description Logics (DLs) that allows to integrate reasoning about conceptual knowledge with reasoning about ``concrete qualities'' of real-world entities such as their sizes, weights, and durations. In this paper, we are concerned with the complexity of Description Logics providing for concrete domains: starting from the complexity result established in [Lutz 2002b], which states that reasoning with the basic propositionally closed DL with concrete domains ALC(D) is PSpace-complete (provided that some weak conditions are satisfied), we perform an in-depth analysis of the complexity of extensions of this logic. More precisely, we consider five natural and seemingly ``harmless'' extensions of ALC(D) and prove that, for all five extensions, reasoning is NExpTime-complete (again if some weak conditions are satisfied). Thus, we show that the PSpace upper bound for reasoning with ALC(D) cannot be considered robust w.r.t. extensions of the language.

@article{ Lutz-ToCL-04, author = {Carsten {Lutz}}, journal = {{ACM} Transactions on Computational Logic}, number = {4}, pages = {669--705}, title = {{NExpTime}-complete Description Logics with Concrete Domains}, volume = {5}, year = {2004}, }

Baris Sertkaya and Halit Oguztuzun:

Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

**Proof of the Basic Theorem on Concept Lattices in Isabelle/HOL**. In C. Aykanat, T. Dayar, and I. Korpeoglu, editors,*Proceedings of the 19th International Symposium on Computer and Information Sciences (ISCIS2004)*, volume 3280 of*Lecture Notes in Computer Science*, pages 976–985. Springer, 2004.Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

This paper presents a machine-checked proof of the Basic Theorem on Concept Lattices, which appears in the book "Formal Concept Analysis" by Ganter and Wille, in the Isabelle/HOL Proof Assistant. As a by-product, the underlying lattice theory by Kammueller has been extended.

@inproceedings{ SertkayaOguztuzunISCIS2004, author = {Baris {Sertkaya} and Halit {Oguztuzun}}, booktitle = {Proceedings of the 19th International Symposium on Computer and Information Sciences ({ISCIS2004})}, editor = {C. {Aykanat} and T. {Dayar} and I. {Korpeoglu}}, pages = {976--985}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Proof of the Basic Theorem on Concept Lattices in Isabelle/HOL}, volume = {3280}, year = {2004}, }

Anni-Yasmin Turhan and Christian Kissig:

Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

**Sonic—Non-standard Inferences go OilEd**. In D. Basin and M. Rusinowitch, editors,*Proceedings of the 2nd International Joint Conference on Automated Reasoning (IJCAR'04)*, volume 3097 of*Lecture Notes in Artificial Intelligence*. Springer-Verlag, 2004.Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

SONIC (``Simple OilEd Non-standard Inference Component'') is the first prototype implementation of non-standard inferences for Description Logics usable via a graphical user interface. The contribution of our implementation is twofold: it extends an earlier implementation of the least common subsumer and of the approximation inference to number restrictions, and it offers these reasoning services via an extension of the graphical ontology editor OilEd.

@inproceedings{ TurhanKissigIJCAR04, author = {Anni-Yasmin {Turhan} and Christian {Kissig}}, booktitle = {Proceedings of the 2nd International Joint Conference on Automated Reasoning ({IJCAR'04})}, editor = {D. {Basin} and M. {Rusinowitch}}, publisher = {Springer-Verlag}, series = {Lecture Notes in Artificial Intelligence}, title = {{\sc Sonic}---Non-standard Inferences go {\sc OilEd}}, volume = {3097}, year = {2004}, }

Anni-Yasmin Turhan and Christian Kissig:

Abstract BibTeX Entry PDF File PS File

**Sonic—System Description**. In*Proceedings of the 2004 International Workshop on Description Logics (DL2004)*,*CEUR-WS*, 2004.Abstract BibTeX Entry PDF File PS File

@inproceedings{ TurhanKissigDL2004, author = {Anni-Yasmin {Turhan} and Christian {Kissig}}, booktitle = {Proceedings of the 2004 International Workshop on Description Logics ({DL2004})}, series = {CEUR-WS}, title = {{\sc Sonic}---System Description}, year = {2004}, }

## 2003

F. Baader:

Abstract BibTeX Entry

**Description Logic Terminology**. In Franz Baader, Diego Calvanese, Deborah McGuinness, Daniele Nardi, and Peter F. Patel-Schneider, editors,*The Description Logic Handbook: Theory, Implementation, and Applications*, pages 485–495. Cambridge University Press, 2003.Abstract BibTeX Entry

The purpose of this appendix is to introduce (in a compact manner) the syntax and semantics of the most prominent DLs occurring in this handbook. More information and explanations as well as some less familiar DLs can be found in the respective chapters. For DL constructors whose semantics cannot be described in a compact manner, we will only introduce the syntax and refer the reader to the respective chapter for the semantics. Following Chapter 2 on Basic Description Logics, we will first introduce the basic DL AL, and then describe several of its extensions. Thereby, we will also fix the notation employed in this handbook.

