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We propose an interactive repair method for the description logic \(\mathcal{EL}\) that is based on the optimal-repair framework. The obtained repair might not be optimal in the theoretical sense, i.e. more than a minimal amount of consequences might have been removed—but from a practical perspective it is superior to a theoretically optimal repair as the interaction strategy enables the users to identify further faulty consequences connected to the initially reported errors.

@inproceedings{ Kr-KRRSAC2025,
  author = {Francesco {Kriegel}},
  booktitle = {Proceedings of the 40th ACM/SIGAPP Symposium On Applied Computing {(SAC 2025)}},
  doi = {https://doi.org/10.1145/3672608.3707750},
  note = {To appear.},
  publisher = {Association for Computing Machinery},
  title = {Beyond Optimal: Interactive Identification of Better-than-optimal Repairs},
  year = {2025},
}

Concrete domains have been introduced in description logic (DL) to enable reference to concrete objects (such as numbers) and predefined predicates on these objects (such as numerical comparisons) when defining concepts. The primary research goal in this context was to find restrictions on the concrete domain such that its integration into certain DLs preserves decidability or tractability. In this article, we complement these investigations by studying the abstract expressive power of both first-order and description logics extended with concrete domains, i.e., we analyze which classes of first-order interpretations can be expressed using these logics, compared to what their counterparts without concrete domains can express. We demonstrate that, under natural conditions on the concrete domain D (which also play a role for decidability), extensions of first-order logic (FOL) or the well-known DL ALC with D share important formal characteristics with FOL, such as the compactness and the Löwenheim-Skolem properties. Nevertheless, these conditions do not ensure that the abstract expressive power of the extensions we consider is contained in that of FOL, though in some cases it is. To be more precise, we show, on the one hand, that unary concrete domains leave the abstract expressive power within FOL if we are allowed to introduce auxiliary predicates. As a by-product, we obtain (semi-)decidability results for some fragments of FOL extended with the concrete domains considered in this article. On the other hand, we show that the ability to express equality between elements of D, another condition employed in the context of showing decidability of ALC(D), is sufficient to push the abstract expressive power of most first-order fragments with concrete domains beyond that of FOL. While for such concrete domains D decidability is retained for ALC(D), we show that the availability of equality in D causes undecidability of the two-variable fragment of FOL(D), although the two-variable fragment of FOL is decidable.

@article{ BaBo-ACR-24,
  address = {New York, NY, USA},
  author = {Franz {Baader} and Filippo {De Bortoli}},
  doi = {https://doi.org/10.1145/3699839.3699840},
  journal = {SIGAPP Appl. Comput. Rev.},
  month = {October},
  number = {3},
  pages = {5--17},
  publisher = {Association for Computing Machinery},
  title = {Logics with Concrete Domains: First-Order Properties, Abstract Expressive Power, and (Un)Decidability},
  volume = {24},
  year = {2024},
}

Concrete domains have been introduced in description logic (DL) to enable reference to concrete objects (such as numbers) and predefined predicates on these objects (such as numerical comparisons) when defining concepts. The primary research goal in this context was to find restrictions on the concrete domain such that its integration into certain DLs preserves decidability or tractability. In this paper, we investigate the abstract expressive power of both first-order and description logics extended with concrete domains, i.e., we analyze which classes of first-order interpretations can be expressed using these logics, compared to what first-order logic without concrete domains can express. We demonstrate that, under natural conditions on the concrete domain D (which also play a role for decidability), extensions of first-order logic (FOL) or the well-known DL ALC with D share important formal characteristics with FOL, such as the compactness and the Löwenheim-Skolem properties. Nevertheless, their abstract expressive power need not be contained in that of FOL, though in some cases it is. To be more precise, we show, on the one hand, that unary concrete domains leave the abstract expressive power within FOL if we are allowed to introduce auxiliary predicates. On the other hand, we exhibit a class of concrete domains that push the abstract expressive power beyond that of FOL. As a by-product of these investigations, we obtain (semi-)decidability results for some of the logics with concrete domains considered in this paper.

@inproceedings{ BaBo-SAC-24,
  address = {New York, NY, USA},
  author = {Franz {Baader} and Filippo {De Bortoli}},
  booktitle = {Proceedings of the 39th {ACM/SIGAPP} Symposium on Applied Computing},
  doi = {https://doi.org/10.1145/3605098.3635984},
  pages = {754--761},
  publisher = {{ACM}},
  series = {SAC '24},
  title = {{The Abstract Expressive Power of First-Order and Description Logics with Concrete Domains}},
  year = {2024},
}

In applications of AI systems where exact definitions of the important notions of the application domain are hard to come by, the use of traditional logic-based knowledge representation languages such as Description Logics may lead to very large and unintuitive definitions, and high complexity of reasoning. To overcome this problem, we define new concept constructors that allow us to define concepts in an approximate way. To be more precise, we present a family τEL(m) of extensions of the lightweight Description Logic EL that use threshold constructors for this purpose. To define the semantics of these constructors we employ graded membership functions m, which for each individual in an interpretation and concept yield a number in the interval [0,1] expressing the degree to which the individual belongs to the concept in the interpretation. Threshold concepts C⋈t for ⋈∈<,≤,>,≥ then collect all the individuals that belong to C with degree ⋈t. The logic τEL(m) extends EL with threshold concepts whose semantics is defined relative to a function m. To construct appropriate graded membership functions, we show how concept measures ∼ (which are graded generalizations of subsumption or equivalence between concepts) can be used to define graded membership functions m∼. Then we introduce a large class of concept measures, called simi-d, for which the logics τEL(m∼) have good algorithmic properties. Basically, we show that reasoning in τEL(m∼) is NP/coNP-complete without TBox, PSpace-complete w.r.t. acyclic TBoxes, and ExpTime-complete w.r.t. general TBoxes. The exception is the instance problem, which is already PSpace-complete without TBox w.r.t. combined complexity. While the upper bounds hold for all elements of simi-d, we could prove some of the hardness results only for a subclass of simi-d. This article considerably improves on and generalizes results we have shown in three previous conference papers and it provides detailed proofs of all our results.

@article{ BaFe-AIJ-24,
  author = {Franz {Baader} and Oliver {Fern{\'{a}}ndez Gil}},
  doi = {https://doi.org/10.1016/j.artint.2023.104034},
  journal = {Artificial Intelligence},
  pages = {104034},
  title = {Extending the description logic EL with threshold concepts induced by concept measures},
  volume = {326},
  year = {2024},
}

Unification has been introduced in Description Logic (DL) as a means to detect redundancies in ontologies. In particular, it was shown that testing unifiability in the DL EL is an NP-complete problem, and this result has been extended in several directions. Surprisingly, it turned out that the complexity increases to PSpace if one disallows the use of the top concept in concept descriptions. Motivated by features of the medical ontology SNOMED CT, we extend this result to a setting where the top concept is disallowed, but there is a background ontology consisting of restricted forms of concept and role inclusion axioms. We are able to show that the presence of such axioms does not increase the complexity of unification without top, i.e., testing for unifiability remains a PSpace-complete problem.

@inproceedings{ BaFe-IJCAR-24,
  author = {Franz {Baader} and Oliver {Fern{\'a}ndez Gil}},
  booktitle = {Automated Reasoning - 12th International Joint Conference, {IJCAR} 2024, Nancy, France, July 1-6, 2024, Proceedings, Part {II}},
  doi = {https://doi.org/10.1007/978-3-031-63501-4_15},
  editor = {Christoph {Benzm{\"u}ller} and Marijn J.H. {Heule} and Renate A. {Schmidt}},
  pages = {279--297},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Unification in the Description Logic {$\mathcal{ELH}_{\mathcal{R}^+}$} without the Top Concept Modulo Cycle-Restricted Ontologies},
  volume = {14740},
  year = {2024},
}

Unification has been introduced in Description Logic (DL) as a means to detect redundancies in ontologies. In particular, it was shown that testing unifiability in the DL EL is an NP-complete problem, and this result has been extended in several directions. Surprisingly, it turned out that the complexity increases to PSpace if one disallows the use of the top concept in concept descriptions. Motivated by features of the medical ontology SNOMED CT, we extend this result to a setting where the top concept is disallowed, but there is a background ontology consisting of restricted forms of concept and role inclusion axioms. We are able to show that the presence of such axioms does not increase the complexity of unification without top, i.e., testing for unifiability remains a PSpace-complete problem.

@inproceedings{ BaFe-DL-24,
  address = {Bergen, Norway},
  author = {Franz {Baader} and Oliver {Fern{\'a}ndez Gil}},
  booktitle = {Proceedings of the 37th International Workshop on Description Logics (DL'24)},
  editor = {Jean Christoph {Jung} and Laura {Giordano} and Ana {Ozaki}},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {Unification in {$\mathcal{ELH}_{\mathcal{R}^+}$} without the Top Concept modulo Cycle-Restricted Ontologies (Extended Abstract)},
  year = {2024},
}

Motivated by an application where we try to make proofs for Description Logic inferences smaller by rewriting, we consider the following decision problem, which we call the small term reachability problem: given a term rewriting system R, a term s, and a natural number n, decide whether there is a term t of size ≤ n reachable from s using the rules of R. We investigate the complexity of this problem depending on how termination of R can be established. We show that the problem is NP-complete for length-reducing term rewriting systems. Its complexity increases to N2ExpTime-complete (NExpTime-complete) if termination is proved using a (linear) polynomial order and to PSpace-complete for systems whose termination can be shown using a restricted class of Knuth-Bendix orders. Confluence reduces the complexity to P for the length-reducing case, but has no effect on the worst-case complexity in the other two cases.

@inproceedings{ BaaderGieslFSCD24,
  address = {Dagstuhl, Germany},
  author = {Franz {Baader} and J\"{u}rgen {Giesl}},
  booktitle = {9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  doi = {https://doi.org/10.4230/LIPIcs.FSCD.2024.16},
  editor = {Jakob {Rehof}},
  pages = {16:1--16:18},
  publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  series = {Leibniz International Proceedings in Informatics (LIPIcs)},
  title = {{On the Complexity of the Small Term Reachability Problem for Terminating Term Rewriting Systems}},
  volume = {299},
  year = {2024},
}

Errors in knowledge bases (KBs) written in a Description Logic (DL) are usually detected when reasoning derives an inconsistency or a consequence that does not hold in the application domain modelled by the KB. Whereas classical repair approaches produce maximal subsets of the KB not implying the inconsistency or unwanted consequence, optimal repairs maximize the consequence sets. In this paper, we extend previous results on how to compute optimal repairs from the DL \(\mathcal{EL}\) to its extension \(\mathcal{EL}^{\bot}\), which in contrast to \(\mathcal{EL}\) can express inconsistency. The problem of how to deal with inconsistency in the context of optimal repairs was addressed previously, but in a setting where the (fixed) terminological part of the KB must satisfy a restriction on cyclic dependencies. Here, we consider a setting where this restriction is not required. We also show how the notion of optimal repairs obtained this way can be used in inconsistency- and error-tolerant reasoning.

@inproceedings{ BaKrNu-FoIKS2024,
  author = {Franz {Baader} and Francesco {Kriegel} and Adrian {Nuradiansyah}},
  booktitle = {Proceedings of the 13th International Symposium on Foundations of Information and Knowledge Systems {(FoIKS 2024)}, April 8--11, 2024, Sheffield, United Kingdom},
  doi = {https://doi.org/10.1007/978-3-031-56940-1_1},
  pages = {3--22},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Inconsistency- and Error-Tolerant Reasoning w.r.t.\ Optimal Repairs of $\mathcal{EL}^{\bot}$ Ontologies},
  volume = {14589},
  year = {2024},
}

Removing unwanted consequences from a knowledge base has been investigated in belief change under the name contraction and is called repair in ontology engineering. Simple repair and contraction approaches based on removing statements from the knowledge base (respectively called belief base contractions and classical repairs) have the disadvantage that they are syntax-dependent and may remove more consequences than necessary. Belief set contractions do not have these problems, but may result in belief sets that have no finite representation if one works with logics that are not fragments of propositional logic. Similarly, optimal repairs, which are syntax-independent and maximize the retained consequences, may not exist. In this paper, we want to leverage advances in characterizing and computing optimal repairs of ontologies based on the description logics \(\mathcal{EL}\) to obtain contraction operations that combine the advantages of belief set and belief base contractions. The basic idea is to employ, in the partial meet contraction approach, optimal repairs instead of optimal classical repairs as remainders. We introduce this new approach in a very general setting, and prove a characterization theorem that relates the obtained contractions with well-known postulates. Then, we consider several interesting instances, not only in the standard repair/contraction setting where one wants to get rid of a consequence, but also in other settings such as variants of forgetting in propositional and description logic. We also show that classical belief set contraction is an instance of our approach.

@inproceedings{ BaWa-KR-24,
  author = {Franz {Baader} and Renata {Wassermann}},
  booktitle = {Proceedings of the 21st International Conference on Principles of Knowledge Representation and Reasoning (KR 2024)},
  doi = {https://doi.org/10.24963/kr.2024/9},
  pages = {94--105},
  title = {Contractions Based on Optimal Repairs},
  year = {2024},
}

Concrete domains have been introduced in the context of Description Logics to allow references to qualitative and quantitative values. In particular, the class of \(\omega\)-admissible concrete domains, which includes Allen's interval algebra, the region connection calculus (RCC8), and the rational numbers with ordering and equality, has been shown to yield extensions of \(\mathcal{ALC}\) for which concept satisfiability w.r.t. a general TBox is decidable. In this paper, we present an algorithm based on type elimination and use it to show that deciding the consistency of an \(\mathcal{ALC}(\mathfrak{D})\) ontology is ExpTime-complete if the concrete domain \(\mathfrak{D}\) is \(\omega\)-admissible and its constraint satisfaction problem is decidable in exponential time. While this allows us to reason with concept and role assertions, we also investigate feature assertions \(f(a,c)\) that can specify a constant \(c\) as the value of a feature \(f\) for an individual \(a\). We show that, under conditions satisfied by all known \(\omega\)-admissible domains, we can add feature assertions without affecting the complexity.

@inproceedings{ BaBoKo-DL-24,
  address = {Bergen, Norway},
  author = {Stefan {Borgwardt} and Filippo {De Bortoli} and Patrick {Koopmann}},
  booktitle = {Proceedings of the 37th International Workshop on Description Logics (DL'24)},
  editor = {Laura {Giordano} and Jean Christoph {Jung} and Ana {Ozaki}},
  publisher = {CEUR-WS},
  series = {{CEUR} Workshop Proceedings},
  title = {{The Precise Complexity of Reasoning in $\mathcal{ALC}$ with $\omega$-Admissible Concrete Domains}},
  volume = {3739},
  year = {2024},
}

Answering temporal CQs over temporalized Description Logic knowledge bases (TKB) is a main technique to realize ontology-based situation recognition. If the collected data in such a knowledge base is inaccurate, important query answers can be missed. In this extended abstract we report on the results from our ECAI'23 paper that introduces the TKB Alignment problem. This problem asks for a given TKB, a non-entailed temporal CQ q and a cost measure, to compute a variant of the TKB that minimally changes the TKB, such that it entails q and is (cost-) optimal. We investigated this problem for ALC TKBs and temporal CQs with LTL operators and devised a solution technique to compute (cost-optimal) alignments of TKBs that extends techniques for the alignment problem for propositional LTL over finite traces.

@inproceedings{ FePaPeTU-DL-24,
  address = {Bergen, Norway},
  author = {Oliver {Fern{\'a}ndez Gil} and Fabio {Patrizi} and Giuseppe {Perelli} and Anni-Yasmin {Turhan}},
  booktitle = {Proceedings of the 37th International Workshop on Description Logics (DL'24)},
  editor = {Jean Christoph {Jung} and Laura {Giordano} and Ana {Ozaki}},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {Optimal Alignment of Temporal Knowledge Bases (Extended Abstract)},
  year = {2024},
}

We present an FCA-based axiomatization method that produces a complete \(\mathcal{EL}\) TBox (the terminological part of an OWL 2 EL ontology) from a graph dataset in at most exponential time. We describe technical details that allow for efficient implementation as well as variations that dispense with the computation of extremely large axioms, thereby rendering the approach applicable albeit some completeness is lost. Moreover, we evaluate the prototype on real-world datasets.

@inproceedings{ Kr-AAAI2024,
  author = {Francesco {Kriegel}},
  booktitle = {Proceedings of the 38th Annual AAAI Conference on Artificial Intelligence {(AAAI 2024)}, February 20--27, 2024, Vancouver, Canada},
  doi = {https://doi.org/10.1609/aaai.v38i9.28930},
  pages = {10597--10606},
  title = {Efficient Axiomatization of OWL 2 EL Ontologies from Data by means of Formal Concept Analysis},
  year = {2024},
}

@inproceedings{ Kr-DL2024,
  author = {Francesco {Kriegel}},
  booktitle = {Proceedings of the 37th International Workshop on Description Logics ({DL} 2024), Bergen, Norway, June 18--21, 2024},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {Efficient Axiomatization of OWL 2 EL Ontologies from Data by means of Formal Concept Analysis (Extended Abstract)},
  volume = {3739},
  year = {2024},
}

@article{ LoGeLaHaDeOvBa-TGDK-2024,
  address = {Dagstuhl, Germany},
  author = {Phillip {Lord} and Bj\"{o}rn {Gehrke} and Martin {Larralde} and Janna {Hastings} and Filippo {De Bortoli} and James A. {Overton} and James P. {Balhoff} and Jennifer {Warrender}},
  doi = {https://doi.org/10.4230/TGDK.2.2.9},
  journal = {Transactions on Graph Data and Knowledge},
  number = {2},
  pages = {9:1--9:14},
  publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  title = {{Horned-OWL: Flying Further and Faster with Ontologies}},
  volume = {2},
  year = {2024},
}

Logic-based approaches to AI have the advantage that their behavior can in principle be explained with the help of proofs of the computed consequences. For ontologies based on Description Logic (DL), we have put this advantage into practice by showing how proofs for consequences derived by DL reasoners can be computed and displayed in a user-friendly way. However, these methods are insufficient in applications where also numerical reasoning is relevant. The present paper considers proofs for DLs extended with concrete domains (CDs) based on the rational numbers, which leave reasoning tractable if integrated into the lightweight DL EL_\bot. Since no implemented DL reasoner supports these CDs, we first develop reasoning procedures for them, and show how they can be combined with reasoning approaches for pure DLs, both for EL_\bot and the more expressive DL ALC. These procedures are designed such that it is easy to extract proofs from them. We show how the extracted CD proofs can be combined with proofs on the DL side into integrated proofs that explain both the DL and the CD reasoning.

@inproceedings{ AlBaBoKoKo-RuleML23,
  author = {Christian {Alrabbaa} and Franz {Baader} and Stefan {Borgwardt} and Patrick {Koopmann} and Alisa {Kovtunova}},
  booktitle = {Rules and Reasoning - 7th International Joint Conference, RuleML+RR 2023, Oslo, Norway, September 18-20},
  title = {Combining Proofs for Description Logic and Concrete Domain Reasoning},
  year = {2023},
}

Reasoning in Description Logics (DLs) with numerical concrete domains combines abstract logical with concrete numerical reasoning. We show how consequences computed by such combined reasoning engines can be explained in a uniform way by proofs that integrate the numerical reasoning steps into the proofs on the DL side.

