Research projects

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},
  note = {(to appear)},
  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)},
  note = {(to appear)},
  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},
}

@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)},
  note = {(to appear)},
  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},
  note = {(to appear)},
  publisher = {CEUR-WS.org},
  title = {Finding Good Proofs for Answers to Conjunctive Queries Mediated by Lightweight Ontologies (Extended Abstract)},
  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},
}

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.

@techreport{ BaKoKrNu-LTCS-22-01,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Patrick {Koopmann} and Francesco {Kriegel} and Adrian {Nuradiansyah}},
  doi = {https://doi.org/10.25368/2022.65},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  number = {22-01},
  title = {Optimal ABox Repair w.r.t.\ Static {$\mathcal{EL}$} TBoxes: from Quantified ABoxes back to ABoxes (Extended Version)},
  type = {LTCS-Report},
  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},
  note = {To appear.},
  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},
}

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. 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.

@techreport{ BaKr-LTCS-22-02,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Francesco {Kriegel}},
  doi = {https://doi.org/10.25368/2022.131},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  number = {22-02},
  title = {Pushing Optimal ABox Repair from {$\mathcal{EL}$} Towards More Expressive Horn-DLs (Extended Version)},
  type = {LTCS-Report},
  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},
}

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},
}

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},
  note = {To appear.},
  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},
}

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},
}

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},
}

Unification in the Description Logic (DL) FL0 is known to be ExpTime-complete, and of unification type zero. We investigate in this paper 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, which is however also of interest in its own right, 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.

@techreport{ BaGiRo21,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Oliver {Fern\'andez Gil} and Maryam {Rostamigiv}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  number = {21-02},
  title = {Restricted Unification in the {DL} {$\mathcal{FL}_0$} (Extended Version)},
  type = {LTCS-Report},
  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},
  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.

@techreport{ BaKoKrNuPe-LTCS-21-04,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Patrick {Koopmann} and Francesco {Kriegel} and Adrian {Nuradiansyah} and Rafael {Pe\~{n}aloza}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  number = {21-04},
  title = {{Privacy-Preserving Ontology Publishing: The Case of Quantified ABoxes w.r.t.\ a Static Cycle-Restricted $\mathcal{EL}$ TBox (Extended Version)}},
  type = {LTCS-Report},
  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},
}

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},
}

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},
}

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.

@techreport{ Ko-LTCS-21-03,
  author = {Patrick {Koopmann}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {\url{https://lat.inf.tu-dresden.de/research/reports.html}},
  number = {21-03},
  title = {Two Ways of Explaining Negative Entailments in Description Logics Using Abduction (Extended Version)},
  type = {LTCS-Report},
  year = {2021},
}

Description Logics are used in a range of different fields. The main research areas study the applications, extensions and their complexity. This thesis is dedicated to evaluate the quality of models for Description Logics. For this purpose, it is shown how weighted alternating tree automata can be used to measure features of models. Afterwards, based on these automata, methods are proposed to enforce features of models to given thresholds. Finally, an alternating tree automaton is defined which accepts exactly those models that conform to the given feature restrictions.

@thesis{ Krud-21,
  address = {Dresden, Germany},
  author = {Jakob {Krude}},
  school = {Technische Universit{\"a}t Dresden},
  title = {Measuring Description Logic Models using Weighted Tree Automata},
  type = {Bachelor's Thesis},
  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},
}

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.

@techreport{ BaKa-LTCS-20-02,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Deepak {Kapur}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  number = {20-02},
  title = {Deciding the Word Problem for Ground Identities with Commutative and Extensional Symbols},
  type = {LTCS-Report},
  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},
}

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.

@techreport{ BaRy-LTCS-20-10,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Jakub {Rydval}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  number = {20-10},
  title = {An Algebraic View on p-Admissible Concrete Domains for Lightweight Description Logics (Extended Version)},
  type = {LTCS-Report},
  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},
}

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},
}

@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},
}

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},
}

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},
}

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.

@techreport{ KoCh-LTCS-20-06,
  author = {Patrick {Koopmann} and Jieying {Chen}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {\url{https://lat.inf.tu-dresden.de/research/reports.html}},
  number = {20-06},
  title = {Deductive Module Extraction for Expressive Description Logics (Extended Version)},
  type = {LTCS-Report},
  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},
}

The reasoning task of a temporal version of ontology-based data access can be solved with the help of a bounded history encoding (BHE). By rewriting temporal queries, the reasoning task can be reduced to query answering over temporal databases. The BHE under consideration in this work is one approach to solve this task [1]. In this thesis, an implementation of this BHE is evaluated, to investigate its helpfulness in a practical application. Criteria to assess the degree of helpfulness are the size of the encoding, the time it takes to answer one query per time point, and the usefulness of the answers. The BHE is applied to observe an online automotive marketplace and then to answer a set of specified queries at each time point. The queries were explicitly chosen to help evaluate the BHE's degree of helpfulness. To provide useful answers, the BHE had to be extended by appropriate operators. The evaluation of the extended BHE shows that it can provide useful answers in reasonable time. An upper bound was found for the size of the encoding, which determines from what number of time points on the BHE is superior.

@thesis{ Nebe-Bac-20,
  address = {Dresden, Germany},
  author = {Thure {Nebendahl}},
  school = {Technische Universit{\"a}t Dresden},
  title = {Experimental Evaluation of a Bounded History Encoding},
  type = {Bachelor's Thesis},
  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},
}

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},
}

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 restrictions 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.

@techreport{ BaBo-LTCS-19-09,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Filippo {De Bortoli}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {\url{https://tu-dresden.de/inf/lat/reports#BaBo-LTCS-19-09}},
  number = {19-09},
  title = {{On the Complexity and Expressiveness of Description Logics with Counting}},
  type = {LTCS-Report},
  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},
}

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.

@techreport{ BaTh-LTCS-19-08,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Cl\'ement {Th\'eron}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {\url{https://tu-dresden.de/inf/lat/reports#BaTh-LTCS-19-08}},
  number = {19-08},
  title = {Role-Value Maps and General Concept Inclusions in the Description Logic {$\mathcal{FL}_0$}},
  type = {LTCS-Report},
  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},
}

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},
}

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 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 lower bound for the setting in which both types of operators can be used together.

@techreport{ Ko-LTCS-19-03,
  address = {Dresden, Germany},
  author = {Patrick {Koopmann}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {see \url{https://lat.inf.tu-dresden.de/research/reports.html}},
  number = {19-03},
  title = {Maybe Eventually? Towards Combining Temporal and Probabilistic Description Logics and Queries (Extended Version)},
  type = {LTCS-Report},
  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},
}

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},
}

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},
}

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.