@incollection{ DLhandbookAppendix, author = {F. {Baader}}, booktitle = {The Description Logic Handbook: Theory, Implementation, and Applications}, editor = {Franz {Baader} and Diego {Calvanese} and Deborah {McGuinness} and Daniele {Nardi} and Peter F. {Patel-Schneider}}, pages = {485--495}, publisher = {Cambridge University Press}, title = {Description Logic Terminology}, year = {2003}, }

F. Baader, J. Hladik, C. Lutz, and F. Wolter:

Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

**From Tableaux to Automata for Description Logics**. In Moshe Vardi and Andrei Voronkov, editors,*Proceedings of the 10th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2003)*, volume 2850 of*Lecture Notes in Computer Science*, pages 1–32. Springer, 2003.Abstract BibTeX Entry PDF File PS File ©Springer-Verlag

This paper investigates the relationship between automata- and tableau-based inference procedures for Description Logics. To be more precise, we develop an abstract notion of what a tableau-based algorithm is, and then show, on this abstract level, how tableau-based algorithms can be converted into automata-based algorithms. In particular, this allows us to characterize a large class of tableau-based algorithms that imply an ExpTime upper-bound for reasoning in the description logics for which such an algorithm exists.

@inproceedings{ BaaHlaLutWol-LPAR03, author = {F. {Baader} and J. {Hladik} and C. {Lutz} and F. {Wolter}}, booktitle = {Proceedings of the 10th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning ({LPAR 2003})}, editor = {Moshe {Vardi} and Andrei {Voronkov}}, pages = {1--32}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {From Tableaux to Automata for Description Logics}, volume = {2850}, year = {2003}, }

F. Baader, R Küsters, and F. Wolter:

Abstract BibTeX Entry

**Extensions to Description Logics**. In Franz Baader, Diego Calvanese, Deborah McGuinness, Daniele Nardi, and Peter F. Patel-Schneider, editors,*The Description Logic Handbook: Theory, Implementation, and Applications*, pages 219–261. Cambridge University Press, 2003.Abstract BibTeX Entry

This chapter considers, on the one hand, extensions of Description Logics by features not available in the basic framework, but considered important for using Description Logics as a modeling language. In particular, it addresses the extensions concerning: concrete domain constraints; modal, epistemic, and temporal operators; probabilities and fuzzy logic; and defaults. On the other hand, it considers non-standard inference problems for Description Logics, i.e., inference problems that—unlike subsumption or instance checking—are not available in all systems, but have turned out to be useful in applications. In particular, it addresses the non-standard inference problems: least common subsumer and most specific concept; unification and matching of concepts; and rewriting.

@incollection{ DLhandbookCh6, author = {F. {Baader} and R {K{\"u}sters} and F. {Wolter}}, booktitle = {The Description Logic Handbook: Theory, Implementation, and Applications}, editor = {Franz {Baader} and Diego {Calvanese} and Deborah {McGuinness} and Daniele {Nardi} and Peter F. {Patel-Schneider}}, pages = {219--261}, publisher = {Cambridge University Press}, title = {Extensions to Description Logics}, year = {2003}, }

F. Baader and W. Nutt:

Abstract BibTeX Entry

**Basic Description Logics**. In Franz Baader, Diego Calvanese, Deborah McGuinness, Daniele Nardi, and Peter F. Patel-Schneider, editors,*The Description Logic Handbook: Theory, Implementation, and Applications*, pages 43–95. Cambridge University Press, 2003.Abstract BibTeX Entry

This chapter provides an introduction to Description Logics as a formal language for representing knowledge and reasoning about it. It first gives a short overview of the ideas underlying Description Logics. Then it introduces syntax and semantics, covering the basic constructors that are used in systems or have been introduced in the literature, and the way these constructors can be used to build knowledge bases. Finally, it defines the typical inference problems, shows how they are interrelated, and describes different approaches for effectively solving these problems. Some of the topics that are only briefly mentioned in this chapter will be treated in more detail in subsequent chapters.

@incollection{ DLhandbookCh2, author = {F. {Baader} and W. {Nutt}}, booktitle = {The Description Logic Handbook: Theory, Implementation, and Applications}, editor = {Franz {Baader} and Diego {Calvanese} and Deborah {McGuinness} and Daniele {Nardi} and Peter F. {Patel-Schneider}}, pages = {43--95}, publisher = {Cambridge University Press}, title = {Basic Description Logics}, year = {2003}, }

F. Baader and U. Sattler:

Abstract BibTeX Entry PDF File PS File Free reprint

**Description Logics with Aggregates and Concrete Domains**.*Information Systems*, 28(8):979–1004, 2003.Abstract BibTeX Entry PDF File PS File Free reprint

Description Logics are a family of knowledge representation formalisms well-suited for intensional reasoning about conceptual models of databases/data warehouses. We extend Description Logics with concrete domains (such as integers and rational numbers) that include aggregation functions over these domains (such as min, max, count, and sum) which are usually available in database systems.<br> We show that the presence of aggregation functions may easily lead to undecidability of (intensional) inference problems such as satisfiability and subsumption. However, there are also extensions for which satisfiability and subsumption are decidable, and we present decision procedures for the relevant inference problems.

@article{ BaaderSattlerIS-02, author = {F. {Baader} and U. {Sattler}}, journal = {Information Systems}, number = {8}, pages = {979--1004}, title = {Description Logics with Aggregates and Concrete Domains}, volume = {28}, year = {2003}, }

Franz Baader:

**Computing the least common subsumer in the description logic**\(\cal EL\)**w.r.t. terminological cycles with descriptive semantics**. In*Proceedings of the 11th International Conferen*