@inproceedings{ AlBaBoKoKo-XLoKR22,
  author = {Christian {Alrabbaa} and Franz {Baader} and Stefan {Borgwardt} and Patrick {Koopmann} and Alisa {Kovtunova}},
  booktitle = {Informal Proceedings of the Explainable Logic-Based Knowledge Representation ({XLoKR} 2023) workshop co-located with the 20th International Conference on Principles of Knowledge Representation and Reasoning ({KR} 2023), Rhodes, Greece, September 2nd},
  title = {Combining Proofs for Description Logic and Concrete Domain Reasoning (Extended Abstract)},
  year = {2023},
}

Understanding logical entailments derived by a description logic reasoner is not always straight-forward for ontology users. For this reason, various methods for explaining entailments using justifications and proofs have been developed and implemented as plug-ins for the ontology editor Protégé. However, when the user expects a missing consequence to hold, it is equally important to explain why it does not follow from the ontology. In this paper, we describe a new version of Evee, a Protégé plugin that now also provides explanations for missing consequences, via existing and new techniques based on abduction and counterexamples.

@inproceedings{ ABFKK-DL23,
  address = {Rhodes, Greece},
  author = {Christian {Alrabbaa} and Stefan {Borgwardt} and Tom {Friese} and Patrick {Koopmann} and Mikhail {Kotlov}},
  booktitle = {Proceedings of the 36th International Workshop on Description Logics (DL'23)},
  editor = {Oliver {Kutz} and Ana {Ozaki}},
  publisher = {CEUR-WS.org},
  title = {Why Not? Explaining Missing Entailments with Evee},
  year = {2023},
}

The question of how a given knowledge base can be modified such that certain unwanted consequences are removed has been investigated in the area of knowledge engineering under the name of repair and in the area of belief change under the name of con- traction. Whereas in the former area the emphasis was more on designing and implementing concrete repair algorithms, the latter area concentrated on characterizing classes of contraction operations by certain postulates they satisfy. In the classical setting, repairs and contractions are subsets of the knowledge base that no longer have the unwanted consequence. This makes these approaches syntax-dependent and may result in removal of more consequences than necessary. To alleviate this problem, gentle repairs and pseudo-constractions have been introduced in the respective research areas, and their connections have been investigated in recent work. Optimal repairs preserve a maximal amount of consequences, but they may not always exist. We show that, if they exist, then they can be obtained by certain pseudo-contraction operations, and thus they comply with the postulates that these operations satisfy. Conversely, under certain conditions, pseudo-contractions are guaranteed to produce optimal repairs.

@inproceedings{ Baader-SAC2023,
  author = {Franz {Baader}},
  booktitle = {Proceedings of the 38th ACM/SIGAPP Symposium on Applied Computing (SAC '23), March 27--31, 2023, Tallinn, Estonia},
  doi = {https://doi.org/10.1145/3555776.3577719},
  pages = {983--990},
  publisher = {Association for Computing Machinery},
  title = {Optimal Repairs in Ontology Engineering as Pseudo-Contractions in Belief Change},
  year = {2023},
}

@inproceedings{ Baader-DL2023,
  author = {Franz {Baader}},
  booktitle = {Proceedings of the 36th International Workshop on Description Logics {(DL} 2023), Rhodes, Greece, September 2--4, 2023},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {Optimal Repairs in Ontology Engineering as Pseudo-Contractions in Belief Change (Extended Abstract)},
  volume = {3515},
  year = {2023},
}

The question of how a given knowledge base can be modified such that certain unwanted consequences are removed has been investigated in the area of ontology engineering under the name of repair and in the area of belief change under the name of contraction. Whereas in the former area the emphasis was more on designing and implementing concrete repair algorithms, the latter area concentrated on characterizing classes of contraction operations by certain postulates they satisfy. In the classical setting, repairs and contractions are subsets of the knowledge base that no longer have the unwanted consequence. This makes these approaches syntax-dependent and may result in removal of more consequences than necessary. To alleviate this problem, gentle repairs and pseudo-constractions have been introduced in the respective research areas, and their connections have been investigated in recent work. Optimal repairs preserve a maximal amount of consequences, but they may not always exist. We show that, if they exist, then they can be obtained by certain pseudo-contraction operations, and thus they comply with the postulates that these operations satisfy. Conversely, under certain conditions, pseudo-contractions are guaranteed to produce optimal repairs. Recently, contraction operations have also been defined for concepts rather than for whole knowledge bases. We show that there is again a close connection between such operations and optimal repairs of a restricted form of knowledge bases.

@article{ BaaderACR23,
  author = {Franz {Baader}},
  doi = {https://doi.org/10.1145/3626307.3626308},
  journal = {ACM SIGAPP Applied Computing Review},
  number = {3},
  pages = {5--18},
  publisher = {ACM},
  title = {Relating Optimal Repairs in Ontology Engineering with Contraction Operations in Belief Change},
  volume = {23},
  year = {2023},
}

Concrete domains have been introduced in Description Logic (DL) to enable reference to concrete objects (such as numbers) and predefined predicates on these objects (such as numerical comparisons) when defining concepts. The primary research goal in this context was to find restrictions on the concrete domain such that its integration into certain DLs preserves decidability or tractability. In this paper, we investigate the abstract expressive power of logics extended with concrete domains, namely which classes of first-order interpretations can be expressed using these logics. In the first part of the paper, we show that, under natural conditions on the concrete domain \(\mathfrak{D}\) (which also play a role for decidability), extensions of first-order logic (\(\texttt{FOL}\)) or \(\mathcal{ALC}\) with \(\mathfrak{D}\) share important formal properties with \(\texttt{FOL}\), such as the compactness and the Löwenheim-Skolem property. Nevertheless, their abstract expressive power need not be contained in that of \(\texttt{FOL}\). In the second part of the paper, we investigate whether finitely bounded homogeneous structures, which preserve decidability if employed as concrete domains, can be used to express certain universal first-order sentences, which then could be added to DL knowledge bases without destroying decidability. We show that this requires rather strong conditions on said sentences or an extended scheme for integrating the concrete domain that leads to undecidability.

@inproceedings{ BaBo-DL-23,
  address = {Rhodes, Greece},
  author = {Franz {Baader} and Filippo {De Bortoli}},
  booktitle = {Proceedings of the 36th International Workshop on Description Logics (DL'23)},
  editor = {Oliver {Kutz} and Ana {Ozaki}},
  publisher = {CEUR-WS},
  series = {CEUR Workshop Proceedings},
  title = {{On the Abstract Expressive Power of Description Logics with Concrete Domains}},
  volume = {3515},
  year = {2023},
}

Ontologies based on Description Logics may contain errors, which are usually detected when reasoning produces consequences that follow from the ontology, but do not hold in the modelled application domain. In previous work, we have introduced repair approaches for \(\mathcal{EL}\) ontologies that are optimal in the sense that they preserve a maximal amount of consequences. In this paper, we will, on the one hand, review these approaches, but with an emphasis on motivation rather than on technical details. On the other hand, we will describe new results that address the problems that optimal repairs may become very large or need not even exist unless strong restrictions on the terminological part of the ontology apply. We will show how one can deal with these problems by introducing concise representations of optimal repairs.

@inproceedings{ BaKoKr-JELIA2023,
  author = {Franz {Baader} and Patrick {Koopmann} and Francesco {Kriegel}},
  booktitle = {Proceedings of the 18th European Conference on Logics in Artificial Intelligence {(JELIA 2023)}, September 20--22, 2023, Dresden, Germany},
  doi = {https://doi.org/10.1007/978-3-031-43619-2_2},
  pages = {11--34},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Optimal Repairs in the Description Logic $\mathcal{EL}$ Revisited},
  volume = {14281},
  year = {2023},
}

@inproceedings{ BaKrNu-DL2023,
  author = {Franz {Baader} and Francesco {Kriegel} and Adrian {Nuradiansyah}},
  booktitle = {Proceedings of the 36th International Workshop on Description Logics ({DL} 2023), Rhodes, Greece, September 2--4, 2023},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {Error-Tolerant Reasoning in $\mathcal{EL}$ w.r.t.\ Optimal {ABox} Repairs (Extended Abstract)},
  volume = {3515},
  year = {2023},
}

Errors in Description Logic (DL) ontologies are often detected when reasoning yields unintuitive consequences. The question is then how to repair the ontology in an optimal way, i.e., such that the unwanted consequences are removed, but a maximal set of the unobjected consequences is kept. Error-tolerant reasoning does not commit to a single optimal repair: brave reasoning asks whether the consequence is entailed by some repair and cautious reasoning whether it is entailed by all repairs. Previous research on repairing ABoxes w.r.t. TBoxes formulated in the DL \(\mathcal{EL}\) has developed methods for computing optimal repairs, and has recently also determined the complexity of error-tolerant reasoning: brave reasoning is in P and cautious reasoning is in coNP. However, in this work the unwanted consequences were restricted to being \(\mathcal{EL}\) instance assertions. In the present paper, we show that the mentioned results can be extended to a setting where also role assertions can be required to be removed. Our solution is based on a two-stage approach where first the unwanted role assertions and then the unwanted concept assertions are removed. We also investigate the complexity of error-tolerant reasoning w.r.t. classical repairs, which are maximal subsets of the ABox that do not have the unwanted consequences, and show that, in this setting, brave reasoning is NP-complete and cautious reasoning is coNP-complete.

@inproceedings{ BaKrNu-SAC2023,
  author = {Franz {Baader} and Francesco {Kriegel} and Adrian {Nuradiansyah}},
  booktitle = {Proceedings of the 38th ACM/SIGAPP Symposium on Applied Computing (SAC '23), March 27--31, 2023, Tallinn, Estonia},
  doi = {https://doi.org/10.1145/3555776.3577630},
  pages = {974--982},
  publisher = {Association for Computing Machinery},
  title = {Treating Role Assertions as First-class Citizens in Repair and Error-tolerant Reasoning},
  year = {2023},
}

@inproceedings{ CaTu-JELIA-2023,
  author = {Igor de Camargo e Souza {C{\^{a}}mara} and Anni{-}Yasmin {Turhan}},
  booktitle = {Logics in Artificial Intelligence - 18th European Conference, {JELIA} 2023, Dresden, Germany, September 20-22, 2023, Proceedings},
  doi = {https://doi.org/10.1007/978-3-031-43619-2_36},
  editor = {Sarah Alice {Gaggl} and Maria Vanina {Martinez} and Magdalena {Ortiz}},
  pages = {531--546},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Deciding Subsumption in Defeasible $\mathcal{ELI}_\bot$ with Typicality Models},
  volume = {14281},
  year = {2023},
}

We introduce an extension of the Description Logic FL0 that allows us to define concepts in an approximate way. More precisely, we extend FL0 with a threshold concept constructor of the form C@t for @ in <,<=,>,>=, whose semantics is given by using a membership distance function (mdf). A membership distance function m assigns to each domain element and concept a distance value expressing how ``close'' is such element to being an instance of the concept. Based on this, a threshold concept C@t is interpreted as the set of all domain elements that have a distance s from C such that s @ t. We provide a framework to obtain membership distance functions based on functions that compare tuples of languages, and we show how weighted looping tree automata over a semiring can be used to define membership distance functions for FL0 concepts.

@inproceedings{ FeMa-DL-23,
  address = {Rhodes, Greece},
  author = {Oliver {Fern{\'a}ndez Gil} and Pavlos {Marantidis}},
  booktitle = {Proceedings of the 36th International Workshop on Description Logics (DL'23)},
  editor = {Oliver {Kutz} and Carsten {Lutz} and Ana {Ozaki}},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {Towards Extending the Description Logic FL0 with Threshold Concepts Using Weighted Tree Automata},
  volume = {3515},
  year = {2023},
}

Answering temporal CQs over temporalized Description Logic knowledge bases (TKB) is a main technique to realize ontology-based situation recognition. In case the collected data in such a knowledge base is inaccurate, important query answers can be missed. In this paper we introduce the TKB Alignment problem, which computes a variant of the TKB that minimally changes the TKB, but entails the given temporal CQ and is in that sense (cost-) optimal. We investigate this problem for ALC TKBs and conjunctive queries with LTL operators and devise a solution technique to compute (cost-optimal) alignments of TKBs that extends techniques for the alignment problem for propositional LTL over finite traces.

@inproceedings{ FeFpGpAt-ECAI-23,
  author = {Oliver {Fern{\'a}ndez Gil} and Fabio {Patrizi} and Giuseppe {Perelli} and Anni-Yasmin {Turhan}},
  booktitle = {Proceedings of the 26th European Conference on Artificial Intelligence (ECAI'23)},
  pages = {708--715},
  publisher = {{IOS} Press},
  series = {Frontiers in Artificial Intelligence and Applications},
  title = {Optimal Alignment of Temporal Knowledge Bases},
  volume = {372},
  year = {2023},
}

@inproceedings{ Kr-KR2023RPR,
  author = {Francesco {Kriegel}},
  booktitle = {Recently Published Research {(RPR)} track of the 20th International Conference on Principles of Knowledge Representation and Reasoning {(KR 2023)}, September 2--8, 2023, Rhodes, Greece},
  doi = {https://doi.org/10.5281/zenodo.8341194},
  title = {Optimal Fixed-Premise Repairs of $\mathcal{EL}$ {TBoxes} (Extended Abstract)},
  year = {2023},
}

OWL is a powerful language to formalize terminologies in an ontology. Its main strength lies in its foundation on description logics, allowing systems to automatically deduce implicit information through logical reasoning. However, since ontologies are often complex, understanding the outcome of the reasoning process is not always straightforward. Unlike already existing tools for exploring ontologies, our visualization tool Evonne is tailored towards explaining logical consequences. In addition, it supports the debugging of unwanted consequences and allows for an interactive comparison of the impact of removing statements from the ontology. Our visual approach combines (1) specialized views for the explanation of logical consequences and the structure of the ontology, (2) employing multiple layout modes for iteratively exploring explanations, (3) detailed explanations of specific reasoning steps, (4) cross-view highlighting and colour coding of the visualization components, (5) features for dealing with visual complexity and (6) comparison and exploration of possible fixes to the ontology. We evaluated Evonne in a qualitative study with 16 experts in logics, and their positive feedback confirms the value of our concepts for explaining reasoning and debugging ontologies.

@article{ MEALKOLABADA-CGF23,
  author = {Juli{\'a}n {M{\'e}ndez} and Christian {Alrabbaa} and Patrick {Koopmann} and Ricardo {Langner} and Franz {Baader} and Raimund {Dachselt}},
  doi = {https://doi.org/10.1111/cgf.14730},
  journal = {Computer Graphics Forum},
  number = {6},
  pages = {e14730},
  title = {Evonne: A Visual Tool for Explaining Reasoning with {OWL} Ontologies and Supporting Interactive Debugging},
  volume = {42},
  year = {2023},
}

@inproceedings{ Tu-DL-2023,
  author = {Anni{-}Yasmin {Turhan}},
  booktitle = {Proceedings of the 36th International Workshop on Description Logics {(DL} 2023) co-located with the 20th International Conference on Principles of Knowledge Representation and Reasoning and the 21st International Workshop on Non-Monotonic Reasoning {(KR} 2023 and {NMR} 2023)., Rhodes, Greece, September 2-4, 2023},
  editor = {Oliver {Kutz} and Carsten {Lutz} and Ana {Ozaki}},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {Brushing-up DLs to Cope with Imperfect Data (Abstract of Joint {DL+NMR} Invited Talk)},
  volume = {3515},
  year = {2023},
}

Explanations for description logic (DL) entailments provide important support for the maintenance of large ontologies. The ``justifications'' usually employed for this purpose in ontology editors pinpoint the parts of the ontology responsible for a given entailment. Proofs for entailments make the intermediate reasoning steps explicit, and thus explain how a consequence can actually be derived. We present an interactive system for exploring description logic proofs, called Evonne, which visualizes proofs of consequences for ontologies written in expressive DLs. We describe the methods used for computing those proofs, together with a feature called signature-based proof condensation. Moreover, we evaluate the quality of generated proofs using real ontologies.

@inproceedings{ ALBABODAKOME-IJCAR22,
  author = {Christian {Alrabbaa} and Franz {Baader} and Stefan {Borgwardt} and Raimund {Dachselt} and Patrick {Koopmann} and Juli\'an {M\'endez}},
  booktitle = {Automated Reasoning - 11th International Joint Conference, {IJCAR} 2022},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {\textsc{Evonne}: Interactive Proof Visualization for Description Logics (System Description)},
  year = {2022},
}

@inproceedings{ ALBOFRKOMEPO-XLoKR22,
  author = {Christian {Alrabbaa} and Stefan {Borgwardt} and Tom {Friese} and Patrick {Koopmann} and Juli\'an {M\'endez} and Alexej {Popovi\v{c}}},
  booktitle = {Informal Proceedings of the Explainable Logic-Based Knowledge Representation (XLoKR 2022) workshop co-located with the 19th International Conference on Principles of Knowledge Representation and Reasoning {(KR} 2022), Haifa, Israel, July 31st},
  title = {Explaining Description Logic Entailments with \textsc{Evee} and \textsc{Evonne}},
  year = {2022},
}

When working with description logic ontologies, understanding entailments derived by a description logic reasoner is not always straightforward. So far, the standard ontology editor offers two services to help: (black-box) justifications for OWL 2 DL ontologies, and (glass-box) proofs for lightweight OWL EL ontologies, where the latter exploits the proof facilities of reasoner Elk. Since justifications are often insufficient in explaining inferences, there is thus only little tool support for explaining inferences in more expressive DLs. In this paper, we introduce Evee-libs, a Java library for computing proofs for DLs up to ALCH, and Evee-protege, a collection of Protégé plugins for displaying those proofs in Protégé. We also give a short glimpse of the latest version of Evonne, a more advanced standalone application for displaying and interacting with proofs computed with Evee-libs.

@inproceedings{ ALBOFRKOMEPO-DL22,
  author = {Christian {Alrabbaa} and Stefan {Borgwardt} and Tom {Friese} and Patrick {Koopmann} and Juli\'an {M\'endez} and Alexej {Popovi\v{c}}},
  booktitle = {Proceedings of the 35th International Workshop on Description Logics {(DL} 2022)},
  publisher = {CEUR-WS.org},
  title = {On the Eve of True Explainability for OWL Ontologies: Description Logic Proofs with \textsc{Evee} and \textsc{Evonne}},
  year = {2022},
}

Ontologies provide the logical underpinning for the Semantic Web, but their consequences can sometimes be surprising and must be explained to users. A promising kind of explanations are proofs generated via automated reasoning. We report about a series of studies with the purpose of exploring how to explain such formal logical proofs to humans. We compare different representations, such as tree- vs. text-based visualizations, but also vary other parameters such as length, interactivity, and the shape of formulas. We did not find evidence to support our main hypothesis that different user groups can understand different proof representations better. Nevertheless, when participants directly compared proof representations, their subjective rankings showed some tendencies such as that most people prefer short tree-shaped proofs. However, this did not impact the user's understanding of the proofs as measured by an objective performance measure.

@inproceedings{ AlBoHiKnKoRoWi-RuleML22,
  author = {Christian {Alrabbaa} and Stefan {Borgwardt} and Anke {Hirsch} and Nina {Knieriemen} and Alisa {Kovtunova} and Anna Milena {Rothermel} and Frederik {Wiehr}},
  booktitle = {Rules and Reasoning - 6th International Joint Conference, RuleML+RR 2022, Virtual, September 26-28, 2022, Proceedings},
  title = {In the Head of the Beholder:\texorpdfstring{\\}{} Comparing Different Proof Representations},
  year = {2022},
}

In ontology-mediated query answering, access to incomplete data sources is mediated by a conceptual layer constituted by an ontology, which can be formulated in a description logic (DL) or using existential rules. Computing the answers to queries requires complex reasoning over the constraints expressed by the ontology. In the literature, there exists a multitude of complex techniques for incorporating ontological knowledge into queries. However, few of these approaches were designed for explainability of the query answers. We tackle this challenge by adapting an existing proof framework toward conjunctive query answering, based on the notion of universal models. We investigate the data and combined complexity of determining the existence of a proof below a given quality threshold, which can be measured in different ways. By distinguishing various parameters such as the shape of the query, we obtain an overview of the complexity of this problem for several Horn DLs.