@techreport{ BaBoKoOzTh-LTCS-17-03,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Stefan {Borgwardt} and Patrick {Koopmann} and Ana {Ozaki} and Veronika {Thost}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {see \url{https://lat.inf.tu-dresden.de/research/reports.html}},
  number = {17-03},
  title = {Metric Temporal Description Logics with Interval-Rigid Names (Extended Version)},
  type = {LTCS-Report},
  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},
}

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},
}

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},
}

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},
}

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 (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},
}

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},
}

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},
}

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},
}

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},
}

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 the possibility to extract terminological knowledge from the Linked Open Data Cloud. We shall also present first experimental results showing that our approach has the potential to be useful for practical applications.

@techreport{ BoDiKr-LTCS-15-13,
  address = {Dresden, Germany},
  author = {Daniel {Borchmann} and Felix {Distel} and Francesco {Kriegel}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {\url{https://tu-dresden.de/inf/lat/reports#BoDiKr-LTCS-15-13}},
  number = {15-13},
  title = {{Axiomatization of General Concept Inclusions from Finite Interpretations}},
  type = {LTCS-Report},
  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.

@techreport{ BoCP-LTCS-15-06,
  address = {Dresden, Germany},
  author = {Stefan {Borgwardt} and Marco {Cerami} and Rafael {Pe{\~n}aloza}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See http://lat.inf.tu-dresden.de/research/reports.html.},
  number = {15-06},
  title = {Subsumption in Finitely Valued Fuzzy {$\mathcal{EL}$}},
  type = {LTCS-Report},
  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},
}

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) 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. Despite its apparent simplicity, developing reasoning techniques for expressive FDLs under this semantics is a hard task. We present a tableau algorithm for deciding consistency of a SROIQ ontology under Gödel semantics. This is the first algorithm that can handle the full expressivity of SROIQ as well as the full Gödel semantics.

@techreport{ BoPe-LTCS-15-18,
  address = {Germany},
  author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}},
  institution = {Chair for Automata Theory, Technische Universit{\"a}t Dresden},
  number = {15-18},
  title = {A Tableau Algorithm for {$\mathcal{SROIQ}$} under Infinitely Valued {G}{\"o}del Semantics},
  type = {LTCS-Report},
  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.

@techreport{ BoPe-LTCS-15-11,
  address = {Dresden, Germany},
  author = {Stefan {Borgwardt} and Rafael {Pe{\~n}aloza}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See http://lat.inf.tu-dresden.de/research/reports.html.},
  number = {15-11},
  title = {Infinitely Valued G{\"o}del Semantics for Expressive Description Logics},
  type = {LTCS-Report},
  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},
}

@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},
}

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},
}

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},
}

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},
}

@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},
}

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},
}

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},
}

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},
}

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.

@techreport{ LuPe-LTCS-14-11,
  address = {Dresden, Germany},
  author = {Michel {Ludwig} and Rafael {Pe{\~n}aloza}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See \url{http://lat.inf.tu-dresden.de/research/reports.html}.},
  number = {14-11},
  title = {Error-Tolerant Reasoning in the Description Logic EL},
  type = {LTCS-Report},
  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.

@techreport{ MaPe-LTCS-14-05,
  address = {Dresden, Germany},
  author = {Yue {Ma} and Rafael {Pe{\~n}aloza}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See \url{http://lat.inf.tu-dresden.de/research/reports.html}.},
  number = {14-05},
  title = {Towards Parallel Repair Using Decompositions},
  type = {LTCS-Report},
  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},
}

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},
}

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},
}

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},
}

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},
}

@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},
}

@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},
}

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},
}

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},
  note = {(to appear)},
  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)},
  note = {(to appear)},
  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},
}

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},
}

Concrete domains have been introduced in the area of 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. 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 \(\mathcal{ALC}\) in the presence of GCIs, quite strong restrictions, 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 \(\mathcal{EL}\) family, achieving decidability of reasoning is not enough. One wants 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 \(\mathcal{ALC}\) yields decidable DLs.

DL systems that can handle concrete domains allow their users to employ a fixed set of predicates of one or more fixed concrete domains when modelling concepts. They do not provide their users with means for defining new predicates, let alone new concrete domains. The good news is that finitely bounded homogeneous structures offer precisely that. We show that integrating concrete domains based on finitely bounded homogeneous structures into \(\mathcal{ALC}\) yields decidable DLs even if we allow predicates specified by first-order formulas. This class of structures also provides effective means for defining new \(\omega\)-admissible concrete domains with at most binary predicates. The bad news is that defining \(\omega\)-admissible concrete domains with predicates of higher arities is computationally hard. We obtain two new lower bounds for this meta-problem, but leave its decidability open. In contrast, we prove that there is no algorithm that would facilitate defining p-admissible concrete domains already for binary signatures.

@thesis{ Rydval-Diss-2022,
  address = {Dresden, Germany},
  author = {Jakub {Rydval}},
  school = {Technische Universit\"{a}t Dresden},
  title = {Using Model Theory to Find Decidable and Tractable Description Logics with Concrete Domains},
  type = {Doctoral Thesis},
  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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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 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 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.

@techreport{ BaRy-LTCS-20-10,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Jakub {Rydval}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  number = {20-10},
  title = {An Algebraic View on p-Admissible Concrete Domains for Lightweight Description Logics (Extended Version)},
  type = {LTCS-Report},
  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},
}

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.

@techreport{ BaRy-LTCS-20-01,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Jakub {Rydval}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  number = {20-01},
  title = {Using Model-Theory to Find $\omega$-Admissible Concrete Domains},
  type = {LTCS-Report},
  year = {2020},
}

@techreport{ BoPaRy-LTCS-20-04,
  address = {Dresden, Germany},
  author = {Manuel {Bodirsky} and Wied {Pakusa} and Jakub {Rydval}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  number = {20-04},
  title = {Temporal Constraint Satisfaction Problems in Fixed-Point Logic},
  type = {LTCS-Report},
  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},
}

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},
}

@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},
}

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},
}

@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},
}

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},
}

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 restrictions 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.

@techreport{ BaBo-LTCS-19-09,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Filippo {De Bortoli}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {\url{https://tu-dresden.de/inf/lat/reports#BaBo-LTCS-19-09}},
  number = {19-09},
  title = {{On the Complexity and Expressiveness of Description Logics with Counting}},
  type = {LTCS-Report},
  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},
}

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},
}

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. Together with the special case of matching, they were first investigated in detail for the DL FL0, where these problems can be reduced to solving certain language equations. In this thesis, we extend this service in two directions. 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, in order to account for potential small modelling errors. 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 particular distance measures. Furthermore, we make a first step towards integrating background knowledge, formulated in so-called TBoxes, by investigating the special case of matching in the presence of TBoxes of different forms. We acquire a tight complexity bound for the general case, while we prove that the problem becomes easier in a restricted setting. To achieve these bounds, we take advantage of an equivalence characterization of FL0 concepts that is based on formal languages. In addition, we incorporate TBoxes in computing concept distances. Even though our results on the approximate setting cannot deal with TBoxes yet, we prepare the framework that future research can build on. Before we journey to the technical details of the above investigations, we showcase our program in the simpler setting of the equational theory ACUI, where we are able to also combine the two extensions. In the course of studying the above problems, we make heavy use of automata theory, where we also derive novel results that could be of independent interest.