@inproceedings{ AlBoKoKo-RuleML2022,
  author = {Christian {Alrabbaa} and Stefan {Borgwardt} and Patrick {Koopmann} and Alisa {Kovtunova}},
  booktitle = {Rules and Reasoning - 6th International Joint Conference, RuleML+RR 2022, Virtual, September 26-28, 2022, Proceedings},
  doi = {https://doi.org/10.1007/978-3-031-21541-4_11},
  title = {Explaining Ontology-Mediated Query Answers using Proofs over Universal Models},
  year = {2022},
}

@inproceedings{ AlBoKoKo-DL22,
  author = {Christian {Alrabbaa} and Stefan {Borgwardt} and Patrick {Koopmann} and Alisa {Kovtunova}},
  booktitle = {Proceedings of the 35th International Workshop on Description Logics {(DL} 2022)},
  publisher = {CEUR-WS.org},
  title = {Finding Good Proofs for Answers to Conjunctive Queries Mediated by Lightweight Ontologies},
  year = {2022},
}

@inproceedings{ AlBoKoKo-XLoKR22,
  author = {Christian {Alrabbaa} and Stefan {Borgwardt} and Patrick {Koopmann} and Alisa {Kovtunova}},
  booktitle = {Informal Proceedings of the Explainable Logic-Based Knowledge Representation (XLoKR 2022) workshop co-located with the 19th International Conference on Principles of Knowledge Representation and Reasoning {(KR} 2022), Haifa, Israel, July 31st},
  publisher = {CEUR-WS.org},
  title = {Finding Good Proofs for Answers to Conjunctive Queries Mediated by Lightweight Ontologies (Extended Abstract)},
  year = {2022},
}

Reasoning results computed by description logic systems can be hard to comprehend. When an ontology does not entail an expected subsumption relationship, generating an explanation of this non-entailment becomes necessary. In this paper, we use countermodels to explain non-entailments. More precisely, we devise relevant parts of canonical models of EL ontologies that serve as explanations and discuss the computational complexity of extracting these parts by means of model transformations. Furthermore, we provide an implementation of these transformations and evaluate it using real ontologies.

@inproceedings{ ALHI-IJCKG22,
  author = {Christian {Alrabbaa} and Willi {Hieke}},
  booktitle = {IJCKG'22: The 11th International Joint Conference on Knowledge Graphs, Virtual Event, Hangzhou, China, October 27 - 29, 2022},
  doi = {https://doi.org/10.1145/3579051.3579060},
  publisher = {{ACM}},
  title = {Explaining Non-Entailment by Model Transformation for the Description Logic {$\mathcal{EL}$}},
  year = {2022},
}

Aiming at ontology-based data access to temporal data, we design two-dimensional temporal ontology and query languages by combining logics from the (extended) DL-Lite family with linear temporal logic LTL over discrete time (Z,<). Our main concern is first-order rewritability of ontology-mediated queries (OMQs) that consist of a 2D ontology and a positive temporal instance query. Our target languages for FO-rewritings are two-sorted FO(<)—first-order logic with sorts for time instants ordered by the built-in precedence relation < and for the domain of individuals—its extension FO(<,≡) with the standard congruence predicates t ≡ 0 (mod n), for any fixed n > 1, and FO(RPR) that admits relational primitive recursion. In terms of circuit complexity, FO(<,≡)- and FO(RPR)-rewritability guarantee answering OMQs in uniform AC0 and NC1, respectively. We proceed in three steps. First, we define a hierarchy of 2D DL-Lite/LTL ontology languages and investigate the FO-rewritability of OMQs with atomic queries by constructing projections onto 1D LTL OMQs and employing recent results on the FO-rewritability of propositional LTL OMQs. As the projections involve deciding consistency of ontologies and data, we also consider the consistency problem for our languages. While the undecidability of consistency for 2D ontology languages with expressive Boolean role inclusions might be expected, we also show that, rather surprisingly, the restriction to Krom and Horn role inclusions leads to decidability (and ExpSpace-completeness), even if one admits full Booleans on concepts. As a final step, we lift some of the rewritability results for atomic OMQs to OMQs with expressive positive temporal instance queries. The lifting results are based on an in-depth study of the canonical models and only concern Horn ontologies.

@article{ jairArtaleKKRWZ22,
  author = {Alessandro {Artale} and Roman {Kontchakov} and Alisa {Kovtunova} and Vladislav {Ryzhikov} and Frank {Wolter} and Michael {Zakharyaschev}},
  doi = {https://doi.org/10.1613/JAIR.1.13511},
  journal = {J. Artif. Intell. Res.},
  pages = {1223--1291},
  title = {First-Order Rewritability and Complexity of Two-Dimensional Temporal Ontology-Mediated Queries},
  volume = {75},
  year = {2022},
}

In a previous paper, we have investigated restricted unification in the Description Logic (DL) \(\mathcal{FL}_0\). Here we extend this investigation to the DL \(\mathcal{FL}_\bot\), which is obtained from \(\mathcal{FL}_0\) by adding the bottom concept. We show that restricted unification in \(\mathcal{FL}_\bot\) is decidable and provide some upper and lower bounds for the complexity. This is particularly interesting since the decidability status of unrestricted unification in \(\mathcal{FL}_\bot\) appears to be still open. We also show an ExpTime lower bound for the unrestricted problem.

@inproceedings{ BaFe-UNIF-22,
  address = {Haifa, Israel},
  author = {Franz {Baader} and Oliver {Fern{\'a}ndez Gil}},
  booktitle = {Proceedings of the 36th International Workshop on Unification ({UNIF 2022})},
  editor = {David {M. Cerna} and Barbara {Morawska}},
  title = {Restricted Unification in the Description Logic {$\mathcal{FL}_{\bot}$}},
  year = {2022},
}

The word problem for a finite set of ground identities is known to be decidable in polynomial time using congruence closure, and this is also the case if some of the function symbols are assumed to be commutative or defined by certain shallow identities, called strongly shallow. We show that decidability in P is preserved if we add the assumption that certain function symbols f are extensional in the sense that f(s1,...,sn) ≈ f(t1,...,tn) implies s1 ≈ t1, ...,sn ≈ tn. In addition, we investigate a variant of extensionality that is more appropriate for commutative function symbols, but which raises the complexity of the word problem to coNP.

@article{ BaaderKapurJAR22,
  address = {Cham},
  author = {Franz {Baader} and Deepak {Kapur}},
  doi = {https://doi.org/10.1007/s10817-022-09624-4},
  journal = {Journal of Automated Reasoning},
  number = {3},
  pages = {301--329},
  publisher = {Springer International Publishing},
  title = {Deciding the Word Problem for Ground and Strongly Shallow Identities w.r.t.\ Extensional Symbols},
  volume = {66},
  year = {2022},
}

Errors in Description Logic (DL) ontologies are often detected when a reasoner computes unwanted consequences. The question is then how to repair the ontology such that the unwanted consequences no longer follow, but as many of the other consequences as possible are preserved. The problem of computing such optimal repairs was addressed in our previous work in the setting where the data (expressed by an ABox) may contain errors, but the schema (expressed by an \(\mathcal{EL}\) TBox) is assumed to be correct. Actually, we consider a generalization of ABoxes called quantified ABoxes (qABoxes) both as input for and as result of the repair process. Using qABoxes for repair allows us to retain more information, but the disadvantage is that standard DL systems do not accept qABoxes as input. This raises the question, investigated in the present paper, whether and how one can obtain optimal repairs if one restricts the output of the repair process to being ABoxes. In general, such optimal ABox repairs need not exist. Our main contribution is that we show how to decide the existence of optimal ABox repairs in exponential time, and how to compute all such repairs in case they exist.

@inproceedings{ BaKoKrNu-ESWC2022,
  author = {Franz {Baader} and Patrick {Koopmann} and Francesco {Kriegel} and Adrian {Nuradiansyah}},
  booktitle = {19th Extended Semantic Web Conference, {ESWC} 2022, Hersonissos, Greece, May 29 -- June 2, 2022, Proceedings},
  doi = {https://doi.org/10.1007/978-3-031-06981-9_8},
  pages = {130--146},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Optimal ABox Repair w.r.t.\ Static {$\mathcal{EL}$} TBoxes: from Quantified ABoxes back to ABoxes},
  volume = {13261},
  year = {2022},
}

@inproceedings{ BaKoKrNu-DL2022,
  author = {Franz {Baader} and Patrick {Koopmann} and Francesco {Kriegel} and Adrian {Nuradiansyah}},
  booktitle = {Proceedings of the 35th International Workshop on Description Logics ({DL} 2022), Haifa, Israel, August 7--10, 2022},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {Optimal {ABox} Repair w.r.t. Static $\mathcal{EL}$ {TBoxes:} from Quantified {ABoxes} back to {ABoxes} (Extended Abstract)},
  year = {2022},
}

@inproceedings{ BaKoMiTuZa-DL-2022,
  author = {Franz {Baader} and Patrick {Koopmann} and Friedrich {Michel} and Anni{-}Yasmin {Turhan} and Benjamin {Zarrie{\ss}}},
  booktitle = {Proceedings of the 35th International Workshop on Description Logics {(DL} 2022) co-located with Federated Logic Conference (FLoC 2022), Haifa, Israel, August 7th to 10th, 2022},
  editor = {Ofer {Arieli} and Martin {Homola} and Jean Christoph {Jung} and Marie{-}Laure {Mugnier}},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {Efficient TBox Reasoning with Value Restrictions Using the FL0wer Reasoner (Extended Abstract)},
  volume = {3263},
  year = {2022},
}

The inexpressive Description Logic (DL) \(\mathcal{FL}_0\), which has conjunction and value restriction as its only concept constructors, had fallen into disrepute when it turned out that reasoning in \(\mathcal{FL}_0\) w.r.t. general TBoxes is ExpTime-complete, i.e., as hard as in the considerably more expressive logic \(\mathcal{ALC}\). In this paper, we rehabilitate \(\mathcal{FL}_0\) by presenting a dedicated subsumption algorithm for \(\mathcal{FL}_0\), which is much simpler than the tableau-based algorithms employed by highly optimized DL reasoners. Our experiments show that the performance of our novel algorithm, as prototypically implemented in our \(\mathcal{FL}_{o}\textit{wer}\) reasoner, compares very well with that of the highly optimized reasoners. \(\mathcal{FL}_{o}\textit{wer}\) can also deal with ontologies written in the extension \(\mathcal{FL}_\bot\) of \(\mathcal{FL}_0\) with the top and the bottom concept by employing a polynomial-time reduction, shown in this paper, which eliminates top and bottom. We also investigate the complexity of reasoning in DLs related to the Horn-fragments of \(\mathcal{FL}_0\) and \(\mathcal{FL}_\bot\).

@article{ BaKoMiTuZa-TPLP-22,
  author = {Franz {Baader} and Patrick {Koopmann} and Friedrich {Michel} and Anni-Yasmin {Turhan} and Benjamin {Zarrie{\ss}}},
  doi = {https://doi.org/10.1017/S1471068421000466},
  journal = {Theory and Practice of Logic Programming},
  number = {2},
  pages = {162--192},
  publisher = {Cambridge University Press},
  title = {Efficient {TBox} Reasoning with Value Restrictions using the $\mathcal{FL}_{o}\textit{wer}$ reasoner},
  volume = {22},
  year = {2022},
}

Ontologies based on Description Logic (DL) represent general background knowledge in a terminology (TBox) and the actual data in an ABox. DL systems can then be used to compute consequences (such as answers to certain queries) from an ontology consisting of a TBox and an ABox. Since both human-made and machine-learned data sets may contain errors, which manifest themselves as unintuitive or obviously incorrect consequences, repairing DL-based ontologies in the sense of removing such unwanted consequences is an important topic in DL research. Most of the repair approaches described in the literature produce repairs that are not optimal, in the sense that they do not guarantee that only a minimal set of consequences is removed. In a series of papers, we have developed an approach for computing optimal repairs, starting with the restricted setting of an \(\mathcal{EL}\) instance store, extending this to the more general setting of a quantified ABox (where some individuals may be anonymous), and then adding a static \(\mathcal{EL}\) TBox.

Here, we extend the expressivity of the underlying DL considerably, by adding nominals, inverse roles, regular role inclusions and the bottom concept to \(\mathcal{EL}\), which yields a fragment of the well-known DL Horn-\(\mathcal{SROIQ}\). The ideas underlying our repair approach still apply to this DL, though several non-trivial extensions are needed to deal with the new constructors and axioms. The developed repair approach can also be used to treat unwanted consequences expressed by certain conjunctive queries or regular path queries, and to handle Horn-\(\mathcal{ALCOI}\) TBoxes with regular role inclusions.

@inproceedings{ BaKr-KR2022,
  author = {Franz {Baader} and Francesco {Kriegel}},
  booktitle = {Proceedings of the 19th International Conference on Principles of Knowledge Representation and Reasoning, {KR} 2022, Haifa, Israel, July 31 -- August 5, 2022},
  doi = {https://doi.org/10.24963/kr.2022/3},
  editor = {Gabriele {Kern{-}Isberner} and Gerhard {Lakemeyer} and Thomas {Meyer}},
  pages = {22--32},
  title = {Pushing Optimal ABox Repair from {$\mathcal{EL}$} Towards More Expressive Horn-DLs},
  year = {2022},
}

Ontologies based on Description Logic (DL) represent general background knowledge in a terminology (TBox) and the actual data in an ABox. Both human-made and machine-learned data sets may contain errors, which are usually detected when the DL reasoner returns unintuitive or obviously incorrect answers to queries. To eliminate such errors, classical repair approaches offer as repairs maximal subsets of the ABox not having the unwanted answers w.r.t. the TBox. It is, however, not always clear which of these classical repairs to use as the new, corrected data set. Error-tolerant semantics instead takes all repairs into account: cautious reasoning returns the answers that follow from all classical repairs whereas brave reasoning returns the answers that follow from some classical repair. It is inspired by inconsistency-tolerant reasoning and has been investigated for the DL \(\mathcal{EL}\), but in a setting where the TBox rather than the ABox is repaired. In a series of papers, we have developed a repair approach for ABoxes that improves on classical repairs in that it preserves a maximal set of consequences (i.e., answers to queries) rather than a maximal set of ABox assertions. The repairs obtained by this approach are called optimal repairs. In the present paper, we investigate error-tolerant reasoning in the DL \(\mathcal{EL}\), but we repair the ABox and use optimal repairs rather than classical repairs as the underlying set of repairs. To be more precise, we consider a static \(\mathcal{EL}\) TBox (which is assumed to be correct), represent the data by a quantified ABox (where some individuals may be anonymous), and use \(\mathcal{EL}\) concepts as queries (instance queries). We show that brave entailment of instance queries can be decided in polynomial time. Cautious entailment can be decided by a coNP procedure, but is still in P if the TBox is empty.

@inproceedings{ BaKrNu-RuleML2022,
  author = {Franz {Baader} and Francesco {Kriegel} and Adrian {Nuradiansyah}},
  booktitle = {Rules and Reasoning - 6th International Joint Conference, RuleML+RR 2022, Virtual, September 26-28, 2022, Proceedings},
  doi = {https://doi.org/10.1007/978-3-031-21541-4_15},
  editor = {Guido {Governatori} and Anni{-}Yasmin {Turhan}},
  pages = {227--243},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Error-Tolerant Reasoning in the Description Logic {$\mathcal{EL}$} Based On Optimal Repairs},
  volume = {13752},
  year = {2022},
}

Concrete domains have been introduced in the area of Description Logic to enable reference to concrete objects (such as numbers) and predefined predicates on these objects (such as numerical comparisons) when defining concepts. Unfortunately, in the presence of general concept inclusions (GCIs), which are supported by all modern DL systems, adding concrete domains may easily lead to undecidability. To regain decidability of the DL ALC in the presence of GCIs, quite strong restrictions, in sum called omega-admissibility, were imposed on the concrete domain. On the one hand, we generalize the notion of omega-admissibility from concrete domains with only binary predicates to concrete domains with predicates of arbitrary arity. On the other hand, we relate omega-admissibility to well-known notions from model theory. In particular, we show that finitely bounded homogeneous structures yield omega-admissible concrete domains. This allows us to show omega-admissibility of concrete domains using existing results from model theory. When integrating concrete domains into lightweight DLs of the EL family, achieving decidability is not enough. One wants reasoning in the resulting DL to be tractable. This can be achieved by using so-called p-admissible concrete domains and restricting the interaction between the DL and the concrete domain. We investigate p-admissibility from an algebraic point of view. Again, this yields strong algebraic tools for demonstrating p-admissibility. In particular, we obtain an expressive numerical p-admissible concrete domain based on the rational numbers. Although omega-admissibility and p-admissibility are orthogonal conditions that are almost exclusive, our algebraic characterizations of these two properties allow us to locate an infinite class of p-admissible concrete domains whose integration into ALC yields decidable DLs

@article{ BaaderRydvalJAR22,
  address = {Cham},
  author = {Franz {Baader} and Jakub {Rydval}},
  doi = {https://doi.org/10.1007/s10817-022-09626-2},
  journal = {Journal of Automated Reasoning},
  number = {3},
  pages = {357--407},
  publisher = {Springer International Publishing},
  title = {Using Model Theory to Find Decidable and Tractable Description Logics with Concrete Domains},
  volume = {66},
  year = {2022},
}

The constraint satisfaction problem (CSP) of a first-order theory \(T\) is the computational problem of deciding whether a given conjunction of atomic formulas is satisfiable in some model of \(T\). We study the computational complexity of \(\text{CSP}(T_1\cup T_2)\) where \(T_1\) and \(T_2\) are theories with disjoint finite relational signatures. We prove that if \(T_1\) and \(T_2\) are the theories of temporal structures, i.e., structures where all relations have a first-order definition in \((Q;<)\), then \(\text{CSP}(T_1\cup T_2)\) is in P or NP-complete. To this end we prove a purely algebraic statement about the structure of the lattice of locally closed clones over the domain \(Q\) that contain \(\text{Aut}(Q;<)\).

@article{ lmcsBodirskyGR22,
  author = {Manuel {Bodirsky} and Johannes {Greiner} and Jakub {Rydval}},
  doi = {https://doi.org/10.46298/LMCS-18(2:11)2022},
  journal = {Log. Methods Comput. Sci.},
  number = {2},
  title = {Tractable Combinations of Temporal CSPs},
  volume = {18},
  year = {2022},
}

State constraints in AI Planning globally restrict the legal environment states. Standard planning languages make closed-domain and closed-world assumptions. Here we address open-world state constraints formalized by planning over a description logic (DL) ontology. Previously, this combination of DL and planning has been investigated for the light-weight DL DL-Lite. Here we propose a novel compilation scheme into standard PDDL with derived predicates, which applies to more expressive DLs and is based on the rewritability of DL queries into Datalog with stratified negation. We also provide a new rewritability result for the DL Horn-ALCHOIQ, which allows us to apply our compilation scheme to quite expressive ontologies. In contrast, we show that in the slight extension Horn-SROIQ no such compilation is possible unless the weak exponential hierarchy collapses. Finally, we show that our approach can outperform previous work on existing benchmarks for planning with DL ontologies, and is feasible on new benchmarks taking advantage of more expressive ontologies.

@inproceedings{ BHKKNS-AAAI-22,
  author = {Stefan {Borgwardt} and J{\"o}rg {Hoffmann} and Alisa {Kovtunova} and Markus {Kr{\"o}tzsch} and Bernhard {Nebel} and Marcel {Steinmetz}},
  booktitle = {Proceedings of the AAAI Conference on Artificial Intelligence},
  doi = {https://doi.org/10.1609/aaai.v36i5.20489},
  month = {Jun.},
  pages = {5503--5511},
  title = {Expressivity of Planning with Horn Description Logic Ontologies},
  volume = {36},
  year = {2022},
}

@inproceedings{ BoHoKoKrNeSt-DL22,
  author = {Stefan {Borgwardt} and J\"org {Hoffmann} and Alisa {Kovtunova} and Markus {Kr\"otzsch} and Bernhard {Nebel} and Marcel {Steinmetz}},
  booktitle = {Proceedings of the 35th International Workshop on Description Logics {(DL} 2022)},
  note = {(to appear)},
  publisher = {CEUR-WS.org},
  title = {Expressivity of Planning with Horn Description Logic Ontologies (Extended Abstract)},
  year = {2022},
}

Natural language generation in real-time settings with raw sensor data is a challenging task. We find that formulating the task as an end-to-end problem leads to two major challenges in content selection – the sensor data is both redundant and diverse across environments, thereby making it hard for the encoders to select and reason on the data. We here present a new corpus for a specific domain that instantiates these properties. It includes handover utterances that an assistant for a semi-autonomous drone uses to communicate with humans during the drone flight. The corpus consists of sensor data records and utterances in 8 different environments. As a structured intermediary representation between data records and text, we explore the use of description logic (DL). We also propose a neural generation model that can alert the human pilot of the system state and environment in preparation of the handover of control.

@inproceedings{ ChangLREC2022,
  address = {Marseille, France},
  author = {Ernie {Chang} and Alisa {Kovtunova} and Stefan {Borgwardt} and Vera {Demberg} and Kathryn {Chapman} and Hui{-}Syuan {Yeh}},
  booktitle = {Proceedings of the 13th Language Resources and Evaluation Conference (LREC'22)},
  pages = {6899--6908},
  publisher = {European Language Resources Association},
  title = {Logic-Guided Message Generation from Raw Real-Time Sensor Data},
  year = {2022},
}

Abduction in description logics finds extensions of a knowledge base to make it entail an observation. As such, it can be used to explain why the observation does not follow, to repair incomplete knowledge bases, and to provide possible explanations for unexpected observations. We consider TBox abduction in the lightweight description logic \(\mathcal{EL}\), where the observation is a concept inclusion and the background knowledge is a TBox, i.e., a set of concept inclusions. To avoid useless answers, such problems usually come with further restrictions on the solution space and/or minimality criteria that help sort the chaff from the grain. We argue that existing minimality notions are insufficient, and introduce connection minimality. This criterion follows Occam's razor by rejecting hypotheses that use concept inclusions unrelated to the problem at hand. We show how to compute a special class of connection-minimal hypotheses in a sound and complete way. Our technique is based on a translation to first-order logic, and constructs hypotheses based on prime implicates. We evaluate a prototype implementation of our approach on ontologies from the medical domain.

@inproceedings{ HaKoSoWe-IJCAR-2022,
  author = {Fajar {Haifani} and Patrick {Koopmann} and Sophie {Tourret} and Christoph {Weidenbach}},
  booktitle = {Automated Reasoning - 11th International Joint Conference, {IJCAR} 2022},
  note = {(to appear)},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Connection-minimal Abduction in {$\mathcal{EL}$} via Translation to FOL},
  year = {2022},
}

Reasoners can be used to derive implicit consequences from an ontology. Sometimes unwanted consequences are revealed, indicating errors or privacy-sensitive information, and the ontology needs to be appropriately repaired. The classical approach is to remove just enough axioms such that the unwanted consequences vanish. However, this is often too rough since mere axiom deletion also erases many other consequences that might actually be desired. The goal should not be to remove a minimal number of axioms but to modify the ontology such that only a minimal number of consequences is removed, including the unwanted ones. Specifically, a repair should rather be logically entailed by the input ontology, instead of being a subset. To this end, we introduce a framework for computing fixed-premise repairs of \(\mathcal{EL}\) TBoxes. In the first variant the conclusions must be generalizations of those in the input TBox, while in the second variant no such restriction is imposed. In both variants, every repair is entailed by an optimal one and, up to equivalence, the set of all optimal repairs can be computed in exponential time. A prototypical implementation is provided. In addition, we show new complexity results regarding gentle repairs.

@inproceedings{ Kr-KI2022,
  author = {Francesco {Kriegel}},
  booktitle = {Proceedings of the 45th German Conference on Artificial Intelligence ({KI} 2022), Virtual in Trier, Germany, September 19--23, 2022},
  doi = {https://doi.org/10.1007/978-3-031-15791-2_11},
  editor = {Ralph {Bergmann} and Lukas {Malburg} and Stephanie C. {Rodermund} and Ingo J. {Timm}},
  pages = {115--130},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Optimal Fixed-Premise Repairs of $\mathcal{EL}$ {TBoxes}},
  volume = {13404},
  year = {2022},
}

Explaining consequences obtained from ontological reasoning is an active research topic. Unlike the computation of the cause of the consequence, the explication of the cause has received little attention so far. However, as many ontologies are designed by experts, the terms and notions used in an explanation need not be known to the user of the ontology-based system, before they can attempt to understand the underlying logical process. In this paper, we address the task of making an explanation of a con- sequence more comprehensible to a variety of users by re-phrasing it in a vocabulary known to them. Assuming the existence of a dictionary, we attempt to rewrite technical jargon into expressions using a simpler vocabulary. We show that solving this problem requires taking several technical issues into account.

@inproceedings{ PeTu-FCR-22,
  author = {Rafael {Pe\~naloza} and Anni-Yasmin {Turhan}},
  booktitle = {Proceedings of the 8th Workshop on Formal and Cognitive Reasoning},
  editor = {Christoph {Beierle} and Marco {Ragni} and Kai {Sauerwald} and Frieder {Stolzenburg} and Matthias {Thimm}},
  series = {CEUR},
  title = {User-aware Explications of Ontology Consequences: Levelling Technicality},
  year = {2022},
}

It is often natural in planning to specify conditions that should be avoided, characterizing dangerous or highly undesirable behavior. PDDL3 supports this with temporal-logic state trajectory constraints. Here we focus on the simpler case where the constraint is a non-temporal formula \(\phi\) – the avoid condition – that must be false throughout the plan. We design techniques tackling such avoid conditions effectively. We show how to learn from search experience which states necessarily lead into \(\phi\), and we show how to tailor abstractions to recognize that avoiding \(\phi\) will not be possible starting from a given state. We run a large-scale experiment, comparing our techniques against compilation methods and against simple state pruning using \(\phi\). The results show that our techniques are often superior.

@inproceedings{ SHKB-AAAI-22,
  author = {Marcel {Steinmetz} and J{\"o}rg {Hoffmann} and Alisa {Kovtunova} and Stefan {Borgwardt}},
  booktitle = {Proceedings of the AAAI Conference on Artificial Intelligence},
  doi = {https://doi.org/10.1609/aaai.v36i9.21232},
  month = {Jun.},
  number = {9},
  pages = {9944--9952},
  title = {Classical Planning with Avoid Conditions},
  volume = {36},
  year = {2022},
}

The authoring of complex concepts or (instance) queries written in a description logic (DL) can be a difficult task. An established approach is to generate such concepts from positive examples is to employ the most specific concept (msc), which generalizes an ABox individual into a concept and the least common subsumer (lcs), which generalizes a collection of concepts into a single concept. These inferences are investigated for the \( \mathcal{EL} \), but so far there are no methods for the 2-dimensional case such as temporalized DLs. We report in this abstract on our computation algorithms for the lcs and the msc in a temporalized DL: \( \mathcal{EL} \) extended by the LTL operators next and global. We sketch the computation algorithms for both inferences—with and without the use of rigid symbols.

@inproceedings{ TiTu-DL2022,
  author = {Satyadharma {Tirtarasa} and Anni-Yasmin {Turhan}},
  booktitle = {Proceedings of the 35th International Workshop on Description Logics ({DL} 2022), Haifa, Israel, August 7--10, 2022},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {A New Dimension to Generalization: Computing Temporal $ \mathcal{EL} $ Concepts from Positive Examples (Extended Abstract))},
  year = {2022},
}

In ontology-based applications, the authoring of complex concepts or queries written in a description logic (DL) is a difficult task. An established approach to generate complex expressions from examples provided a user, is the bottom-up approach. This approach employs two inferences: the most specific concept (MSC), which generalizes an ABox individual into a concept and the least common subsumer (LCS), which generalizes a collection of concepts into a single concept. In ontology-based situation recognition the situation to be recognized is formalized by a DL query using temporal operators and that is to answered over a sequence of ABoxes. Now, while the bottom-up approach is well-investigated for the DL EL, there are so far no methods for temporalized DLs.

We consider here the temporalized DL that extends the DL EL with the LTL operators next and global and we present an approach that extends the LCS and the MSC to the temporalized setting. We provide computation algorithms for both inferences –even in the presence of rigid symbols– and show their correctness.

@inproceedings{ TiTu-SAC2022,
  author = {Satyadharma {Tirtarasa} and Anni-Yasmin {Turhan}},
  booktitle = {Proceedings of the 37th Annual ACM Symposium on Applied Computing (SAC '22), April 25--29, 2022, Virtual Event},
  doi = {https://doi.org/10.1145/3477314.3507136},
  pages = {903--910},
  publisher = {Association for Computing Machinery},
  title = {{Computing Generalizations of Temporal $\mathcal{E\!L}$ Concepts with Next and Global}},
  year = {2022},
}

Defeasible description logics (DDLs) support nonmonotonic reasoning by admitting defeasible concept inclusions in the knowledge base. Early reasoning methods for subsumption did not always use defeasible information for objects in the scope of nested quantifiers and thus neglected un-defeated information. The reasoning approach employing typicality models for the DDL \(\mathcal{EL}_{\bot}\) overcomes this effect for existentially quantified objects. In this extended abstract we report on how to lift typicality model-based reasoning to the DDL \(\mathcal{ELI}_{\bot}\), which extends \(\mathcal{EL}_{\bot}\) with inverse roles. These can capture a form of universal quantification and extend expressivity of the DDL substantially. Reasoning in DDLs often employs rational closure according to the propositional KLM postulates. We can show that the proposed subsumption algorithm yields more entailments than rational propositional entailment.

@inproceedings{ CaTu-NMR-22,
  author = {Igor {de Camargo e Souza C\^{a}mara} and Anni-Yasmin {Turhan}},
  booktitle = {Proceedings of the 20th International Workshop on Non-Monotonic Reasoning},
  editor = {Ofer {Arieli} and Giovanni {Casini} and Laura {Giordano}},
  pages = {159--162},
  series = {CEUR},
  title = {Rational Defeasible Subsumption in DLs with Nested Quantifiers: the Case of $\mathcal{ELI}_\bot$},
  volume = {3197},
  year = {2022},
}

Logic-based approaches to AI have the advantage that their behavior can in principle be explained to a user. If, for instance, a Description Logic reasoner derives a consequence that triggers some action of the overall system, then one can explain such an entailment by presenting a proof of the consequence in an appropriate calculus. How comprehensible such a proof is depends not only on the employed calculus, but also on the properties of the particular proof, such as its overall size, its depth, the complexity of the employed sentences and proof steps, etc. For this reason, we want to determine the complexity of generating proofs that are below a certain threshold w.r.t. a given measure of proof quality. Rather than investigating this problem for a fixed proof calculus and a fixed measure, we aim for general results that hold for wide classes of calculi and measures. In previous work, we first restricted the attention to a setting where proof size is used to measure the quality of a proof. We then extended the approach to a more general setting, but important measures such as proof depth were not covered. In the present paper, we provide results for a class of measures called recursive, which yields lower complexities and also encompasses proof depth. In addition, we close some gaps left open in our previous work, thus providing a comprehensive picture of the complexity landscape.

@inproceedings{ AlBaBoKoKo-CADE2021,
  author = {Christian {Alrabbaa} and Franz {Baader} and Stefan {Borgwardt} and Patrick {Koopmann} and Alisa {Kovtunova}},
  booktitle = {Proceedings of the 28th International Conference on Automated Deduction (CADE-28), July 11--16, 2021, Virtual Event, United States},
  doi = {https://doi.org/10.1007/978-3-030-79876-5_17},
  editor = {Andr{\'e} {Platzer} and Geoff {Sutcliffe}},
  pages = {291--308},
  series = {Lecture Notes in Computer Science},
  title = {Finding Good Proofs for Description Logic Entailments Using Recursive Quality Measures},
  volume = {12699},
  year = {2021},
}

@inproceedings{ AlrabbaaBBKK21,
  author = {Christian {Alrabbaa} and Franz {Baader} and Stefan {Borgwardt} and Patrick {Koopmann} and Alisa {Kovtunova}},
  booktitle = {Proceedings of the 34th International Workshop on Description Logics {(DL} 2021) part of Bratislava Knowledge September {(BAKS} 2021), Bratislava, Slovakia, September 19th to 22nd, 2021},
  editor = {Martin {Homola} and Vladislav {Ryzhikov} and Renate A. {Schmidt}},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {Finding Good Proofs for Description Logic Entailments Using Recursive Quality Measures (Extended Abstract)},
  volume = {2954},
  year = {2021},
}

@inproceedings{ AlrabbaaBKKRW21,
  author = {Christian {Alrabbaa} and Stefan {Borgwardt} and Nina {Knieriemen} and Alisa {Kovtunova} and Anna Milena {Rothermel} and Frederik {Wiehr}},
  booktitle = {Proceedings of the 34th International Workshop on Description Logics {(DL} 2021) part of Bratislava Knowledge September {(BAKS} 2021), Bratislava, Slovakia, September 19th to 22nd, 2021},
  editor = {Martin {Homola} and Vladislav {Ryzhikov} and Renate A. {Schmidt}},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {In the Hand of the Beholder: Comparing Interactive Proof Visualizations},
  volume = {2954},
  year = {2021},
}

@inproceedings{ BoHiKoWi-XLoKR21,
  author = {Christian {Alrabbaa} and Stefan {Borgwardt} and Nina {Knieriemen} and Alisa {Kovtunova} and Anna Milena {Rothermel} and Frederik {Wiehr}},
  booktitle = {Informal Proceedings of the Explainable Logic-Based Knowledge Representation (XLoKR 2021) workshop co-located with the 18th International Conference on Principles of Knowledge Representation and Reasoning {(KR} 2021), Online Event [Hanoi, Vietnam], November 3rd to 5th, 2021},
  title = {In the Hand of the Beholder: Comparing Interactive Proof Visualizations (Extended Abstract)},
  year = {2021},
}

When subsumption relationships unexpectedly fail to be detected by a description logic reasoner, the cause for this non-entailment need not be evident. In this case, succinct automatically generated explanations would be helpful. Reasoners for the description logic EL compute the canonical model of a TBox in order to perform subsumption tests. We devise substructures of such models as relevant parts for explanation and propose an approach based on graph transductions to extract such relevant parts from canonical models.

@inproceedings{ AlHiTu-FCR-2021,
  author = {Christian {Alrabbaa} and Willi {Hieke} and Anni-Yasmin {Turhan}},
  booktitle = {Proceedings of the 7th Workshop on Formal and Cognitive Reasoning (FCR-2021) co-located with the 44th German Conference on Artificial Intelligence (KI-2021)},
  editor = {Christoph {Beierle} and Marco {Ragni} and Frieder {Stolzenburg} and Matthias {Thimm}},
  pages = {9--22},
  publisher = {CEUR-WS.org},
  series = {CEUR Workshop Proceedings},
  title = {Counter Model Transformation for Explaining Non-Subsumption in $\mathcal{EL}$},
  volume = {2961},
  year = {2021},
}

When subsumption relationships unexpectedly fail to be detected by a description logic reasoner, the cause for this non-entailment need not be evident. In this case, succinct automatically generated explanations would be helpful. We devise substructures of such models as relevant parts suitable for explaining the non-entailment to users of description logic systems.

@inproceedings{ AlHiTu-XLoKR-2021,
  author = {Christian {Alrabbaa} and Willi {Hieke} and Anni-Yasmin {Turhan}},
  booktitle = {Informal Proceedings of the 2nd Workshop on Explainable Logic-Based Knowledge Representation (XLoKR-2021) co-located with the 18th international Conference on Principles of Knowledge Representation and Reasoning (KR-2021)},
  title = {Relevant Parts of Counter Models as Explanations for {$\mathcal{EL}$} Non-Subsumptions (Extended Abstract)},
  year = {2021},
}

@inproceedings{ BaFeRo-DL-21,
  author = {Franz {Baader} and Oliver {Fern{\'a}ndez Gil} and Maryam {Rostamigiv}},
  booktitle = {Proceedings of the 34th International Workshop on Description Logics ({DL} 2021), Hybrid Event, Bratislava, Slovakia, September 19--22, 2021},
  editor = {Martin {Homola} and Vladislav {Ryzhikov} and Renate A. {Schmidt}},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {Restricted Unification in the DL {$\mathcal{FL}_0$} (Extended Abstract)},
  volume = {2954},
  year = {2021},
}

Unification in the Description Logic (DL) FL0 is known to be ExpTime-complete and of unification type zero. We investigate whether a lower complexity of the unification problem can be achieved by either syntactically restricting the role depth of concepts or semantically restricting the length of role paths in interpretations. We show that the answer to this question depends on whether the number formulating such a restriction is encoded in unary or binary: for unary coding, the complexity drops from ExpTime to PSpace. As an auxiliary result, we prove a PSpace-completeness result for a depth-restricted version of the intersection emptiness problem for deterministic root-to-frontier tree automata. Finally, we show that the unification type of FL0 improves from type zero to unitary (finitary) for unification without (with) constants in the restricted setting.

@inproceedings{ BaGiRo-FroCoS21,
  author = {Franz {Baader} and Oliver {Fern\'andez Gil} and Maryam {Rostamigiv}},
  booktitle = {Proc. of the 13th International Symposium on Frontiers of Combining Systems ({FroCoS} 2021)},
  doi = {https://doi.org/10.1007/978-3-030-86205-3_5},
  editor = {Boris {Konev} and Giles {Reger}},
  pages = {81--97},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Restricted Unification in the {DL} {$\mathcal{FL}_0$}},
  volume = {12941},
  year = {2021},
}

The application of automated reasoning approaches to Description Logic (DL) ontologies may produce certain consequences that either are deemed to be wrong or should be hidden for privacy reasons. The question is then how to repair the ontology such that the unwanted consequences can no longer be deduced. An optimal repair is one where the least amount of other consequences is removed. Most of the previous approaches to ontology repair are of a syntactic nature in that they remove or weaken the axioms explicitly present in the ontology, and thus cannot achieve semantic optimality. In previous work, we have addressed the problem of computing optimal repairs of (quantified) ABoxes, where the unwanted consequences are described by concept assertions of the light-weight DL \(\mathcal{E\!L}\). In the present paper, we improve on the results achieved so far in two ways. First, we allow for the presence of terminological knowledge in the form of an \(\mathcal{E\!L}\) TBox. This TBox is assumed to be static in the sense that it cannot be changed in the repair process. Second, the construction of optimal repairs described in our previous work is best case exponential. We introduce an optimized construction that is exponential only in the worst case. First experimental results indicate that this reduces the size of the computed optimal repairs considerably.