@thesis{ Marantidis-Diss-2019,
  address = {Dresden, Germany},
  author = {Pavlos {Marantidis}},
  school = {Technische Universit\"{a}t Dresden},
  title = {Quantitative Variants of Language Equations and their Applications to Description Logics},
  type = {Doctoral Thesis},
  year = {2019},
}

Description Logics (DLs) are increasingly successful knowledge representation formalisms, useful for any application requiring implicit derivation of knowledge from explicitly known facts. A prominent example domain benefiting from these formalisms since the 1990s is the biomedical field. This area contributes an intangible amount of facts and relations between low- and high-level concepts such as the constitution of cells or interactions between studied illnesses, their symptoms and remedies. DLs are well-suited for handling large formal knowledge repositories and computing inferable coherences throughout such data, relying on their well-founded first-order semantics. In particular, DLs of reduced expressivity have proven a tremendous worth for handling large ontologies due to their computational tractability. In spite of these assets and prevailing influence, classical DLs are not well-suited to adequately model some of the most intuitive forms of reasoning. The capability for abductive reasoning is imperative for any field subjected to incomplete knowledge and the motivation to complete it with typical expectations. When such default expectations receive contradicting evidence, an abductive formalism is able to retract previously drawn, conflicting conclusions. Common examples often include human reasoning or a default characterisation of properties in biology, such as the normal arrangement of organs in the human body. Treatment of such defeasible knowledge must be aware of exceptional cases - such as a human suffering from the congenital condition situs inversus - and therefore accommodate for the ability to retract defeasible conclusions in a non-monotonic fashion. Specifically tailored non-monotonic semantics have been continuously investigated for DLs in the past 30 years. A particularly promising approach, is rooted in the research by Kraus, Lehmann and Magidor for preferential (propositional) logics and Rational Closure (RC). The biggest advantages of RC are its well-behaviour in terms of formal inference postulates and the efficient computation of defeasible entailments, by relying on a tractable reduction to classical reasoning in the underlying formalism. A major contribution of this work is a reorganisation of the core of this reasoning method, into an abstract framework formalisation. This framework is then easily instantiated to provide the reduction method for RC in DLs as well as more advanced closure operators, such as Relevant or Lexicographic Closure. In spite of their practical aptitude, we discovered that all reduction approaches fail to provide any defeasible conclusions for elements that only occur in the relational neighbourhood of the inspected elements. More explicitly, a distinguishing advantage of DLs over propositional logic is the capability to model binary relations and describe aspects of a related concept in terms of existential and universal quantification. Previous approaches to RC (and more advanced closures) are not able to derive typical behaviour for the concepts that occur within such quantification. The main contribution of this work is to introduce stronger semantics for the lightweight DL EL_bot with the capability to infer the expected entailments, while maintaining a close relation to the reduction method. We achieve this by introducing a new kind of first-order interpretation that allocates defeasible information on its elements directly. This allows to compare the level of typicality of such interpretations in terms of defeasible information satisfied at elements in the relational neighbourhood. A typicality preference relation then provides the means to single out those sets of models with maximal typicality. Based on this notion, we introduce two types of nested rational semantics, a sceptical and a selective variant, each capable of deriving the missing entailments under RC for arbitrarily nested quantified concepts. As a proof of versatility for our new semantics, we also show that the stronger Relevant Closure, can be imbued with typical information in the successors of binary relations. An extensive investigation into the computational complexity of our new semantics shows that the sceptical nested variant comes at considerable additional effort, while the selective semantics reside in the complexity of classical reasoning in the underlying DL, which remains tractable in our case.

@thesis{ Pensel-Diss-2019,
  address = {Dresden, Germany},
  author = {Maximilian {Pensel}},
  school = {Technische Universit\"{a}t Dresden},
  title = {A Lightweight Defeasible Description Logic in Depth: Quantification in Rational Reasoning and Beyond},
  type = {Doctoral Thesis},
  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},
}

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.

@techreport{ BaFePe-LTCS-18-04,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Oliver {Fern{\'a}ndez Gil} and Maximilian {Pensel}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See http://lat.inf.tu-dresden.de/research/reports.html},
  number = {18-04},
  title = {Standard and Non-Standard Inferences in the Description Logic $\mathcal{FL}_0$ Using Tree Automata},
  type = {LTCS-Report},
  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},
}

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},
}

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},
}

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},
}

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},
}

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. In this report, we present a new approach for EL_bot that alleviates this problem for relevant closure (the strongest form of preferential reasoning currently investigated) by the use of typicality models that extend classical canonical models by domain elements that individually satisfy any amount of consistent defeasible knowledge. We also show that a certain restriction on the domain of the typicality models in this approach yields inference results that correspond to the (weaker) more commonly known rational closure.

@techreport{ PeTu-LTCS-17-01,
  address = {Dresden, Germany},
  author = {Maximilian {Pensel} and Anni-Yasmin {Turhan}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See http://lat.inf.tu-dresden.de/research/reports.html},
  number = {17-01},
  title = {Making Quantification Relevant again---the Case of Defeasible $\mathcal{EL}_{\bot}$},
  type = {LTCS-Report},
  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},
}

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 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).

@techreport{ BaFe-LTCS-16-07,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Oliver {Fern{\'a}ndez Gil}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See http://lat.inf.tu-dresden.de/research/reports.html},
  number = {16-07},
  title = {Decidability and Complexity of Threshold Description Logics Induced by Concept Similarity Measures},
  type = {LTCS-Report},
  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.

@techreport{ BaFe-LTCS-16-02,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Oliver {Fern{\'a}ndez Gil}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See http://lat.inf.tu-dresden.de/research/reports.html},
  number = {16-02},
  title = {Extending the Description Logic $\tau\mathcal{EL}(deg)$ with Acyclic TBoxes},
  type = {LTCS-Report},
  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},
}

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.

@techreport{ BaFM-LTCS-16-08,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Oliver {Fern{\'a}ndez Gil} and Pavlos {Marantidis}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See http://lat.inf.tu-dresden.de/research/reports.html},
  number = {16-08},
  title = {Approximation in Description Logics: How Weighted Tree Automata Can Help to Define the Required Concept Comparison Measures in $\mathcal{FL}_0$},
  type = {LTCS-Report},
  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 \(\mathcal{FL}_0\), 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 \(\mathcal{FL}_0\) can be reduced to approximately solving language equations, and devise algorithms for solving the latter problem for two particular distance measures.