@inproceedings{ BaKoKrNu-CADE2021,
  author = {Franz {Baader} and Patrick {Koopmann} and Francesco {Kriegel} and Adrian {Nuradiansyah}},
  booktitle = {Proceedings of the 28th International Conference on Automated Deduction (CADE-28), July 11--16, 2021, Virtual Event, United States},
  doi = {https://doi.org/10.1007/978-3-030-79876-5_18},
  editor = {Andr{\'e} {Platzer} and Geoff {Sutcliffe}},
  pages = {309--326},
  series = {Lecture Notes in Computer Science},
  title = {{Computing Optimal Repairs of Quantified ABoxes w.r.t. Static $\mathcal{E\!L}$ TBoxes}},
  volume = {12699},
  year = {2021},
}

@inproceedings{ BaKoKrNu-KR2021,
  author = {Franz {Baader} and Patrick {Koopmann} and Francesco {Kriegel} and Adrian {Nuradiansyah}},
  booktitle = {Recent Published Research (RPR) track of the 18th International Conference on Principles of Knowledge Representation and Reasoning, {KR} 2021, Virtual Event, November 3--12, 2021},
  doi = {https://doi.org/10.5281/zenodo.8341301},
  title = {{Computing Optimal Repairs of Quantified ABoxes w.r.t.\ Static $\mathcal{EL}$ TBoxes (Extended Abstract)}},
  year = {2021},
}

We review our recent work on how to compute optimal repairs, optimal compliant anonymizations, and optimal safe anonymizations of ABoxes containing possibly anonymized individuals. The results can be used both to remove erroneous consequences from a knowledge base and to hide secret information before publication of the knowledge base, while keeping as much as possible of the original information.

@inproceedings{ BaKoKrNuPe-DL-2021,
  author = {Franz {Baader} and Patrick {Koopmann} and Francesco {Kriegel} and Adrian {Nuradiansyah} and Rafael {Pe\~{n}aloza}},
  booktitle = {Proceedings of the 34th International Workshop on Description Logics ({DL} 2021), Hybrid Event, Bratislava, Slovakia, September 19--22, 2021},
  editor = {Martin {Homola} and Vladislav {Ryzhikov} and Renate A. {Schmidt}},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {{Privacy-Preserving Ontology Publishing: The Case of Quantified ABoxes w.r.t.\ a Static Cycle-Restricted $\mathcal{EL}$ TBox}},
  volume = {2954},
  year = {2021},
}

In recent work, we have shown how to compute compliant anonymizations of quantified ABoxes w.r.t. \(\mathcal{E\!L}\) policies. In this setting, quantified ABoxes can be used to publish information about individuals, some of which are anonymized. The policy is given by concepts of the Description Logic (DL) \(\mathcal{E\!L}\), and compliance means that one cannot derive from the ABox that some non-anonymized individual is an instance of a policy concept. If one assumes that a possible attacker could have additional knowledge about some of the involved non-anonymized individuals, then compliance with a policy is not sufficient. One wants to ensure that the quantified ABox is safe in the sense that none of the secret instance information is revealed, even if the attacker has additional compliant knowledge. In the present paper, we show that safety can be decided in polynomial time, and that the unique optimal safe anonymization of a non-safe quantified ABox can be computed in exponential time, provided that the policy consists of a single \(\mathcal{E\!L}\) concept.

@inproceedings{ BaKrNuPe-SAC2021,
  author = {Franz {Baader} and Francesco {Kriegel} and Adrian {Nuradiansyah} and Rafael {Pe{\~n}aloza}},
  booktitle = {Proceedings of the 36th Annual ACM Symposium on Applied Computing (SAC '21), March 22--26, 2021, Virtual Event, Republic of Korea},
  doi = {https://doi.org/10.1145/3412841.3441961},
  pages = {863--872},
  publisher = {Association for Computing Machinery},
  title = {{Safety of Quantified ABoxes w.r.t.\ Singleton $\mathcal{E\!L}$ Policies}},
  year = {2021},
}

Research on unification in Description Logic (DL) has concentrated on the lightweight DLs FL0 and EL. For both DLs, the unification type is zero, which is the worst possible type. The complexity of deciding unifiability is ExpTime-complete for FL0 and NP-complete for EL. In a recent paper, we have shown that, for FL0, both the unification type and the complexity of the decision problem can be improved by considering restricted versions of the unification problem where either the role depth of concepts is restricted syntactically or the length of role paths in interpretations is restricted semantically. In the present paper, we show that no such improvements can be obtained for EL: both in the syntactically and in the semantically restricted case, the unification type stays zero, and the complexity of the decision problem stays NP-complete.

@inproceedings{ BaRo-DL-2021,
  author = {Franz {Baader} and Maryam {Rostamigiv}},
  booktitle = {Proceedings of the 34th International Workshop on Description Logics ({DL} 2021), Hybrid Event, Bratislava, Slovakia, September 19--22, 2021},
  editor = {Martin {Homola} and Vladislav {Ryzhikov} and Renate A. {Schmidt}},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {Restricted Unification in the DL {$\mathcal{EL}$}},
  volume = {2954},
  year = {2021},
}

Concrete domains have been introduced in Description Logics (DLs) to enable reference to concrete objects (such as numbers) and predefined predicates on these objects (such as numerical comparisons) when defining concepts. To retain decidability when integrating a concrete domain into a decidable DL, the domain must satisfy quite strong restrictions. In previous work, we have analyzed the most prominent such condition, called omega-admissibility, from an algebraic point of view. This provided us with useful algebraic tools for proving omega-admissibility, which allowed us to find new examples for concrete domains whose integration leaves the prototypical expressive DL ALC decidable. When integrating concrete domains into lightweight DLs of the EL family, achieving decidability is not enough. One wants reasoning in the resulting DL to be tractable. This can be achieved by using so-called p-admissible concrete domains and restricting the interaction between the DL and the concrete domain. In the present paper, we investigate p-admissibility from an algebraic point of view. Again, this yields strong algebraic tools for demonstrating p-admissibility. In particular, we obtain an expressive numerical p-admissible concrete domain based on the rational numbers. Although omega-admissibility and p-admissibility are orthogonal conditions that are almost exclusive, our algebraic characterizations of these two properties allow us to locate an infinite class of p-admissible concrete domains whose integration into ALC yields decidable DLs.

@inproceedings{ BaRy-JELIA-21,
  address = {Cham},
  author = {Franz {Baader} and Jakub {Rydval}},
  booktitle = {Proceedings of the 17th European Conference on Logics in Artificial Intelligence (JELIA 2021)},
  editor = {Wolfgang {Faber} and Gerhard {Friedrich} and Martin {Gebser} and Michael {Morak}},
  pages = {194--209},
  publisher = {Springer International Publishing},
  series = {Lecture Notes in Computer Science},
  title = {An Algebraic View on p-Admissible Concrete Domains for Lightweight Description Logics},
  volume = {12678},
  year = {2021},
}

We discuss explanations in Description Logics (DLs), a family of logics used for knowledge representation. Initial work on explaining consequences for DLs had focused on justifications, which are minimal subsets of axioms that entail the consequence. More recently, it was proposed that proofs can provide more detailed information about why a consequence follows. Moreover, several measures have been proposed to estimate the comprehensibility of justifications and proofs, for example, their size or the complexity of logical expressions. In this paper, we analyze the connection between these measures, e.g. whether small justifications necessarily give rise to small proofs. We use a dataset of DL proofs that was constructed last year based on the ontologies of the OWL Reasoner Evaluation 2015. We find that, in general, less complex justifications indeed correspond to less complex proofs, and discuss some exceptions from this rule.

@inproceedings{ Borg-XLoKR21,
  address = {Online [Hanoi, Vietnam]},
  author = {Stefan {Borgwardt}},
  booktitle = {2nd Workshop on Explainable Logic-Based Knowledge Representation (XLoKR'21)},
  editor = {Bart {Bogaerts}},
  title = {Concise Justifications Versus Detailed Proofs for Description Logic Entailments},
  year = {2021},
}

@inproceedings{ BorgwardtCCDKY21,
  author = {Stefan {Borgwardt} and Ernie {Chang} and Kathryn {Chapman} and Vera {Demberg} and Alisa {Kovtunova} and Hui{-}Syuan {Yeh}},
  booktitle = {Proceedings of the 34th International Workshop on Description Logics {(DL} 2021) part of Bratislava Knowledge September {(BAKS} 2021), Bratislava, Slovakia, September 19th to 22nd, 2021},
  editor = {Martin {Homola} and Vladislav {Ryzhikov} and Renate A. {Schmidt}},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {Logic-Guided Neural Utterance Generation from Drone Sensory Data (Extended Abstract)},
  volume = {2954},
  year = {2021},
}

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. Many real-world applications, like processing electronic health records (EHRs), also 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. Our contribution consists of two main parts: In the first part we introduce 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. In the second part, we extend this minimal-world semantics for answering metric temporal conjunctive queries with negation over the lightweight temporal logic \(\mathcal{TELH}_{\bot}^{♢c,lhs,-}\) and obtain similar rewritability and complexity results.

@article{ BoFK-TPLP21,
  author = {Stefan {Borgwardt} and Walter {Forkel} and Alisa {Kovtunova}},
  doi = {https://doi.org/10.1017/S1471068421000119},
  journal = {Theory and Practice of Logic Programming},
  title = {Temporal Minimal-World Query Answering over Sparse {AB}oxes},
  year = {2021},
}

@inproceedings{ Borgwardt0KS21,
  author = {Stefan {Borgwardt} and J{\"{o}}rg {Hoffmann} and Alisa {Kovtunova} and Marcel {Steinmetz}},
  booktitle = {Proceedings of the 34th International Workshop on Description Logics {(DL} 2021) part of Bratislava Knowledge September {(BAKS} 2021), Bratislava, Slovakia, September 19th to 22nd, 2021},
  editor = {Martin {Homola} and Vladislav {Ryzhikov} and Renate A. {Schmidt}},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {Making DL-Lite Planning Practical (Extended Abstract)},
  volume = {2954},
  year = {2021},
}

Planning in the presence of background ontologies is a topic of long-standing interest in AI. It combines the problems of (1) belief update complexity and (2) state-space combinatorics. DL-Lite offers an attractive solution to (1), with belief updates possible at the ABox level. Indeed, it has been shown that DL-Lite planning can be compiled into the commonly used planning language PDDL. Yet that compilation was previously found to be infeasible for off-the-shelf planning systems. Here we analyze the reasons for this problem and find that the bottleneck lies in the planner pre-processes, in particular in the naive DNF transformations used to compile the PDDL input into the planners' internal representations. Consequently, we design a PDDL pre-compiler realizing a polynomial DNF transformation. We leverage a particular PDDL language feature (derived predicates) to avoid the need for excessive control structure. Our pre-compiler turns out to be quite effective: the previous bottleneck disappears, and experiments on a broad range of benchmarks demonstrate the first practical technology for DL-Lite planning.

@inproceedings{ BHKS-KR21,
  author = {Stefan {Borgwardt} and J{\"o}rg {Hoffmann} and Alisa {Kovtunova} and Marcel {Steinmetz}},
  booktitle = {Proceedings of the 18th International Conference on Principles of Knowledge Representation and Reasoning (KR'21)},
  doi = {http://dx.doi.org/10.24963/kr.2021/61},
  editor = {Meghyn {Bienvenu} and Gerhard {Lakemeyer}},
  note = {Short paper.},
  pages = {641--645},
  publisher = {IJCAI},
  title = {Making {DL-Lite} Planning Practical},
  year = {2021},
}

Probabilistic model checking (PMC) is a well-established method for the quantitative analysis of state based operational models such as Markov decision processes. Description logics (DLs) provide a well-suited formalism to describe and reason about knowledge and are used as basis for the web ontology language (OWL). We investigate how such knowledge described by DLs can be integrated into the PMC process, introducing ontology-mediated PMC. Specifically, we propose ontologized programs as a formalism that links ontologies to behaviors specified by probabilistic guarded commands, the de-facto standard input formalism for PMC tools such as Prism. Through DL reasoning, inconsistent states in the modeled system can be detected. We present three ways to resolve these inconsistencies, leading to different Markov decision process semantics. We analyze the computational complexity of checking whether an ontologized program is consistent under these semantics. Further, we present and implement a technique for the quantitative analysis of ontologized programs relying on standard DL reasoning and PMC tools. This way, we enable the application of PMC techniques to analyze knowledge-intensive systems.We evaluate our approach and implementation on amulti-server systemcase study,where different DL ontologies are used to provide specifications of different server platforms and situations the system is executed in.

@article{ DuKoTu-FAC-2021,
  author = {Clemens {Dubslaff} and Patrick {Koopmann} and Anni-Yasmin {Turhan}},
  doi = {https://doi.org/10.1007/s00165-021-00549-0},
  journal = {Formal Aspects of Computing},
  publisher = {Springer},
  title = {Enhancing Probabilistic Model Checking with Ontologies},
  year = {2021},
}

Many stream reasoning applications make use of ontology reasoning to deal with incomplete data. To this end, definitions of complex concepts and elaborate ontologies are already used in event descriptions and queries. On the other hand, model checking can support stream reasoning, e.g., by runtime verification to predict future events or by classical offline verification. For such a combined use of model checking and stream reasoning, it is crucial that events are modeled in a compatible way. We have recently introduced and implemented a framework for ontology-mediated probabilistic model checking, which would allow to use the same ontology and event descriptions in both: the stream reasoner and the model checker. In this short paper we present this framework and discuss and motivate its use in the context of stream reasoning.

@inproceedings{ DKT-SR-21,
  author = {Clemens {Dubslaff} and Patrick {Koopmann} and Anni-Yasmin {Turhan}},
  booktitle = {Informal proceedings of the Stream Reasoning Workshop},
  editor = {Emanuele Della {Valle} and Thomas {Eiter} and Danh Le {Phuoc} and Konstantin {Schekotihin}},
  title = {Supporting Ontology-Mediated Stream Reasoning with Model Checking},
  year = {2021},
}

Classical regular path queries (RPQs) can be too restrictive for some applications and answering such queries under approximate semantics to relax the query is desirable. While for answering regular path queries over graph databases under approximate semantics algorithms are available, such algorithms are scarce for the ontology-mediated setting. In this paper we extend an approach for answering RPQs over graph databases that uses weighted transducers to approximate paths from the query in two ways. The first extension is to answering approximate conjunctive 2-way regular path queries (C2RPQs) over graph databases and the second is to answering C2RPQs over ELH and DL-Lite_R ontologies. We provide results on the computational complexity of the underlying reasoning problems and devise approximate query answering algorithms.

@inproceedings{ FeAt-AAAI-21,
  author = {Oliver {Fern{\'a}ndez Gil} and Anni-Yasmin {Turhan}},
  booktitle = {Proceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI'21)},
  pages = {6340--6348},
  publisher = {{AAAI} Press},
  title = {Answering Regular Path Queries Under Approximate Semantics in Lightweight Description Logics},
  year = {2021},
}

We present a technique for performing TBox abduction in the description logic \(\mathcal{EL}\). The input problem is converted into first-order formulas on which a prime implicate generation technique is applied, then \(\mathcal{EL}\) hypotheses are reconstructed by combining the generated positive and negative implicates.

@inproceedings{ HaKoTo-SOQE-21,
  author = {Fajar {Haifani} and Patrick {Koopmann} and Sophie {Tourret}},
  booktitle = {Proceedings of the Second Workshop on Second-Order Quantifier Elimination and Related Topics {(SOQE} 2021) associated with the 18th International Conference on Principles of Knowledge Representation and Reasoning {(KR} 2021), Online Event, November 4, 2021},
  editor = {Renate A. {Schmidt} and Christoph {Wernhard} and Yizheng {Zhao}},
  pages = {46--58},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {Abduction in {$\mathcal{EL}$} via Translation to {FOL}},
  volume = {3009},
  year = {2021},
}

We introduce a new, explanation-oriented, minimality notion for abduction in the description logic \(\mathcal{EL}\). It rejects solutions where a random concept inclusion, disconnected from the problem at hand, is used.

@inproceedings{ HaKoTo-XLoKR-2021,
  author = {Fajar {Haifani} and Patrick {Koopmann} and Sophie {Tourret}},
  booktitle = {Informal Proceedings of the 2nd Workshop on Explainable Logic-Based Knowledge Representation (XLoKR-2021) co-located with the 18th international Conference on Principles of Knowledge Representation and Reasoning (KR-2021)},
  title = {Introducing Connection Minimal Abduction for $\mathcal{EL}$ Ontologies},
  year = {2021},
}

Knowledge engineers might face situations in which an unwanted consequence is derivable from an ontology. It is then desired to revise the ontology such that it no longer entails the consequence. For this purpose, we introduce a novel technique for repairing TBoxes formulated in the description logic \(\mathcal{EL}\). Specifically, we first compute a canonical model of the TBox and then transform it into a countermodel to the unwanted consequence. As formalism for the model transformation we employ transductions. We then obtain a TBox repair as the axiomatization of the logical intersection of the original TBox and the theory of the countermodel. In fact, we construct a set of countermodels, each of which induces a TBox repair. For the actual computation of the repairs we use results from Formal Concept Analysis.

@inproceedings{ HiKrNu-DL-2021,
  author = {Willi {Hieke} and Francesco {Kriegel} and Adrian {Nuradiansyah}},
  booktitle = {Proceedings of the 34th International Workshop on Description Logics ({DL} 2021), Hybrid Event, Bratislava, Slovakia, September 19--22, 2021},
  editor = {Martin {Homola} and Vladislav {Ryzhikov} and Renate A. {Schmidt}},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {{Repairing $\mathcal{EL}$ TBoxes by Means of Countermodels Obtained by Model Transformation}},
  volume = {2954},
  year = {2021},
}

In ABox abduction, we are given a knowledge base together with an ABox — the observation — that is not logically entailed by the knowledge base, and are looking for another ABox — the hypothesis — that, when added to the knowledge base, would make the observation entailed. This has applications in explaining negative entailments and missing query answers, as well as in diagnosis. To get useful hypotheses, in signature-based abduction, we additionally provide a signature of abducible names, and require the hypothesis to use only names from that signature. In the variant we are considering, the hypothesis may otherwise use fresh individual names, as well as complex concepts constructed in arbitrary way using the names in the signature. It was recently shown that this variant of abduction is in N2ExpTime^NP, and that hypotheses may require concepts that are of triple exponential size. We complement those results by showing a matching N2ExpTime^NP lower bound, and show that in the worst case, hypotheses may also use a double exponential number of fresh individual names.

@inproceedings{ Ko-SOQE-21,
  author = {Patrick {Koopmann}},
  booktitle = {Proceedings of the Second Workshop on Second-Order Quantifier Elimination and Related Topics {(SOQE} 2021) associated with the 18th International Conference on Principles of Knowledge Representation and Reasoning {(KR} 2021), Online Event, November 4, 2021},
  editor = {Renate A. {Schmidt} and Christoph {Wernhard} and Yizheng {Zhao}},
  pages = {61--74},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {Signature-Based ABox Abduction in {$\mathcal{ALC}$} is Hard},
  volume = {3009},
  year = {2021},
}

Given a knowledge base and an observation as a set of facts, ABox abduction aims at computing a hypothesis that, when added to the knowledge base, is sufficient to entail the observation. In signature-based ABox abduction, the hypothesis is further required to use only names from a given set. This form of abduction has applications such as diagnosis, KB repair, or explaning missing entailments. It is possible that hypotheses for a given observation only exist if we admit the use of fresh individuals and/or complex concepts built from the given signature, something most approaches for ABox abduction so far do not allow or only allow with restrictions. In this paper, we investigate the computational complexity of this form of abduction—allowing either fresh individuals, complex concepts, or both—for various description logics, and give size bounds on the hypotheses if they exist.

@inproceedings{ Ko-IJCAI2021,
  author = {Patrick {Koopmann}},
  booktitle = {Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence, {IJCAI} 2021, Virtual Event / Montreal, Canada, 19-27 August 2021},
  doi = {https://doi.org/10.24963/ijcai.2021/266},
  editor = {Zhi{-}Hua {Zhou}},
  pages = {1929--1935},
  publisher = {ijcai.org},
  title = {Signature-Based Abduction with Fresh Individuals and Complex Concepts for Description Logics},
  year = {2021},
}

We discuss two ways of using abduction to explain missing entailments from description logic knowledge bases, one more common, one more unusual, and then have a closer look at how current results/implementations on abduction could be used towards generating such explanations, and what still needs to be done.

@inproceedings{ Ko-XLoKR-2021,
  author = {Patrick {Koopmann}},
  booktitle = {Informal Proceedings of the 2nd Workshop on Explainable Logic-Based Knowledge Representation (XLoKR-2021) co-located with the 18th international Conference on Principles of Knowledge Representation and Reasoning (KR-2021)},
  title = {Two Ways of Explaining Negative Entailments in Description Logics Using Abduction},
  year = {2021},
}

The \(\mathcal{EL}\) subsumption hierarchy consists of all \(\mathcal{EL}\) concept descriptions and is partially ordered by subsumption. In order to navigate within this hierarchy, one can go up to subsumers and down to subsumees. We analyze how smallest steps can be made. Specifically, we show how all upper neighbors as well as all lower neighbors of a given \(\mathcal{EL}\) concept description can be efficiently computed, where two concepts are neighbors if one subsumes the other and there is no third concept in between. We further show that the hierarchy contains very long chains: there is a sequence of concepts \(C_n\) with size linear in \(n\) such that each chain of neighbors from \(\top\) to \(C_n\) has at least \(n\)-fold exponential length. As applications, we provide a template for determining upper complexity bounds for deciding whether a concept is maximally general or maximally specific w.r.t. a property, we construct a metric on the set of all \(\mathcal{EL}\) concept descriptions, we introduce a similarity measure that fulfills the triangle inequality, and we conclude that an uninformed search for a target concept by subsequently computing neighbors or, equivalently, along an ideal refinement operator is not feasible in practical applications.

@inproceedings{ Kr-DL-2021,
  author = {Francesco {Kriegel}},
  booktitle = {Proceedings of the 34th International Workshop on Description Logics ({DL} 2021), Hybrid Event, Bratislava, Slovakia, September 19--22, 2021},
  editor = {Martin {Homola} and Vladislav {Ryzhikov} and Renate A. {Schmidt}},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {{Navigating the $\mathcal{EL}$ Subsumption Hierarchy}},
  volume = {2954},
  year = {2021},
}

Stream reasoning systems often rely on complex temporal queries that are answered over enriched data sources. While there are systems for answering such queries, automated support for building tem- poral queries is rare. We present in this paper initial results on how to derive a temporalized concept from a set of examples. The resulting con- cept can then be used to retrieve objects that change over time. We consider the temporalized description logic that extends the description Logic EL with the LTL operators next (X) and global (G) and we present an approach that extends generalization inferences for classical EL.

@inproceedings{ TT-SR-21,
  author = {Satyadharma {Tirtarasa} and Anni-Yasmin {Turhan}},
  booktitle = {Informal proceedings of the Stream Reasoning Workshop},
  editor = {Emanuele Della {Valle} and Thomas {Eiter} and Danh Le {Phuoc} and Konstantin {Schekotihin}},
  title = {Towards Reverse Engineering Temporal Queries: Generalizing $\mathcal{EL}$ Concepts with Next and Global},
  year = {2021},
}

In highly automated driving, it is still an open question how machines can safely hand over control to humans and if an advance notice with additional explanations can be beneficial in critical situations. Conceptually, formal methods from AI – description logic (DL) and automated planning – in order to more reliably predict when a handover is necessary, and to increase the advance notice for handovers by planning ahead at runtime can provide a technological support for explanations using natural language generation. However, in this work we address the user’s perspective only with two contributions: First, we evaluate our concept in a driving simulator study (N=23) and find that an advance notice and spoken explanations were preferred over classical handover methods. Second, we propose a framework and an example test scenario specific to handovers that is based on the results of our study.

@inproceedings{ WHSK-ICMI21,
  author = {Frederik {Wiehr} and Anke {Hirsch} and Lukas {Schmitz} and Nina {Knieriemen} and Antonio {Kr{\"{u}}ger} and Alisa {Kovtunova} and Stefan {Borgwardt} and Ernie {Chang} and Vera {Demberg} and Marcel {Steinmetz} and J{\"{o}}rg {Hoffmann}},
  booktitle = {{ICMI} '21: International Conference on Multimodal Interaction, Montr{\'{e}}al, QC, Canada, October 18-22, 2021},
  doi = {https://doi.org/10.1145/3462244.3479884},
  editor = {Zakia {Hammal} and Carlos {Busso} and Catherine {Pelachaud} and Sharon L. {Oviatt} and Albert Ali {Salah} and Guoying {Zhao}},
  pages = {308--317},
  publisher = {{ACM}},
  title = {Why Do {I} Have to Take Over Control? Evaluating Safe Handovers with Advance Notice and Explanations in {HAD}},
  year = {2021},
}

Logic-based approaches to AI have the advantage that their behaviour can in principle be explained by providing their users with proofs for the derived consequences. However, if such proofs get very large, then it may be hard to understand a consequence even if the individual derivation steps are easy to comprehend. This motivates our interest in finding small proofs for Description Logic (DL) entailments. Instead of concentrating on a specific DL and proof calculus for this DL, we introduce a general framework in which proofs are represented as labeled, directed hypergraphs, where each hyperedge corresponds to a single sound derivation step. On the theoretical side, we investigate the complexity of deciding whether a certain consequence has a proof of size at most n along the following orthogonal dimensions: (i) the underlying proof system is polynomial or exponential; (ii) proofs may or may not reuse already derived consequences; and (iii) the number n is represented in unary or binary. We have determined the exact worst-case complexity of this decision problem for all but one of the possible combinations of these options. On the practical side, we have developed and implemented an approach for generating proofs for expressive DLs based on a non-standard reasoning task called forgetting. We have evaluated this approach on a set of realistic ontologies and compared the obtained proofs with proofs generated by the DL reasoner ELK, finding that forgetting-based proofs are often better w.r.t. different measures of proof complexity.

@inproceedings{ AlBaBoKoKo-20,
  author = {Christian {Alrabbaa} and Franz {Baader} and Stefan {Borgwardt} and Patrick {Koopmann} and Alisa {Kovtunova}},
  booktitle = {LPAR-23: 23rd International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  doi = {https://doi.org/10.29007/nhpp},
  editor = {Elvira {Albert} and Laura {Kovacs}},
  pages = {32--67},
  publisher = {EasyChair},
  series = {EPiC Series in Computing},
  title = {Finding Small Proofs for Description Logic Entailments: Theory and Practice},
  volume = {73},
  year = {2020},
}

If a Description Logic (DL) system derives a consequence, then one can in principle explain such an entailment by presenting a proof of the consequence in an appropriate calculus. Intuitively, good proofs are ones that are simple enough to be comprehensible to a user of the system. In recent work, we have introduced a general framework in which proofs are represented as labeled, directed hypergraphs, and have investigated the complexity of finding small proofs. However, large size is not the only reason that can make a proof complex. In the present paper, we introduce other measures for the complexity of a proof, and analyze the computational complexity of deciding whether a given consequence has a proof of complexity at most \(q\). This problem can be NP-complete even for \(\mathcal{EL}\), but we also identify measures where it can be decided in polynomial time.

@inproceedings{ AlBaBoKoKo-DL-20,
  author = {Christian {Alrabbaa} and Franz {Baader} and Stefan {Borgwardt} and Patrick {Koopmann} and Alisa {Kovtunova}},
  booktitle = {{DL 2020:} International Workshop on Description Logics},
  publisher = {CEUR-WS.org},
  series = {CEUR-WS},
  title = {On the Complexity of Finding Good Proofs for Description Logic Entailments},
  year = {2020},
}

The classical approach for repairing a Description Logic (DL) ontology in the sense of removing an unwanted consequence is to delete a minimal number of axioms from the ontology such that the resulting ontology no longer has the consequence. While there are automated tools for computing all possible such repairs, the user still needs to decide by hand which of the (potentially exponentially many) repairs to choose. In this paper, we argue that exploring a proof of the unwanted consequence may help us to locate other erroneous consequences within the proof, and thus allows us to make a more informed decision on which axioms to remove. In addition, we suggest that looking at the so-called atomic decomposition, which describes the modular structure of the ontology, enables us to judge the impact that removing a certain axiom has. Since both proofs and atomic decompositions of ontologies may be large, visual support for inspecting them is required. We describe a prototypical system that can visualize proofs and the atomic decomposition in an integrated visualization tool to support ontology debugging.

@inproceedings{ AlBaDaFlKo-DL-20,
  author = {Christian {Alrabbaa} and Franz {Baader} and Raimund {Dachselt} and Tamara {Flemisch} and Patrick {Koopmann}},
  booktitle = {{DL 2020:} International Workshop on Description Logics},
  publisher = {CEUR-WS.org},
  series = {CEUR-WS},
  title = {Visualising Proofs and the Modular Structure of Ontologies to Support Ontology Repair},
  year = {2020},
}

Approaches in knowledge representation based on formal logics and rule-based formalisms have the advantage that each step of reasoning can be understood by a user. However, often many of these inference steps are necessary, leading to a proof of the final conclusion that is hard to understand. If the set of inference rules is small, proofs may also look repetitious. Implemented systems (including the description logic (DL) reasoner ELK) that are able to produce formal proofs, are often bound to such predefined sets. In this work we present a black-box approach to generate proofs for expressive description logics (DLs) that are not based on a set of inference rules. Instead, it exploits the non-standard inference forgetting to generate intermediate proof steps. We have evaluated this approach on a set of realistic ontologies and compared the proofs obtained using the existing forgetting tools LETHE and Fame with ones generated by ELK.

@inproceedings{ AlBoKoKo-XLoKR-20,
  author = {Christian {Alrabbaa} and Stefan {Borgwardt} and Patrick {Koopmann} and Alisa {Kovtunova}},
  booktitle = {Explainable Logic-Based Knowledge Representation (XLoKR 2020)},
  title = {Finding Proofs for Description Logic Entailments in Practice},
  year = {2020},
}

We introduce and investigate the expressive description logic (DL) ALCSCC++, in which the global and local cardinality constraints introduced in previous papers can be mixed. We prove that the added expressivity does not increase the complexity of satisfiability checking and other standard inference problems. However, reasoning in ALCSCC++ becomes undecidable if inverse roles are added or conjunctive query entailment is considered. We prove that decidability of querying can be regained if global and local constraints are not mixed and the global constraints are appropriately restricted. In this setting, query entailment can be shown to be EXPTIME-complete and hence not harder than reasoning in ALC.

@inproceedings{ BaBaRu-ECAI20,
  author = {Franz {Baader} and Bartosz {Bednarczyk} and Sebastian {Rudolph}},
  booktitle = {Proceedings of the 24th European Conference on Artificial Intelligence ({ECAI} 2020)},
  doi = {https://doi.org/10.3233/FAIA200146},
  pages = {616--623},
  publisher = {IOS Press},
  series = {Frontiers in Artificial Intelligence and Applications},
  title = {Satisfiability and Query Answering in Description Logics with Global and Local Cardinality Constraints},
  volume = {325},
  year = {2020},
}

In contrast to qualitative linear temporal logics, which can be used to state that some property will eventually be satisfied, metric temporal logics allow us 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 is a growing interest in extending this work to the quantitative case. In this article, we complement existing results on the combination of DLs with metric temporal logics by introducing interval-rigid concept and role names. Elements included in an interval-rigid concept or role name are required to stay in it for some specified amount of time. We investigate several combinations of (metric) temporal logics with ALC by either allowing temporal operators only on the level of axioms or also applying them to concepts. In contrast to most existing work on the topic, we consider a timeline based on the integers and also allow assertional axioms. We show that the worst-case complexity does not increase beyond the previously known bound of 2-ExpSpace and investigate in detail how this complexity can be reduced by restricting the temporal logic and the occurrences of interval-rigid names.

@article{ BaBoKoOzTh-TOCL20,
  author = {Franz {Baader} and Stefan {Borgwardt} and Patrick {Koopmann} and Ana {Ozaki} and Veronika {Thost}},
  doi = {https://doi.org/10.1145/3399443},
  journal = {ACM Transactions on Computational Logic},
  month = {August},
  number = {4},
  pages = {30:1--30:46},
  title = {Metric Temporal Description Logics with Interval-Rigid Names},
  volume = {21},
  year = {2020},
}

The project "Semantic Technologies for Situation Awareness" was concerned with detecting certain critical situations from data obtained by observing a complex hard- and software system, in order to trigger actions that allow this system to save energy. The general idea was to formalize situations as ontology-mediated queries, but in order to express the relevant situations, both the employed ontology language and the query language had to be extended. In this paper we sketch the general approach and then concentrate on reporting the formal results obtained for reasoning in these extensions, but do not describe the application that triggered these extensions in detail.

@article{ BBKTT-KI20,
  author = {Franz {Baader} and Stefan {Borgwardt} and Patrick {Koopmann} and Veronika {Thost} and Anni-Yasmin {Turhan}},
  doi = {https://doi.org/10.1007/s13218-020-00694-3},
  journal = {{KI} -- K{\"u}nstliche Intelligenz},
  number = {4},
  pages = {291--301},
  title = {Semantic Technologies for Situation Awareness},
  volume = {34},
  year = {2020},
}

Simple counting quantifiers that can be used to compare the number of role successors of an individual or the cardinality of a concept with a fixed natural number have been employed in Description Logics (DLs) for more than two decades under the respective names of number restrictions and cardinality restriction on concepts. Recently, we have considerably extended the expressivity of such quantifiers by allowing to impose set and cardinality constraints formulated in the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA) on sets of role successors and concepts, respectively. We were able to prove that this extension does not increase the complexity of reasoning. In the present paper, we investigate the expressive power of the DLs obtained this way, using appropriate bisimulation characterizations and 0-1 laws as tools for distinguishing the expressiveness of different logics. In particular, we show that, in contrast to most classical DLs, these logics are no longer expressible in first-order predicate logic (FOL), and we characterize their first-order fragments. In most of our previous work on DLs with QFBAPA-based set and cardinality constraints we have employed finiteness restrictions on interpretations to ensure that the obtained sets are finite. Here we dispense with these restrictions to make the comparison with classical DLs, where one usually considers arbitrary models rather than finite ones, easier. It turns out that doing so does not change the complexity of reasoning.

@inproceedings{ BaBo-ANDREI60-20,
  author = {Franz {Baader} and Filippo {De Bortoli}},
  booktitle = {ANDREI-60. Automated New-era Deductive Reasoning Event in Iberia},
  doi = {https://doi.org/10.29007/ltzn},
  editor = {Laura {Kovacs} and Konstantin {Korovin} and Giles {Reger}},
  pages = {1--25},
  publisher = {EasyChair},
  series = {EPiC Series in Computing},
  title = {Description Logics That Count, and What They Can and Cannot Count},
  volume = {68},
  year = {2020},
}

Simple counting quantifiers that can be used to compare the number of role successors of an individual or the cardinality of a concept with a fixed natural number have been employed in Description Logics (DLs) for more than two decades under the respective names of number restrictions and cardinality restriction on concepts. Recently, we have considerably extended the expressivity of such quantifiers by allowing to impose set and cardinality constraints formulated in the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA) on sets of role successors and concepts, respectively. We were able to prove that this extension does not increase the complexity of reasoning. In the present paper, we investigate the expressive power of the DLs obtained this way, using appropriate bisimulation characterizations and 0-1 laws as tools for distinguishing the expressiveness of different logics. In particular, we show that, in contrast to most classical DLs, these logics are no longer expressible in first-order predicate logic (FOL), and we characterize their first-order fragments. In most of our previous work on DLs with QFBAPA-based set and cardinality constraints we have employed finiteness restrictions on interpretations to ensure that the obtained sets are finite. Here we dispense with these restrictions to make the comparison with classical DLs, where one usually considers arbitrary models rather than finite ones, easier. It turns out that doing so does not change the complexity of reasoning.

@inproceedings{ BaDeBo-DL-20,
  address = {Online},
  author = {Franz {Baader} and Filippo {De Bortoli}},
  booktitle = {Proceedings of the 33rd International Workshop on Description Logics (DL'20)},
  editor = {Stefan {Borgwardt} and Thomas {Meyer}},
  publisher = {CEUR-WS},
  series = {CEUR Workshop Proceedings},
  title = {Description Logics that Count, and What They Can and Cannot Count (Extended Abstract)},
  volume = {2663},
  year = {2020},
}

The word problem for a finite set of ground identities is known to be decidable in polynomial time using congruence closure, and this is also the case if some of the function symbols are assumed to be commutative. We show that decidability in P is preserved if we add the assumption that certain function symbols f are extensional in the sense that f(s₁,...,s_n) = f(t₁,...,t_n) implies s₁ = t₁, ..., s_n = t_n. In addition, we investigate a variant of extensionality that is more appropriate for commutative function symbols, but which raises the complexity of the word problem to coNP.

@inproceedings{ BaKa-IJCAR20,
  author = {Franz {Baader} and Deepak {Kapur}},
  booktitle = {Proceedings of the International Joint Conference on Automated Reasoning ({IJCAR} 2020)},
  doi = {https://doi.org/10.1007/978-3-030-51074-9_10},
  editor = {Viorica {Sofronie-Stokkermans} and Nicolas {Peltier}},
  pages = {163--180},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Deciding the Word Problem for Ground Identities with Commutative and Extensional Symbols},
  volume = {12166},
  year = {2020},
}

The generation of proof certificates and the use of proof checkers is nowadays standard in first-order automated theorem proving and related areas. They have, to the best of our knowledge, not yet been employed in Description Logics, where the focus was on detecting and repairing errors in the ontology, rather than on catching erroneous consequences created by an incorrect reasoner. This paper reports on first steps towards remedying this deficit for subsumptions computed by the DL reasoner ELK. We use an existing tool for generating proofs of consequences from ELK, and transform these proofs into a format that is accepted as certificates by our proof checker. The checker is obtained as an instance of a generic certification tool based on the Logical Framework with Side Conditions (LFSC), by formalizing the inference rules of ELK in LFSC. We report on the results of applying this approach to the classification of a large number of real-world OWL 2 EL ontologies.