@techreport{ BaMaOk-LTCS-16-04,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Pavlos {Marantidis} and Alexander {Okhotin}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See http://lat.inf.tu-dresden.de/research/reports.html},
  number = {16-04},
  title = {Approximate Unification in the Description Logic {$\mathcal{FL}_0$}},
  type = {LTCS-Report},
  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 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 \(\ell\) violations for a given threshold value \(\ell\).

@techreport{ BaMaOk-LTCS-16-03,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Pavlos {Marantidis} and Alexander {Okhotin}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See http://lat.inf.tu-dresden.de/research/reports.html},
  number = {16-03},
  title = {Approximately Solving Set Equations},
  type = {LTCS-Report},
  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},
}

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 a concrete domain 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 decidability was open. More generally, this result holds for all negation-closed concrete domains with the EHD-property, which stands for `the existence of a homomorphism is definable'. Such technique has recently been used to show decidability of CTL* with local constraints over the integers.

@techreport{ CaTu-LTCS-16-01,
  address = {Dresden, Germany},
  author = {Claudia {Carapelle} and Anni-Yasmin {Turhan}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  number = {16-01},
  title = {Decidability of $\mathcal{ALC}^P\!(\mathcal{D})$ for concrete domains with the EHD-property},
  type = {LTCS-Report},
  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},
}

Description Logics (DLs) are a family of logic-based knowledge representation languages used to describe the knowledge of an application domain and reason about it in formally well-defined way. They allow users to describe the important notions and classes of the knowledge domain as concepts, which formalize the necessary and sufficient conditions for individual objects to belong to that concept. A variety of different DLs exist, differing in the set of properties one can use to express concepts, the so-called concept constructors, as well as the set of axioms available to describe the relations between concepts or individuals. However, all classical DLs have in common that they can only express exact knowledge, and correspondingly only allow exact inferences. Either we can infer that some individual belongs to a concept, or we can't, there is no in-between. In practice though, knowledge is rarely exact. Many definitions have their exceptions or are vaguely formulated in the first place, and people might not only be interested in exact answers, but also in alternatives that are "close enough".

This thesis is aimed at tackling how to express that something "close enough", and how to integrate this notion into the formalism of Description Logics. To this end, we will use the notion of similarity and dissimilarity measures as a way to quantify how close exactly two concepts are. We will look at how useful measures can be defined in the context of DLs, and how they can be incorporated into the formal framework in order to generalize it. In particular, we will look closer at two applications of thus measures to DLs: Relaxed instance queries will incorporate a similarity measure in order to not just give the exact answer to some query, but all answers that are reasonably similar. Prototypical definitions on the other hand use a measure of dissimilarity or distance between concepts in order to allow the definitions of and reasoning with concepts that capture not just those individuals that satisfy exactly the stated properties, but also those that are "close enough".

@thesis{ Ecke-PhD-2016,
  address = {Dresden, Germany},
  author = {Andreas {Ecke}},
  school = {Technische Universit\"{a}t Dresden},
  title = {Quantitative Methods for Similarity in Description Logics},
  type = {Doctoral Thesis},
  year = {2016},
}

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},
}

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},
}

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 tel(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 tel(deg) with the relaxed instance queries of Ecke et al.

@techreport{ BaBrF-LTCS-15-09,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Gerhard {Brewka} and Oliver Fern{\'a}ndez {Gil}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See http://lat.inf.tu-dresden.de/research/reports.html.},
  number = {15-09},
  title = {Adding Threshold Concepts to the Description Logic $\mathcal{E\!L}$},
  type = {LTCS-Report},
  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},
}

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 the possibility to extract terminological knowledge from the Linked Open Data Cloud. We shall also present first experimental results showing that our approach has the potential to be useful for practical applications.

@techreport{ BoDiKr-LTCS-15-13,
  address = {Dresden, Germany},
  author = {Daniel {Borchmann} and Felix {Distel} and Francesco {Kriegel}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {\url{https://tu-dresden.de/inf/lat/reports#BoDiKr-LTCS-15-13}},
  number = {15-13},
  title = {{Axiomatization of General Concept Inclusions from Finite Interpretations}},
  type = {LTCS-Report},
  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},
}

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},
}

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},
}

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.

@techreport{ BaLi-LTCS-14-01,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Marcel {Lippmann}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See \url{http://lat.inf.tu-dresden.de/research/reports.html}.},
  number = {14-01},
  title = {Runtime Verification Using a Temporal Description Logic Revisited},
  type = {LTCS-Report},
  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},
}

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},
}

Description logics (DLs) are used to represent knowledge of an application domain and provide standard reasoning services to infer consequences of this knowledge. However, classical DLs are not suited to represent vagueness in the description of the knowledge. We consider a combination of DLs and Fuzzy Logics to address this task. In particular, we consider the t-norm-based semantics for fuzzy DLs introduced by Hajek in 2005. Since then, many tableau algorithms have been developed for reasoning in fuzzy DLs. Another popular approach is to reduce fuzzy ontologies to classical ones and use existing highly optimized classical reasoners to deal with them. However, a systematic study of the computational complexity of the different reasoning problems is so far missing from the literature on fuzzy DLs. Recently, some of the developed tableau algorithms have been shown to be incorrect in the presence of general concept inclusion axioms (GCIs). In some fuzzy DLs, reasoning with GCIs has even turned out to be undecidable. This work provides a rigorous analysis of the boundary between decidable and undecidable reasoning problems in t-norm-based fuzzy DLs, in particular for GCIs. Existing undecidability proofs are extended to cover large classes of fuzzy DLs, and decidability is shown for most of the remaining logics considered here. Additionally, the computational complexity of reasoning in fuzzy DLs with semantics based on finite lattices is analyzed. For most decidability results, tight complexity bounds can be derived.

@thesis{ Borgwardt-Diss-2014,
  address = {Dresden, Germany},
  author = {Stefan {Borgwardt}},
  school = {Technische Universit\"{a}t Dresden},
  title = {Fuzzy Description Logics with General Concept Inclusions},
  type = {Doctoral Thesis},
  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},
}

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},
}

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},
}

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},
}

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},
}

We present a general form of attribute exploration, a knowledge completion algorithm from formal concept analysis. The aim of this generalization is to extend the applicability of attribute exploration by a general description. Additionally, this may also allow for viewing different existing variants of attribute exploration as instances of a general form, as for example exploration on partial contexts.

@techreport{ Borc-LTCS-13-02,
  address = {Dresden, Germany},
  author = {Daniel {Borchmann}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See http://lat.inf.tu-dresden.de/research/reports.html.},
  number = {13-02},
  title = {{A General Form of Attribute Exploration}},
  type = {LTCS-Report},
  year = {2013},
}

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. We present in this work a generalization of attribute exploration based on the notion of confidence, which will allow for the exploration of implications which are not necessarily valid in the initial data, but instead enjoy a minimal confidence therein.

@techreport{ Borch-LTCS-13-04,
  address = {Dresden, Germany},
  author = {Daniel {Borchmann}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See http://lat.inf.tu-dresden.de/research/reports.html.},
  number = {13-04},
  title = {{Exploration by Confidence}},
  type = {LTCS-Report},
  year = {2013},
}

We present an extensions of our previous work on axiomatizing confident general concept inclusions in given finite interpretations. Within this extension we allow external experts to interactively provide counterexamples to general concept inclusions with otherwise enough confidence in the given data. This extensions allows us to distinguish between erroneous counterexamples in the data and rare, but valid counterexamples.

@techreport{ Borc-LTCS-13-11,
  address = {Dresden, Germany},
  author = {Daniel {Borchmann}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See http://lat.inf.tu-dresden.de/research/reports.html.},
  number = {13-11},
  title = {{Model Exploration by Confidence with Completely Specified Counterexamples}},
  type = {LTCS-Report},
  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},
}

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},
}

The notion of concept similarity is central to several ontology tasks and can be employed to realize relaxed versions of classical reasoning services. In this paper we investigate the reasoning service of answering instance queries in a relaxed fashion, where the query concept is relaxed by means of a concept similarity measure (CSM). To this end we investigate CSMs that assess the similarity of EL-concepts defined w.r.t. a general EL-TBox. We derive such a family of CSMs from a family of similarity measures for finite interpretations and show in both cases that the resulting measures enjoy a collection of formal properties. These properties allow us to devise an algorithm for computing relaxed instances w.r.t. general EL-TBoxes, where users can specify the `appropriate' notion of similarity by instanciating our CSM appropriately.

@techreport{ EcTu-TR-13,
  address = {Dresden, Germany},
  author = {Andreas {Ecke} and Anni-Yasmin {Turhan}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See \url{http://lat.inf.tu-dresden.de/research/reports.html}.},
  number = {13-12},
  title = {Similarity Measures for Computing Relaxed Instances w.r.t.\ General $\mathcal{EL}$-{TBoxes}},
  type = {LTCS-Report},
  year = {2013},
}

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},
  note = {To appear.},
  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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

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},
}

A rise in the number of ontologies that are integrated and distributed in numerous application systems may provide the users to access the ontologies with different privileges and purposes. In this situation, preserving confidential information from possible unauthorized disclosures becomes a critical requirement. For instance, in the clinical sciences, unauthorized disclosures of medical information do not only threaten the system but also, most importantly, the patient data. Motivated by this situation, this thesis initially investigates a privacy problem, called the identity problem, where the identity of (anonymous) objects stored in Description Logic ontologies can be revealed or not. Then, we consider this problem in the context of role-based access control to ontologies and extend it to the problem asking if the identity belongs to a set of known individuals of cardinality smaller than the number k. If it is the case that some confidential information of persons, such as their identity, their relationships or their other properties, can be deduced from an ontology, which implies that some privacy policy is not fulfilled, then one needs to repair this ontology such that the modified one complies with the policies and preserves the information from the original ontology as much as possible. The repair mechanism we provide is called gentle repair and performed via axiom weakening instead of axiom deletion which was commonly used in classical approaches of ontology repair. However, policy compliance itself is not enough if there is a possible attacker that can obtain relevant information from other sources, which together with the modified ontology still violates the privacy policies. Safety property is proposed to alleviate this issue and we investigate this in the context of privacy-preserving ontology publishing. Inference procedures to solve those privacy problems and additional investigations on the complexity of the procedures, as well as the worst-case complexity of the problems, become the main contributions of this thesis.

@thesis{ Nuradiansyah-Diss-2019,
  address = {Dresden, Germany},
  author = {Adrian {Nuradiansyah}},
  school = {Technische Universit\"{a}t Dresden},
  title = {Reasoning in Description Logic Ontologies for Privacy Management},
  type = {Doctoral Thesis},
  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},
}

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.

@techreport{ TiZa-LTCS-19-04,
  address = {Dresden, Germany},
  author = {Satyadharma {Tirtarasa} and Benjamin {Zarrie{\ss}}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {see \url{https://lat.inf.tu-dresden.de/research/reports.html}},
  number = {19-04},
  title = {Projection in a Description Logic of Context with Actions (Extended Version)},
  type = {LTCS-Report},
  year = {2019},
}

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 way of repair in which axioms are not necessarily 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 \(\mathcal{E\mkern-1.618mu L}\).

@techreport{ BaKrNuPe-LTCS-18-01,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Francesco {Kriegel} and Adrian {Nuradiansyah} and Rafael {Pe\~{n}aloza}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {\url{https://tu-dresden.de/inf/lat/reports#BaKrNuPe-LTCS-18-01}},
  number = {18-01},
  title = {{Repairing Description Logic Ontologies by Weakening Axioms}},
  type = {LTCS-Report},
  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},
}

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 a modern world software systems are literally everywhere. These should cope with very complex scenarios including the ability of context-awareness and self-adaptability. The concept of roles provide the means to model such complex, context-dependent systems. In role-based systems, the relational and context-dependent properties of objects are transferred into the roles that the object plays in a certain context. However, even if the domain can be expressed in a well-structured and modular way, role-based models can still be hard to comprehend due to the sophisticated semantics of roles, contexts and different constraints. Hence, unintended implications or inconsistencies may be overlooked. A feasible logical formalism is required here. In this setting Description Logics (DLs) fit very well as a starting point for further considerations since as a decidable fragment of first-order logic they have both an underlying formal semantics and decidable reasoning problems. DLs are a well-understood family of knowledge representation formalisms which allow to represent application domains in a well-structured way by DL-concepts, i.e. unary predicates, and DL-roles, i.e. binary predicates. However, classical DLs lack expressive power to formalise contextual knowledge which is crucial for formalising role-based systems. We investigate a novel family of contextualised description logics that is capable of expressing contextual knowledge and preserves decidability even in the presence of rigid DL-roles, i.e. relational structures that are context-independent. For these contextualised description logics we thoroughly analyse the complexity of the consistency problem. Furthermore, we present a mapping algorithm that allows for an automated translation from a formal role-based model, namely a Compartment Role Object Model (CROM), into a contextualised DL ontology. We prove the semantical correctness and provide ideas how features extending CROM can be expressed in our contextualised DLs. As final step for a completely automated analysis of role-based models, we investigate a practical reasoning algorithm and implement the first reasoner that can process contextual ontologies.