@inproceedings{ BaKoTi-DL-20,
  author = {Franz {Baader} and Patrick {Koopmann} and Cesare {Tinelli}},
  booktitle = {{DL 2020:} International Workshop on Description Logics},
  publisher = {CEUR-WS.org},
  series = {CEUR-WS},
  title = {First Results on How to Certify Subsumptions Computed by the EL Reasoner ELK Using the Logical Framework with Side Conditions},
  year = {2020},
}

We adapt existing approaches for privacy-preserving publishing of linked data to a setting where the data are given as Description Logic (DL) ABoxes with possibly anonymised (formally: existentially quantified) individuals and the privacy policies are expressed using sets of concepts of the DL \(\mathcal{E\!L}\). We provide a chacterization of compliance of such ABoxes w.r.t. \(\mathcal{E\!L}\) policies, and show how optimal compliant anonymisations of ABoxes that are non-compliant can be computed. This work extends previous work on privacy-preserving ontology publishing, in which a very restricted form of ABoxes, called instance stores, had been considered, but restricts the attention to compliance. The approach developed here can easily be adapted to the problem of computing optimal repairs of quantified ABoxes.

@inproceedings{ BaKrNuPe-ISWC2020,
  author = {Franz {Baader} and Francesco {Kriegel} and Adrian {Nuradiansyah} and Rafael {Pe{\~n}aloza}},
  booktitle = {Proceedings of the 19th International Semantic Web Conference (ISWC 2020), Part {I}, Athens, Greece, November 2-6, 2020},
  doi = {https://doi.org/10.1007/978-3-030-62419-4_1},
  editor = {Jeff Z. {Pan} and Valentina A. M. {Tamma} and Claudia {d'Amato} and Krzysztof {Janowicz} and Bo {Fu} and Axel {Polleres} and Oshani {Seneviratne} and Lalana {Kagal}},
  pages = {3--20},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {{Computing Compliant Anonymisations of Quantified ABoxes w.r.t. $\mathcal{E\!L}$ Policies}},
  volume = {12506},
  year = {2020},
}

The theory ACUI of an associative, commutative, and idempotent binary function symbol + with unit 0 was one of the first equational theories for which the complexity of testing solvability of unification problems was investigated in detail. In this paper, we investigate two extensions of ACUI. On the one hand, we consider approximate ACUI-unification, where we use appropriate measures to express how close a substitution is to being a unifier. On the other hand, we extend ACUI-unification to ACUIG-unification, i.e., unification in equational theories that are obtained from ACUI by adding a finite set G of ground identities. Finally, we combine the two extensions, i.e., consider approximate ACUIG-unification. For all cases we are able to determine the exact worst-case complexity of the unification problem.

@article{ BaMaMoOk-MSCS-20,
  author = {Franz {Baader} and Pavlos {Marantidis} and Antoine {Mottet} and Alexander {Okhotin}},
  doi = {https://doi.org/10.1017/S0960129519000185},
  journal = {Mathematical Structures in Computer Science},
  number = {6},
  pages = {597--626},
  title = {Extensions of Unification Modulo {$\mathit{ACUI}$}},
  volume = {30},
  year = {2020},
}

Concrete domains have been introduced in the area of Description Logic to enable reference to concrete objects (such as numbers) and predefined predicates on these objects (such as numerical comparisons) when defining concepts. Unfortunately, in the presence of general concept inclusions (GCIs), which are supported by all modern DL systems, adding concrete domains may easily lead to undecidability. One contribution of this paper is to strengthen the existing undecidability results further by showing that concrete domains even weaker than the ones considered in the previous proofs may cause undecidability. To regain decidability in the presence of GCIs, quite strong restrictions, in sum called omega-admissiblity, need to be imposed on the concrete domain. On the one hand, we generalize the notion of omega-admissiblity from concrete domains with only binary predicates to concrete domains with predicates of arbitrary arity. On the other hand, we relate omega-admissiblity to well-known notions from model theory. In particular, we show that finitely bounded, homogeneous structures yield omega-admissible concrete domains. This allows us to show omega-admissibility of concrete domains using existing results from model theory.

@inproceedings{ BaRy-IJCAR20,
  author = {Franz {Baader} and Jakub {Rydval}},
  booktitle = {Proceedings of the International Joint Conference on Automated Reasoning ({IJCAR} 2020)},
  doi = {https://doi.org/10.1007/978-3-030-51074-9_24},
  editor = {Viorica {Sofronie-Stokkermans} and Nicolas {Peltier}},
  pages = {413--431},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Description Logics with Concrete Domains and General Concept Inclusions Revisited},
  volume = {12166},
  year = {2020},
}

Concrete domains have been introduced in the area of Description Logic to enable reference to concrete objects (such as numbers) and predefined predicates on these objects (such as numerical comparisons) when defining concepts. Unfortunately, in the presence of general concept inclusions (GCIs), which are supported by all modern DL systems, adding concrete domains may easily lead to undecidability. One contribution of this paper is to strengthen the existing undecidability results further by showing that concrete domains even weaker than the ones considered in the previous proofs may cause undecidability. To regain decidability in the presence of GCIs, quite strong restrictions, in sum called omega-admissiblity, need to be imposed on the concrete domain. On the one hand, we generalize the notion of omega-admissiblity from concrete domains with only binary predicates to concrete domains with predicates of arbitrary arity. On the other hand, we relate omega-admissiblity to well-known notions from model theory. In particular, we show that finitely bounded, homogeneous structures yield omega-admissible concrete domains. This allows us to show omega-admissibility of concrete domains using existing results from model theory.

@inproceedings{ BaRy-DL-20,
  address = {Online},
  author = {Franz {Baader} and Jakub {Rydval}},
  booktitle = {Proceedings of the 33rd International Workshop on Description Logics (DL'20)},
  editor = {Stefan {Borgwardt} and Thomas {Meyer}},
  publisher = {CEUR-WS},
  series = {CEUR Workshop Proceedings},
  title = {Description Logics with Concrete Domains and General Concept Inclusions Revisited (Extended Abstract)},
  volume = {2663},
  year = {2020},
}

We investigate the impact that general concept inclusions and role-value maps have on the complexity and decidability of reasoning in the Description Logic FL₀. On the one hand, we give a more direct proof for ExpTime-hardness of subsumption w.r.t. general concept inclusions in FL₀. On the other hand, we determine restrictions on role-value maps that ensure decidability of subsumption, but we also show undecidability for the cases where these restrictions are not satisfied.

@article{ BaTh-KI-20,
  author = {Franz {Baader} and Cl\'ement {Th\'eron}},
  doi = {https://dx.doi.org/10.1007/s13218-020-00651-0},
  journal = {{KI} -- K{\"u}nstliche Intelligenz},
  number = {3},
  pages = {291--301},
  title = {Role-Value Maps and General Concept Inclusions in the Minimal Description Logic with Value Restrictions -- or Revisiting Old Skeletons in the DL Cupboard},
  volume = {34},
  year = {2020},
}

Finite-domain constraint satisfaction problems are either solvable by Datalog, or not even expressible in fixed-point logic with counting. The border between the two regimes can be described by a strong height-one Maltsev condition. For infinite-domain CSPs, the situation is more complicated even if the template structure of the CSP is model-theoretically tame. We prove that there is no Maltsev condition that characterizes Datalog already for the CSPs of first-order reducts of (Q;<); such CSPs are called temporal CSPs and are of fundamental importance in infinite-domain constraint satisfaction. Our main result is a complete classification of temporal CSPs that can be expressed in one of the following logical formalisms: Datalog, fixed-point logic (with or without counting), or fixed-point logic with the Boolean rank operator. The classification shows that many of the equivalent conditions in the finite fail to capture expressibility in Datalog or fixed-point logic already for temporal CSPs.

@inproceedings{ BoRy-LICS20,
  address = {New York, NY, USA},
  author = {Manuel {Bodirsky} and Wied {Pakusa} and Jakub {Rydval}},
  booktitle = {Proceedings of the Symposium on Logic in Computer Science ({LICS} 2020)},
  doi = {https://doi.org/10.1145/3373718.3394750},
  pages = {237--251},
  publisher = {Association for Computing Machinery},
  title = {Temporal Constraint Satisfaction Problems in Fixed-Point Logic},
  year = {2020},
}

@inproceedings{ BorgwardtFK20,
  author = {Stefan {Borgwardt} and Walter {Forkel} and Alisa {Kovtunova}},
  booktitle = {Proceedings of the 33rd International Workshop on Description Logics {(DL} 2020) co-located with the 17th International Conference on Principles of Knowledge Representation and Reasoning {(KR} 2020), Online Event [Rhodes, Greece], September 12th to 14th, 2020},
  editor = {Stefan {Borgwardt} and Thomas {Meyer}},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {Finding New Diamonds: Temporal Minimal-World Query Answering over Sparse ABoxes (Extended Abstract)},
  volume = {2663},
  year = {2020},
}

Although logical entailments are often considered explainable, experience with justifications in DLs has shown that explaining why a logical consequence holds still requires some effort. However, a full formal proof of a DL entailment may be considered too long-winded, and a textual representation of a proof may be preferred. It may also depend on the user's experience and individual preferences which representation of a proof constitutes a good explanation for them. Building on previous work on explaining DL consequences to users, we ran an experiment to compare 4 different forms of proofs: formal proofs and textual proofs, which are either very detailed or condensed. A multiple linear regression with contrast coding revealed that the participants rated short proofs as being easier than long proofs, independent of their representation. On the other hand, we could not verify any influence of prior experience with logic on how easy or difficult the different kinds of proofs were considered.

@inproceedings{ BorgwardtHKW20,
  author = {Stefan {Borgwardt} and Anke {Hirsch} and Alisa {Kovtunova} and Frederik {Wiehr}},
  booktitle = {Proceedings of the 33rd International Workshop on Description Logics {(DL} 2020) co-located with the 17th International Conference on Principles of Knowledge Representation and Reasoning {(KR} 2020), Online Event [Rhodes, Greece], September 12th to 14th, 2020},
  editor = {Stefan {Borgwardt} and Thomas {Meyer}},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {In the Eye of the Beholder: Which Proofs are Best?},
  volume = {2663},
  year = {2020},
}

@inproceedings{ BoHiKoWi-XLoKR20,
  author = {Stefan {Borgwardt} and Anke {Hirsch} and Alisa {Kovtunova} and Frederik {Wiehr}},
  booktitle = {Informal Proceedings of the Explainable Logic-Based Knowledge Representation (XLoKR 2020) workshop co-located with the 17th International Conference on Principles of Knowledge Representation and Reasoning {(KR} 2020), Online Event [Rhodes, Greece], September 13th to 14th, 2020},
  title = {In the Eye of the Beholder: Which Proofs are Best? (Extended Abstract)},
  year = {2020},
}

Recently, we have introduced ontologized programs as a formalism to link description logic ontologies with programs specified in the guarded command language, the de-facto standard input formalism for probabilistic model checking tools such as Prism, to allow for an ontology-mediated verification of stochastic systems. Central to our approach is a complete separation of the two formalisms involved: guarded command language to describe the dynamics of the stochastic system and description logics are used to model background knowledge about the system in an ontology. In ontologized programs, these two languages are loosely coupled by an interface that mediates between these two worlds. Under the original semantics defined for ontologized programs, a program may enter a state that is inconsistent with the ontology, which limits the capabilities of the description logic component. We approach this issue in different ways by introducing consistency notions, and discuss two alternative semantics for ontologized programs. Furthermore, we present complexity results for checking whether a program is consistent under the different semantics.

@inproceedings{ DuKoTu-DL-20,
  author = {Clemens {Dubslaff} and Patrick {Koopmann} and Anni-Yasmin {Turhan}},
  booktitle = {{DL 2020:} International Workshop on Description Logics},
  publisher = {CEUR-WS.org},
  series = {CEUR-WS},
  title = {Give Inconsistency a Chance: Semantics for Ontology-Mediated Verification},
  year = {2020},
}

Metric Temporal Logic (MTL) and Timed Propositional Temporal Logic (TPTL) are quantitative extensions of Linear Temporal Logic (LTL) that are prominent and widely used in the verification of real-timed systems. We study MTL and TPTL as specification languages for one-counter machines. It is known that model checking one-counter machines against formulas of Freeze LTL (FLTL), a strict fragment of TPTL, is undecidable. We prove that in our setting, MTL is strictly less expressive than TPTL, and incomparable in expressiveness to FLTL, so undecidability for MTL is not implied by the result for FLTL. We show, however, that the model-checking problem for MTL is undecidable. We further prove that the satisfiability problem for the unary fragments of TPTL and MTL are undecidable; for TPTL, this even holds for the fragment in which only one register and the finally modality is used. This is opposed to a known decidability result for the satisfiability problem for the same fragment of FLTL.

@article{ FengCFQ-TOCL-20,
  author = {Shiguang {Feng} and Claudia {Carapelle} and Oliver {Fern{\'{a}}ndez Gil} and Karin {Quaas}},
  doi = {https://doi.org/10.1145/3372789},
  journal = {{ACM} Trans. Comput. Log.},
  number = {2},
  pages = {12:1--12:34},
  title = {{MTL} and {TPTL} for One-Counter Machines: Expressiveness, Model Checking, and Satisfiability},
  volume = {21},
  year = {2020},
}

Classical regular path queries (RPQs) can be too restrictive for some applications and answering such queries under approximate semantics to relax the query is desirable. While for answering regular path queries over graph databases under approximate semantics algorithms are available, such algorithms are scarce for the ontology-mediated setting. In this paper we extend an approach for answering RPQs over graph databases that uses weighted transducers to approximate paths from the query in two ways. The first extension is to answering approximate conjunctive 2-way regular path queries (C2RPQs) over graph databases and the second is to answering C2RPQs over ELH and DL-LITE_R ontologies. We provide results on the computational complexity of the underlying reasoning problems and devise approximate query answering algorithms.

@inproceedings{ FeAt-DL-20,
  author = {Oliver {Fern{\'a}ndez Gil} and Anni-Yasmin {Turhan}},
  booktitle = {Proceedings of the 33rd International Workshop on Description Logics (DL'20)},
  publisher = {{CEUR-WS.org}},
  series = {{CEUR} Workshop Proceedings},
  title = {Relaxed Regular Path Queries in Lightweight DLs (Extended Abstract)},
  volume = {2663},
  year = {2020},
}

@inproceedings{ FlLaAlDa-VOILA-20,
  author = {Tamara {Flemisch} and Ricardo {Langner} and Christian {Alrabbaa} and Raimund {Dachselt}},
  booktitle = {Proceedings of the Fifth International Workshop on Visualization and Interaction for Ontologies and Linked Data co-located with the 19th International Semantic Web Conference {(ISWC} 2020), Virtual Conference (originally planned in Athens, Greece), November 02, 2020},
  editor = {Valentina {Ivanova} and Patrick {Lambrix} and Catia {Pesquita} and Vitalis {Wiens}},
  pages = {28--40},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {Towards Designing a Tool For Understanding Proofs in Ontologies through Combined Node-Link Diagrams},
  volume = {2778},
  year = {2020},
}

We define a notion of relevance of a clause for proving a particular entailment by the resolution calculus. We think that our notion of relevance is useful for explaining why an entailment holds. A clause is relevant if there is no proof of the entailment without it. It is semi-relevant if there is a proof of the entailment using it. It is irrelevant if it is not needed in any proof. By using well-known translations of description logics to first-order clause logic, we show that all three notions of relevance are decidable for a number of description logics, including EL and ALC. We provide effective tests for (semi-)relevance. The (semi-)relevance of a DL axiom is defined with respect to the (semi-)relevance of the respective clauses resulting from the translation.

@inproceedings{ HaKoToWe-DL-20,
  author = {Fajar {Haifani} and Patrick {Koopmann} and Sophie {Tourret} and Christoph {Weidenbach}},
  booktitle = {{DL 2020:} International Workshop on Description Logics},
  publisher = {CEUR-WS.org},
  series = {CEUR-WS},
  title = {On a Notion of Relevance},
  year = {2020},
}

Models for Description Logic (DL) ontologies can be used for explanation purposes, but the models computed by standard DL reasoner systems are not necessarily suitable for this task. In this paper we investigate the general task of transforming an arbitrary model into a target model that admits the desired property. To this end, we introduce a general framework for model transformation that abstracts from the DL in use, the property of the target model and the transformation formalism. We consider instantiations of the framework for the DLs \(\mathcal{ALC}\) and \(\mathcal{EL}\) and use transductions as transformation formalism.

@inproceedings{ HiTu-FCR20,
  author = {Willi {Hieke} and Anni-Yasmin {Turhan}},
  booktitle = {Proceedings of the 6th Workshop on Formal and Cognitive Reasoning (FCR-2020) co-located with 43rd German Conference on Artificial Intelligence (KI-2020)},
  editor = {Christoph {Beierle} and Marco {Ragni} and Frieder {Stolzenburg} and Matthias {Thimm}},
  pages = {69--82},
  publisher = {CEUR-WS.org},
  series = {CEUR Workshop Proceedings},
  title = {Towards Model Transformation in Description Logics --- Investigating the Case of Transductions},
  volume = {2680},
  year = {2020},
}

Uniform interpolation and forgetting describe the task of projecting a given ontology into a user-specified vocabulary, that is, of computing a new ontology that only uses names from a specified set of names, while preserving all logical entailments that can be expressed with those names. This is useful for ontology analysis, ontology reuse and privacy. LETHE is a tool for performing uniform interpolation on ontologies in expressive description logics, and it can be used from the command line, using a graphical interface, and as a Java library. It furthermore implements methods for computing logical difference and performing abduction using uniform interpolation. We present the tool together with an evaluation on a varied corpus of realistic ontologies.

@article{ Ko-KI-20,
  author = {Patrick {Koopmann}},
  doi = {https://dx.doi.org/10.1007/s13218-020-00655-w},
  journal = {KI - K\"unstliche Intelligenz},
  title = {LETHE: Forgetting and Uniform Interpolation for Expressive Description Logics},
  year = {2020},
}

In deductive module extraction, we determine a small subset of an ontology for a given vocabulary that preserves all logical entailments that can be expressed in that vocabulary. While in the literature stronger module notions have been discussed, we argue that for applications in ontology analysis and ontology reuse, deductive modules, which are decidable and potentially smaller, are often sufficient. We present methods based on uniform interpolation for extracting different variants of deductive modules, satisfying properties such as completeness, minimality and robustness under replacements, the latter being particularly relevant for ontology reuse. An evaluation of our implementation shows that the modules computed by our method are often significantly smaller than those computed by existing methods.

@inproceedings{ KoCh-IJCAI-20,
  author = {Patrick {Koopmann} and Jieying {Chen}},
  booktitle = {Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, {IJCAI-20}},
  doi = {https://doi.org/10.24963/ijcai.2020/227},
  editor = {Christian {Bessiere}},
  month = {7},
  note = {Main track},
  pages = {1636--1643},
  publisher = {International Joint Conferences on Artificial Intelligence Organization},
  title = {Deductive Module Extraction for Expressive Description Logics},
  year = {2020},
}

@inproceedings{ KoCh-DL-20,
  author = {Patrick {Koopmann} and Jieying {Chen}},
  booktitle = {{DL 2020:} International Workshop on Description Logics},
  publisher = {CEUR-WS.org},
  series = {CEUR-WS},
  title = {Deductive Module Extraction for Expressive Description Logics (Extended Abstract)},
  year = {2020},
}

Signature-based abduction aims at building hypotheses over a specified set of names, the signature, that explain an observation relative to some background knowledge. This type of abduction is useful for tasks such as diagnosis, where the vocabulary used for observed symptoms differs from the vocabulary expected to explain those symptoms. We present the first complete method solving signature-based abduction for observations expressed in the expressive description logic \(\mathcal{ALC}\), which can include TBox and ABox axioms. The method is guaranteed to compute a finite and complete set of hypotheses, and is evaluated on a set of realistic knowledge bases.

@inproceedings{ KoDeToSc-KR-20,
  author = {Patrick {Koopmann} and Warren {Del-Pinto} and Sophie {Tourret} and Renate {Schmidt}},
  booktitle = {Proceedings of the 17th International Conference on Principles of Knowledge Representation and Reasoning (KR 2020)},
  doi = {https://doi.org/10.24963/kr.2020/59},
  title = {Signature-Based Abduction for Expressive Description Logics},
  year = {2020},
}

My thesis describes how methods from Formal Concept Analysis can be used for constructing and extending description logic ontologies. In particular, it is shown how concept inclusions can be axiomatized from data in the description logics \(\mathcal{E\mkern-1.618mu L}\), \(\mathcal{M}\), \(\textsf{Horn-}\mathcal{M}\), and \(\textsf{Prob-}\mathcal{E\mkern-1.618mu L}\). All proposed methods are not only sound but also complete, i.e., the result not only consists of valid concept inclusions but also entails each valid concept inclusion. Moreover, a lattice-theoretic view on the description logic \(\mathcal{E\mkern-1.618mu L}\) is provided. For instance, it is shown how upper and lower neighbors of \(\mathcal{E\mkern-1.618mu L}\) concept descriptions can be computed and further it is proven that the set of \(\mathcal{E\mkern-1.618mu L}\) concept descriptions forms a graded lattice with a non-elementary rank function.

@article{ Kr-KI20,
  author = {Francesco {Kriegel}},
  doi = {https://doi.org/10.1007/s13218-020-00673-8},
  journal = {KI - K{\"{u}}nstliche Intelligenz},
  pages = {399--403},
  title = {{Constructing and Extending Description Logic Ontologies using Methods of Formal Concept Analysis: A Dissertation Summary}},
  volume = {34},
  year = {2020},
}

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-DAM20,
  author = {Francesco {Kriegel}},
  doi = {https://doi.org/10.1016/j.dam.2019.01.029},
  journal = {Discrete Applied Mathematics},
  pages = {172--204},
  title = {{Most Specific Consequences in the Description Logic $\mathcal{E\mkern-1.618mu L}$}},
  volume = {273},
  year = {2020},
}

This work is initially motivated by a privacy scenario in which the confdential information about persons or its properties formulated in description logic (DL) ontologies should be kept hidden. We investigate procedures to detect whether this confidential information can be disclosed in a certain situation by using DL formalisms. If it is the case that this information can be deduced from the ontologies, which implies certain privacy policies are not fulfilled, then one needs to consider methods to repair these ontologies in a minimal way such that the modified ontologies complies with the policies. However, privacy compliance itself is not enough if a possible attacker can also obtain relevant information from other sources, which together with the modified ontologies might violate the privacy policy. This article provides a summary of studies and results from Adrian Nuradiansyah’s Ph.D. dissertation that are corresponding to the addressed problem above with a special emphasis on the investigations on the worst-case complexities of those problems as well as the complexity of the procedures and algorithms solving the problems.

@article{ Nu-KI20,
  author = {Adrian {Nuradiansyah}},
  doi = {https://doi.org/10.1007/s13218-020-00681-8},
  journal = {KI - K{\"{u}}nstliche Intelligenz},
  title = {{Reasoning in Description Logic Ontologies for Privacy Management}},
  year = {2020},
}

@article{ Pe-KI20,
  author = {Maximilian {Pensel}},
  doi = {https://doi.org/10.1007/s13218-020-00644-z},
  journal = {KI - K{\"{u}}nstliche Intelligenz},
  title = {{A Lightweight Defeasible Description Logic in Depth - Quantification in Rational Reasoning and Beyond}},
  year = {2020},
}

A context-sensitive system is often employed in a dynamic environment due to its adaptivity. To represent temporal properties over an evolving system, we study an extension of Contextualised Description Logics (ConDLs) with linear temporal logic (LTL) operators, where ConDL axioms are used in place of propositional variables. The resulting language is interpreted over an infinite sequence of nested DL-interpretations. With El, ALC and SHOQ in consideration, we show that the formalism is rather well-behaved in the sense that the satisfiability problem in most of the instances have the same complexity with underlying ConDLs. This holds even in the presence of rigidity constraints on the object level.

@inproceedings{ Ti-DL2020,
  author = {Satyadharma {Tirtarasa}},
  booktitle = {Proceedings of the 33rd International Workshop on Description Logics {(DL} 2020) co-located with the 17th International Conference on Principles of Knowledge Representation and Reasoning {(KR} 2020), Online Event [Rhodes, Greece], September 12th to 14th, 2020},
  editor = {Stefan {Borgwardt} and Thomas {Meyer}},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {Temporal Properties over Contextualized Description Logics},
  volume = {2663},
  year = {2020},
}

For mixed-initiative control between cyber-physical systems (CPS) and its users, it is still an open question of how machines can safely hand over control to humans. In this work, we propose a concept to provide technological support that uses formal methods from AI - description logic (DL) and automated planning - to predict more reliably when a handover is necessary, and to increase the advance notice for handovers by planning ahead of runtime. We combine this with methods from human-computer interaction and natural language generation to develop solutions for safe and smooth handovers and provide an exemplary automated driving scenario. A possible study design is explained, where the assessment of qualitative feedback, cognitive load and trust in automation can be used for the proposed concept.

@inproceedings{ WiHiDaKrChDeKoBoStHo-CHI20,
  author = {Frederik {Wiehr} and Anke {Hirsch} and Florian {Daiber} and Antonio {Kr\"uger} and Ernie {Chang} and Vera {Demberg} and Alisa {Kovtunova} and Stefan {Borgwardt} and Marcel {Steinmetz} and J\"org {Hoffmann}},
  booktitle = {CHI 2020 workshop: {Designing Safety Critical Interactions: Hunting Down Human Error}},
  series = {CHI '20},
  title = {{Safe Handover in Mixed-Initiative Control for Cyber-Physical Systems}},
  year = {2020},
}

We present a method for answering ontology-mediated queries for DL-Lite extended with a concrete domain, where we allow concrete domain predicates to be used in the query as well. Our method is based on query rewriting, a well-known technique for ontology-based query answering (OBQA), where the knowledge provided by the ontology is compiled into the query so that the rewritten query can be evaluated directly over a database. This technique reduces the problem of query answering w.r.t. an ontology to query evaluation over a database instance. Specifically, we consider members of the DL-Lite family extended with unary and binary concrete domain predicates over the real numbers. While approaches for query rewriting DL-Lite with these concrete domain have been investigated theoretically, these approaches use a combined approach in which also the data is processed, and require the concrete domain values occurring in the data to be known in advance, which makes the procedure data-dependent. In contrast, we show how rewritings can be computed in a data-independent fashion.

@inproceedings{ AlKoTu-GCAI-19,
  author = {Christian {Alrabbaa} and Patrick {Koopmann} and Anni-Yasmin {Turhan}},
  booktitle = {GCAI 2019. Proceedings of the 5th Global Conference on Artificial Intelligence},
  doi = {https://doi.org/10.29007/gqll},
  editor = {Diego {Calvanese} and Luca {Iocchi}},
  pages = {15--27},
  publisher = {EasyChair},
  series = {EPiC Series in Computing},
  title = {Practical Query Rewriting for DL-Lite with Numerical Predicates},
  volume = {65},
  year = {2019},
}

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},
}

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 the DL ALC and in its extension 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.

@article{ Baader-ACR-19,
  author = {Franz {Baader}},
  doi = {https://doi.org/10.1145/3372001.3372002},
  journal = {ACM SIGAPP Applied Computing Review},
  pages = {5--17},
  publisher = {ACM},
  title = {Expressive Cardinality Restrictions on Concepts in a Description Logic with Expressive Number Restrictions},
  volume = {19},
  year = {2019},
}

We consider an expressive description logic (DL) in which the global and local cardinality constraints introduced in previous papers can be mixed. On the one hand, we show that this does not increase the complexity of satisfiability checking and other standard inference problems. On the other hand, conjunctive query entailment in this DL turns out to be undecidable. We prove that decidability of querying can be regained if global and local constraints are not mixed and the global constraints are appropriately restricted.

@inproceedings{ BaBR-DL-19,
  author = {Franz {Baader} and Bartosz {Bednarczyk} and Sebastian {Rudolph}},
  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 = {Satisfiability Checking and Conjunctive Query Answering in Description Logics with Global and Local Cardinality Constraints},
  volume = {2373},
  year = {2019},
}

Selecting patients for clinical trials is very labor-intensive. Our goal is to design (semi-)automated techniques that can support clinical researchers in this task. In this paper we summarize our recent advances towards such a system: First, we present the challenges involved when representing electronic health records and eligibility criteria for clinical trials in a formal language. Second, we introduce temporal conjunctive queries with negation as a formal language suitable to represent clinical trials. Third, we describe our methodology for automatic translation of clinical trial eligibility criteria from natural language into our query language. The evaluation of our prototypical implementation shows promising results. Finally, we talk about the parts we are currently working on and the challenges involved.

@inproceedings{ BBFKXZHQA19,
  address = {Marina del Rey, USA},
  author = {Franz {Baader} and Stefan {Borgwardt} and Walter {Forkel} and Alisa {Kovtunova} and Chao {Xu} and Beihai {Zhou}},
  booktitle = {2nd International Workshop on Hybrid Question Answering with Structured and Unstructured Knowledge (HQA'19)},
  editor = {Franz {Baader} and Brigitte {Grau} and Yue {Ma}},
  title = {Temporalized Ontology-Mediated Query Answering under Minimal-World Semantics},
  year = {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},
}

The probabilistic Description Logic ALC^ME 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^ME, 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^ME 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},
}

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},
}

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://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},
}

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},
  doi = {https://doi.org/10.1007/978-3-030-30179-8_7},
  editor = {Christoph {Benzm{\"u}ller} and Heiner {Stuckenschmidt}},
  pages = {87--100},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Mixing Description Logics in Privacy-Preserving Ontology Publishing},
  volume = {11793},
  year = {2019},
}

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},
}

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-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},
}

@inproceedings{ BoFo-IJCAI19,
  address = {Macao, China},
  author = {Stefan {Borgwardt} and Walter {Forkel}},
  booktitle = {Proceedings of the 28th International Joint Conference on Artificial Intelligence (IJCAI'19)},
  doi = {https://doi.org/10.24963/ijcai.2019/849},
  editor = {Sarit {Kraus}},
  note = {Invited contribution to Sister Conference Best Paper Track.},
  pages = {6131--6135},
  publisher = {IJCAI},
  title = {Closed-World Semantics for Conjunctive Queries with Negation over {$\mathcal{ELH}_\bot$} Ontologies},
  year = {2019},
}

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},
}

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},
}

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)},
  doi = {https://doi.org/10.1007/978-3-030-31095-0_1},
  editor = {Paul {Fodor} and Marco {Montali} and Diego {Calvanese} and Dumitru {Roman}},
  pages = {3--18},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Finding New Diamonds: {T}emporal Minimal-World Query Answering over Sparse {AB}oxes},
  volume = {11784},
  year = {2019},
}

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},
}

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},
}

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-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},
}

Probabilistic model checking (PMC) is a well-established method for the quantitative analysis of dynamic systems. Description logics (DLs) provide a well-suited formalism to describe and reason about terminological knowledge, used in many areas to specify background knowledge on the domain. We investigate how such knowledge can be integrated into the PMC process, introducing ontology-mediated PMC. Specifically, we propose a formalism that links ontologies to dynamic behaviors specified by guarded commands, the de-facto standard input formalism for PMC tools such as Prism. Further, we present and implement a technique for their analysis relying on existing DL-reasoning and PMC tools. This way, we enable the application of standard PMC techniques to analyze knowledge-intensive systems. Our approach is implemented and evaluated on a multi-server system case study, where different DL-ontologies are used to provide specifications of different server platforms and situations the system is executed in.

@inproceedings{ DKT-iFM-19,
  author = {Clemens {Dubslaff} and Patrick {Koopmann} and Anni{-}Yasmin {Turhan}},
  booktitle = {Proceedings of the 15th International Conference on Integrated Formal Methods (iFM'19)},
  doi = {https://doi.org/10.1007/978-3-030-34968-4\_11},
  editor = {Wolfgang {Ahrendt} and Silvia Lizeth {Tapia Tarifa}},
  note = {Best Paper Award.},
  pages = {194--211},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Ontology-Mediated Probabilistic Model Checking},
  volume = {11918},
  year = {2019},
}

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},
}

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},
}

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-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},
}

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://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},
}

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://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},
}

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)},
  doi = {https://doi.org/10.1007/978-3-030-31095-0\_9},
  editor = {Paul {Fodor} and Marco {Montalil}},
  publisher = {Springer},
  series = {LNCS},
  title = {Efficient TBox Reasoning with Value Restrictions---Introducing the FLower Reasoner},
  year = {2019},
}

Many SPARQL benchmark generation techniques rely on SPARQL query templates or on selecting representative queries from a set of input queries by inspecting their syntactic features. Hence, prototype queries from such benchmarks mainly capture combinations of SPARQL features, but not the semantics nor the conceptual association between queries. We present congenial benchmarks—–a novel type of benchmark that can detect conceptual associations and thus reflect prototypical user intentions when selecting prototype queries. We study Sparrow, an instantiation of congenial benchmarks, where the conceptual associations of SPARQL queries are measured by concept similarity measures. To this end, we transform unary acyclic conjunctive SPARQL queries into ELH-description logic concepts. Our evaluation of three popular triple stores on two datasets shows that the benchmarks generated by Sparrow differ considerably from benchmarks generated using a feature-based approach. Moreover, our evaluation suggests that Sparrow can characterize the performance of common triple stores with respect to user needs by exploiting conceptual associations to detect prototypical user needs.

@inproceedings{ NCPT-KCap-19,
  author = {Axel-Cyrille Ngonga {Ngomo} and Felix {Conrads} and Maximilian {Pensel} and Anni-Yasmin {Turhan}},
  booktitle = {Proceedings of the 10th International Conference on Knowledge Capture (K-CAP 2019)},
  doi = {https://doi.org/10.1145/3360901.3364429},
  editor = {Mayank {Kejriwal} and Pedro A. {Szekely} and Rapha{\"{e}}l {Troncy}},
  month = {November 19-21},
  pages = {213--221},
  title = {Congenial Benchmarking of RDF Storage Solutions},
  year = {2019},
}

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 ALCO is the underlying DL.

@inproceedings{ TiZa-GCAI-19,
  author = {Satyadharma {Tirtarasa} and Benjamin {Zarrie{\ss}}},
  booktitle = {GCAI 2019. Proceedings of the 5th Global Conference on Artificial Intelligence},
  doi = {https://doi.org/10.29007/s7cm},
  editor = {Diego {Calvanese} and Luca {Iocchi}},
  pages = {81--93},
  publisher = {EasyChair},
  series = {EPiC Series in Computing},
  title = {Projection in a Description Logic of Context with Actions},
  volume = {65},
  year = {2019},
}

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},
}

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://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},
}

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 = {Martin {Boeker} and Ludger {Jansen} and Frank {Loebe} and Stefan {Schulz}},
  series = {CEUR Workshop Proceedings},
  title = {Automatic Translation of Clinical Trial Eligibility Criteria into Formal Queries},
  volume = {2518},
  year = {2019},
}

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},
}

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://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},
}

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{ 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://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},
}

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://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},
}

@inproceedings{ BaFeRo-DL-21,
  author = {Franz {Baader} and Oliver {Fern{\'a}ndez Gil} and Maximilian {Pensel}},
  booktitle = {Proceedings of the 31th International Workshop on Description Logics ({DL} 2018), Arizona, US, October 27--29, 2018},
  editor = {Magdalena {Ortiz} and Thomas {Schneider}},
  publisher = {CEUR-WS.org},
  series = {{CEUR} Workshop Proceedings},
  title = {Standard and Non-Standard Inferences in the Description Logic {$\mathcal{FL}_0$} Using Tree Automata},
  volume = {2211},
  year = {2018},
}

@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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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_bot 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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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{ 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},
}

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},
}

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{ 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},
}

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},
}

@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},
}

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},
}

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},
}

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},
}

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://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},
}

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},
}

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://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},
}

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},
}

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},
}

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},
}

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},
}

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^PP-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},
}

@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},
}

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},
}

@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},
}

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},
}

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},
}

@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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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://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},
}

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},
}

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},
}

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},
}

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},
}

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://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},
}

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},
}

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},
}

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_bot 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://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},
}

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_bot 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},
}

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},
}

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://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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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{ ecaiBaFe16,
  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},
}

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},
}

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},
}

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},
}

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://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},
}

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},
}

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},
}

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-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},
}

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},
}

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},
}

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},
}

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://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},
}

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^PP-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},
}

@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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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-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},
}

@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},
}

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},
}

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},
}

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},
}

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},
}

@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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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-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 {$\mathcal{EL}$}},
  volume = {1350},
  year = {2015},
}

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},
}

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},
}

@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},
}

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},
}

@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},
}

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://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},
}

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},
}

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},
}

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://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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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 {Mailis} 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},
}

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://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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

@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},
}

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},
}

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},
}

We study the fuzzy extension of FL₀ 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},
}

We study the fuzzy extension of the Description Logic FL₀ 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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

@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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

@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},
}

@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},
}

@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},
}

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 C², 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},
}

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 C² 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},
}

Adequate encodings for high-level constraints are a key ingredient for the application of SAT technology. In particular, cardinality constraints state that at most (at least, or exactly) \(k\) out of \(n\) propositional variables can be true. They are crucial in many applications. Although sophisticated encodings for cardinality constraints exist, it is well known that for small \(n\) and \(k\) straightforward encodings without auxiliary variables sometimes behave better, and that the choice of the right trade-off between minimizing either the number of variables or the number of clauses is highly application-dependent. Here we build upon previous work on Cardinality Networks to get the best of several worlds: we develop an arc-consistent encoding that, by recursively de-composing the constraint into smaller ones, allows one to decide which encoding to apply to each sub-constraint. This process minimizes a function \(λ·numvars+numclauses\), being \(λ\) a parameter that can be tuned by the user. Our careful experimental evaluation shows that (e.g., for \(λ=5\) ) this new technique produces much smaller encodings in variables and clauses, and indeed strongly improves SAT solvers' performance.

@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},
}

@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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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{ 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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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_core-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},
}

@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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

@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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

@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},
}

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-EL⁰1: 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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

@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},
}

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},
}

@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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

@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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

@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},
}

@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},
}

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},
}

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},
}

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},
}

@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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

Axiom-Pinpointing bestimmt die f&uuml;r eine Konsequenz verantwortlichen Axiome einer Ontologie und unterst&uuml;tzt dadurch die Suche und Behebung von Fehlern. In der Dissertation von Rafael Pe&ntilde;aloza, deren Resultate hier zusammengefasst werden, wurde untersucht, unter welchen Bedingungen sich tableau-artige und auf automaten-basierte Schlussfolgerungsverfahren f&uuml;r Beschreibungslogiken stets zu Pinpointing-Verfahren erweitern lassen. Zus&auml;tzlich wurde die Komplexit&auml;t 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},
}

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_core^H, DL-Lite_krom^H and DL-Lite_horn^N TBoxes MinAs are efficiently enumerable with polynomial delay, but for DL-Lite_bool 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},
}

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},
}

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},
}

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-EL⁰1.

@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},
}

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-EL⁰1.

@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},
}

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 &mdash; 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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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{ 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},
}

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},
}

The diversity of today’s 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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

@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},
}

@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},
}

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},
}

@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},
}

@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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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{ 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},
}

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},
}

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},
}

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},
}

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},
}

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&mdash;based on a method from formal concept analysis&mdash;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},
}

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},
}