@thesis{ Boehme-Diss-2017,
  address = {Dresden, Germany},
  author = {Stephan {B\"{o}hme}},
  school = {Technische Universit\"{a}t Dresden},
  title = {Context Reasoning for Role-Based Models},
  type = {Doctoral Thesis},
  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},
}

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},
}

Probabilistic data and knowledge bases are becoming increasingly important in academia and industry. They are continuously extended with new data, powered by modern information extraction tools that associate probabilities with knowledge base facts. The state of the art to store and process such data is founded on probabilistic database systems, which are widely and successfully employed. Beyond all the success stories, however, such systems still lack the fundamental machinery to convey some of the valuable knowledge hidden in them to the end user, which limits their potential applications in practice. In particular, in their classical form, such systems are typically based on strong, unrealistic limitations, such as the closed-world assumption, the closed-domain assumption, the tuple-independence assumption, and the lack of commonsense knowledge. These limitations do not only lead to unwanted consequences, but also put such systems on weak footing in important tasks, querying answering being a very central one. In this thesis, we enhance probabilistic data and knowledge bases with more realistic data models, thereby allowing for better means for querying them. Building on the long endeavor of unifying logic and probability, we develop different rigorous semantics for probabilistic data and knowledge bases, analyze their computational properties and identify sources of (in)tractability and design practical scalable query answering algorithms whenever possible. To achieve this, the current work brings together some recent paradigms from logics, probabilistic inference, and database theory.

@thesis{ Ceylan-Diss-2017,
  address = {Dresden, Germany},
  author = {{\.I}smail {\.I}lkan {Ceylan}},
  school = {Technische Universit\"{a}t Dresden},
  title = {Query Answering in Probabilistic Data and Knowledge Bases},
  type = {Doctoral Thesis},
  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},
}

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},
}

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},
}

@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},
}

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 involving ALC, SHOQ, and EL.

@techreport{ BoLi-LTCS-15-04,
  author = {Stephan {B{\"o}hme} and Marcel {Lippmann}},
  institution = {Chair of Automata Theory, TU Dresden},
  note = {See \url{http://lat.inf.tu-dresden.de/research/reports.html}.},
  number = {15-04},
  title = {Description Logics of Context with Rigid Roles Revisited},
  type = {LTCS-Report},
  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},
}

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},
}

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},
}

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.

@techreport{ BaKoKrNu-LTCS-22-01,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Patrick {Koopmann} and Francesco {Kriegel} and Adrian {Nuradiansyah}},
  doi = {https://doi.org/10.25368/2022.65},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  number = {22-01},
  title = {Optimal ABox Repair w.r.t.\ Static {$\mathcal{EL}$} TBoxes: from Quantified ABoxes back to ABoxes (Extended Version)},
  type = {LTCS-Report},
  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},
  note = {To appear.},
  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},
}

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. 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.

@techreport{ BaKr-LTCS-22-02,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Francesco {Kriegel}},
  doi = {https://doi.org/10.25368/2022.131},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  number = {22-02},
  title = {Pushing Optimal ABox Repair from {$\mathcal{EL}$} Towards More Expressive Horn-DLs (Extended Version)},
  type = {LTCS-Report},
  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},
  note = {To appear.},
  title = {Optimal Fixed-Premise Repairs of $\mathcal{EL}$ {TBoxes}},
  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.

@techreport{ Kr-LTCS-22-04,
  address = {Dresden, Germany},
  author = {Francesco {Kriegel}},
  doi = {https://doi.org/10.25368/2022.321},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  number = {22-04},
  title = {Optimal Fixed-Premise Repairs of {$\mathcal{EL}$} TBoxes (Extended Version)},
  type = {LTCS-Report},
  year = {2022},
}

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 \(\mathcal{EL}\). 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 \(\mathcal{EL}\) 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.

@techreport{ BaKoKrNu-LTCS-21-01,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Patrick {Koopmann} and Francesco {Kriegel} and Adrian {Nuradiansyah}},
  doi = {https://doi.org/10.25368/2022.64},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  number = {21-01},
  title = {Computing Optimal Repairs of Quantified ABoxes w.r.t. Static {$\mathcal{EL}$} TBoxes (Extended Version)},
  type = {LTCS-Report},
  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},
  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.

@techreport{ BaKoKrNuPe-LTCS-21-04,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Patrick {Koopmann} and Francesco {Kriegel} and Adrian {Nuradiansyah} and Rafael {Pe\~{n}aloza}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  number = {21-04},
  title = {{Privacy-Preserving Ontology Publishing: The Case of Quantified ABoxes w.r.t.\ a Static Cycle-Restricted $\mathcal{EL}$ TBox (Extended Version)}},
  type = {LTCS-Report},
  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},
}

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},
}

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},
}

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.

@techreport{ BaKrNuPe-LTCS-20-08,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Francesco {Kriegel} and Adrian {Nuradiansyah} and Rafael {Pe\~{n}aloza}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  number = {20-08},
  title = {Computing Compliant Anonymisations of Quantified ABoxes w.r.t. $\mathcal{E\!L}$ Policies (Extended Version)},
  type = {LTCS-Report},
  year = {2020},
}

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.

@techreport{ BaKrNuPe-LTCS-20-09,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Francesco {Kriegel} and Adrian {Nuradiansyah} and Rafael {Pe\~{n}aloza}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  number = {20-09},
  title = {Computing Safe Anonymisations of Quantified ABoxes w.r.t.\ $\mathcal{E\!L}$ Policies (Extended Version)},
  type = {LTCS-Report},
  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},
}

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.

@techreport{ BaKrNu-LTCS-19-01,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Francesco {Kriegel} and Adrian {Nuradiansyah}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {\url{https://tu-dresden.de/inf/lat/reports#BaKrNu-LTCS-19-01}},
  number = {19-01},
  title = {{Privacy-Preserving Ontology Publishing for $\mathcal{EL}$ Instance Stores (Extended Version)}},
  type = {LTCS-Report},
  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},
}

@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},
}

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 way of repair in which axioms are not necessarily 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 \(\mathcal{E\mkern-1.618mu L}\).

@techreport{ BaKrNuPe-LTCS-18-01,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Francesco {Kriegel} and Adrian {Nuradiansyah} and Rafael {Pe\~{n}aloza}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {\url{https://tu-dresden.de/inf/lat/reports#BaKrNuPe-LTCS-18-01}},
  number = {18-01},
  title = {{Repairing Description Logic Ontologies by Weakening Axioms}},
  type = {LTCS-Report},
  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},
}

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},
}

Unification in the Description Logic (DL) FL0 is known to be ExpTime-complete, and of unification type zero. We investigate in this paper 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, which is however also of interest in its own right, 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.

@techreport{ BaGiRo21,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Oliver {Fern\'andez Gil} and Maryam {Rostamigiv}},
  institution = {Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  number = {21-02},
  title = {Restricted Unification in the {DL} {$\mathcal{FL}_0$} (Extended Version)},
  type = {LTCS-Report},
  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},
}

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 such queries over ELH and DL-LiteR ontologies. We provide results on the computational complexity of the underlying reasoning problems and devise approximate query answering algorithms.

@techreport{ FeAt-LTCS-20-05,
  address = {Dresden, Germany},
  author = {Oliver {Fern{\'a}ndez Gil} and Anni-Yasmin {Turhan}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See http://lat.inf.tu-dresden.de/research/reports.html},
  number = {20-05},
  title = {Answering Regular Path Queries Under Approximate Semantics in Lightweight Description Logics},
  type = {LTCS-Report},
  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},
}

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},
}

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. Together with the special case of matching, they were first investigated in detail for the DL FL0, where these problems can be reduced to solving certain language equations. In this thesis, we extend this service in two directions. 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, in order to account for potential small modelling errors. 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 particular distance measures. Furthermore, we make a first step towards integrating background knowledge, formulated in so-called TBoxes, by investigating the special case of matching in the presence of TBoxes of different forms. We acquire a tight complexity bound for the general case, while we prove that the problem becomes easier in a restricted setting. To achieve these bounds, we take advantage of an equivalence characterization of FL0 concepts that is based on formal languages. In addition, we incorporate TBoxes in computing concept distances. Even though our results on the approximate setting cannot deal with TBoxes yet, we prepare the framework that future research can build on. Before we journey to the technical details of the above investigations, we showcase our program in the simpler setting of the equational theory ACUI, where we are able to also combine the two extensions. In the course of studying the above problems, we make heavy use of automata theory, where we also derive novel results that could be of independent interest.

@thesis{ Marantidis-Diss-2019,
  address = {Dresden, Germany},
  author = {Pavlos {Marantidis}},
  school = {Technische Universit\"{a}t Dresden},
  title = {Quantitative Variants of Language Equations and their Applications to Description Logics},
  type = {Doctoral Thesis},
  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{ 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.

@techreport{ BaFePe-LTCS-18-04,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Oliver {Fern{\'a}ndez Gil} and Maximilian {Pensel}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See http://lat.inf.tu-dresden.de/research/reports.html},
  number = {18-04},
  title = {Standard and Non-Standard Inferences in the Description Logic $\mathcal{FL}_0$ Using Tree Automata},
  type = {LTCS-Report},
  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},
}

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},
}

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},
}

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},
}

%!TEX root = ./paper.tex [1]blue#1 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.

@techreport{ AlKoTu-LTCS-19-06,
  address = {Dresden, Germany},
  author = {Christian {Alrabbaa} and Patrick {Koopmann} and Anni-Yasmin {Turhan}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See \url{https://lat.inf.tu-dresden.de/research/reports.html}},
  number = {19-06},
  title = {Practical Query Rewriting for \textit{DL-Lite} with Numerical Predicates (Extended Version)},
  type = {LTCS-Report},
  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},
}

Probabilistic model checking (PMC) is a well-established method for the quantitative analysis of dynamic systems. On the other hand, description logics (DLs) provide a well-suited formalism to describe and reason about static knowledge, used in many areas to specify domain knowledge in an ontology. 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.

@techreport{ DuKoTu-LTCS-19-05,
  address = {Dresden, Germany},
  author = {Clemens {Dubslaff} and Patrick {Koopmann} and Anni-Yasmin {Turhan}},
  institution = {TU Dresden},
  note = {see \url{https://lat.inf.tu-dresden.de/research/reports.html}},
  number = {19-05},
  title = {Ontology-Mediated Probabilistic Model Checking (Extended Version)},
  type = {LTCS-Report},
  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},
}

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},
}

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},
}

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.

@techreport{ CaGoKo-18-14,
  author = {David {Carral} and Larry {Gonz\'alez} and Patrick {Koopmann}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See \url{https://lat.inf.tu-dresden.de/research/reports.html}},
  number = {18-14},
  title = {From {Horn}-{$\mathcal{SRIQ}$} to {Datalog}: A Data-Independent Transformation that Preserves Assertion Entailment (Extended Version)},
  type = {LTCS-Report},
  year = {2018},
}

Modeling context-dependent systems for their analysis is challenging as verification tools usually rely on an input language close to imperative programming languages which need not support description of contexts well. We introduce the concept of contextualized programs where operational behaviors and context knowledge are modeled separately using domain-specific formalisms. For behaviors specified in stochastic guarded-command language and contextual knowledge given by OWL description logic ontologies, we develop a technique to eficiently incorporate contextual information into behavioral descriptions by reasoning about the ontology. We show how our presented concepts support and facilitate the quantitative analysis of context-dependent systems using probabilistic model checking. For this, we evaluate our implementation on a case study issuing a multi-server system.

@techreport{ DuKoTu-LTCS-18-09,
  address = {Dresden, Germany},
  author = {Clemens {Dubslaff} and Patrick {Koopmann} and Anni-Yasmin {Turhan}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {see \url{https://lat.inf.tu-dresden.de/research/reports.html}},
  number = {18-09},
  title = {Contextualized Programs for Ontology-Mediated Probabilistic System Analysis},
  type = {LTCS-Report},
  year = {2018},
}

Description Logic actions specify adaptations of description logic interpretations based on some preconditions defined using a description logic. We consider DL actions in which preconditions can be specified using DL axioms as well as using conjunctive queries, and combinatiosn thereof. We investigate complexity bounds for the executability and the projection problem for these actions, which respectively ask whether an action can be executed on models of an interpretation, and which entailments are satisfied after an action has been executed on this model. In addition, we consider a set of new reasoning tasks concerned with conflicts and interactions that may arise if two action are executed at the same time. Since these problems have not been investigated before for Description Logic actions, we investigate the complexity of these tasks both for actions with conjunctive queries and without those. Finally, we consider the verification problem for Golog programs formulated over our famility of actions. Our complexity analysis considers several expressive DLs, and we provide tight complexity bounds for those for which the exact complexity of conjunctive query entailment is known.

@techreport{ Ko-LTCS-18-08,
  address = {Dresden, Germany},
  author = {Patrick {Koopmann}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {see \url{https://lat.inf.tu-dresden.de/research/reports.html}},
  number = {18-08},
  title = {Actions with Conjunctive Queries: Projection, Conflict Detection and Verification},
  type = {LTCS-Report},
  year = {2018},
}

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.

@techreport{ Koopmann18tr,
  address = {Dresden, Germany},
  author = {Patrick {Koopmann}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {see \url{https://lat.inf.tu-dresden.de/research/reports.html}},
  number = {18-13},
  title = {Ontology-Based Query Answering for Probabilistic Temporal Data (Extended Version)},
  type = {LTCS-Report},
  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},
}

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.

@techreport{ Ko-LTCS-18-07,
  address = {Dresden, Germany},
  author = {Patrick {Koopmann}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {see \url{https://lat.inf.tu-dresden.de/research/reports.html}},
  number = {18-07},
  title = {Ontology-Mediated Query Answering for Probabilistic Temporal Data with {$\mathcal{EL}$} Ontologies (Extended Version)},
  type = {LTCS-Report},
  year = {2018},
}

Golog programs allow to model complex behaviour of agents by combining primitive actions defined in a Situation Calculus theory using imperative and non-deterministic programming language constructs. In general, verifying temporal properties of Golog programs is undecidable. One way to establish decidability is to restrict the logic used by the program to a Description Logic (DL), for which recently some complexity upper bounds for verification problem have been established. However, so far it was open whether these results are tight, and lightweight DLs such as EL have not been studied at all. Furthermore, these results only apply to a setting where actions do not consume time, and the properties to be verified only refer to the timeline in a qualitative way. In a lot of applications, this is an unrealistic assumption. In this work, we study the verification problem for timed Golog programs, in which actions can be assigned differing durations, and temporal properties are specified in a metric branching time logic. This allows to annotate temporal properties with time intervals over which they are evaluated, to specify for example that some property should hold for at least n time units, or should become specified within some specified time window. We establish tight complexity bounds of the verification problem for both expressive and lightweight DLs. Our lower bounds already apply to a very limited fragment of the verification problem, and close open complexity bounds for the non-metrical cases studied before.

@techreport{ KoZa-LTCS-18-06,
  address = {Dresden, Germany},
  author = {Patrick {Koopmann} and Benjamin {Zarrie{\ss}}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {see \url{https://lat.inf.tu-dresden.de/research/reports.html}},
  number = {18-06},
  title = {On the Complexity of Verifying Timed {Golog} Programs over Description Logic Actions (Extended Version)},
  type = {LTCS-Report},
  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},
}

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},
}

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.

@techreport{ BaBoKoOzTh-LTCS-17-03,
  address = {Dresden, Germany},
  author = {Franz {Baader} and Stefan {Borgwardt} and Patrick {Koopmann} and Ana {Ozaki} and Veronika {Thost}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {see \url{https://lat.inf.tu-dresden.de/research/reports.html}},
  number = {17-03},
  title = {Metric Temporal Description Logics with Interval-Rigid Names (Extended Version)},
  type = {LTCS-Report},
  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},
}

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.

@techreport{ BaBL-LTCS-17-04,
  address = {Germany},
  author = {Franz {Baader} and Stefan {Borgwardt} and Marcel {Lippmann}},
  institution = {Chair for Automata Theory, Technische Universit{\"a}t Dresden},
  note = {see \url{https://lat.inf.tu-dresden.de/research/reports.html}},
  number = {17-04},
  title = {Query Rewriting for \textit{{DL-Lite}} with {$n$}-ary Concrete Domains (Extended Version)},
  type = {LTCS-Report},
  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},
}

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 continuous probability distributions than by discrete probabilities for numerical facts concerning exact values. For this reason, we extend existing approaches 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.

@techreport{ BaKoTu-LTCS-17-05,
  address = {Germany},
  author = {Franz {Baader} and Patrick {Koopmann} and Anni-Yasmin {Turhan}},
  institution = {Chair for Automata Theory, Technische Universit{\"a}t Dresden},
  note = {See \url{https://lat.inf.tu-dresden.de/research/reports.html}},
  number = {17-05},
  title = {Using Ontologies to Query Probabilistic Numerical Data (Extended Version)},
  type = {LTCS-Report},
  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},
}

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},
}

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.

@techreport{ BoTu-LTCS-17-06,
  address = {Dresden, Germany},
  author = {Camille {Bourgaux} and Anni-Yasmin {Turhan}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {see \url{http://lat.inf.tu-dresden.de/research/reports.html}},
  number = {17-06},
  title = {Temporal Query Answering in {DL-Lite} over Inconsistent Data},
  type = {LTCS-Report},
  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},
}

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},
}

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 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. In this report, we present a new approach for EL_bot that alleviates this problem for relevant closure (the strongest form of preferential reasoning currently investigated) by the use of typicality models that extend classical canonical models by domain elements that individually satisfy any amount of consistent defeasible knowledge. We also show that a certain restriction on the domain of the typicality models in this approach yields inference results that correspond to the (weaker) more commonly known rational closure.

@techreport{ PeTu-LTCS-17-01,
  address = {Dresden, Germany},
  author = {Maximilian {Pensel} and Anni-Yasmin {Turhan}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  note = {See http://lat.inf.tu-dresden.de/research/reports.html},
  number = {17-01},
  title = {Making Quantification Relevant again---the Case of Defeasible $\mathcal{EL}_{\bot}$},
  type = {LTCS-Report},
  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},
}

Ontology-based data access (OBDA) augments classical query answering in databases by including domain knowledge provided by an ontology. An ontology captures the terminology of an application domain and describes domain knowledge in a machine-processable way. Formal ontology languages additionally provide semantics to these specifications. Systems for OBDA thus may apply logical reasoning to answer queries; they use the ontological knowledge to infer new information, which is only implicitly given in the data. Moreover, they usually employ the open-world assumption, which means that knowledge not stated explicitly in the data or inferred is neither assumed to be true nor false. Classical OBDA regards the knowledge however only w.r.t. a single moment, which means that information about time is not used for reasoning and hence lost; in particular, the queries generally 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, such as context recognition.

@thesis{ Thost-Diss-2017,
  address = {Dresden, Germany},
  author = {Veronika {Thost}},
  school = {Technische Universit\"{a}t Dresden},
  title = {Using Ontology-Based Data Access to Enable Context Recognition in the Presence of Incomplete Information},
  type = {Doctoral Thesis},
  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},
}

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},
}

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},
}

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},
}

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 a concrete domain 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 decidability was open. More generally, this result holds for all negation-closed concrete domains with the EHD-property, which stands for `the existence of a homomorphism is definable'. Such technique has recently been used to show decidability of CTL* with local constraints over the integers.

@techreport{ CaTu-LTCS-16-01,
  address = {Dresden, Germany},
  author = {Claudia {Carapelle} and Anni-Yasmin {Turhan}},
  institution = {Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universit{\"a}t Dresden},
  number = {16-01},
  title = {Decidability of $\mathcal{ALC}^P\!(\mathcal{D})$ for concrete domains with the EHD-property},
  type = {LTCS-Report},
  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 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},
}

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},
}

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.

@techreport{ BaBL-LTCS-15-17,
  address = {Germany},
  author = {Franz {Baader} and Stefan {Borgwardt} and Marcel {Lippmann}},
  institution = {Chair for Automata Theory, Technische Universit{\"a}t Dresden},
  number = {15-17},
  title = {Temporal Conjunctive Queries in Expressive {DLs} with Non-simple Roles},
  type = {LTCS-Report},
  year = {2015},
}

Ontology-based data access (OBDA) generalizes query answering in databases towards deductive