Reasoning on DL-LiteR with Defeasibility in ASP

Reasoning on defeasible knowledge is a topic of interest in the area of description logics, as it is related to the need of representing exceptional instances in knowledge bases. In this direction, in our previous works we presented a framework for representing (contextualized) OWL RL knowledge bases with a notion of justified exceptions on defeasible axioms: reasoning in such framework is realized by a translation into ASP programs. The resulting reasoning process for OWL RL, however, introduces a complex encoding in order to capture reasoning on the negative information needed for reasoning on exceptions. In this paper, we apply the justified exception approach to knowledge bases in DL-LiteR, i.e., the language underlying OWL QL. We provide a definition for DL-LiteR knowledge bases with defeasible axioms and study their semantic and computational properties. In particular, we study the effects of exceptions over unnamed individuals. The limited form of DL-LiteR axioms allows us to formulate a simpler ASP encoding, where reasoning on negative information is managed by direct rules. The resulting materialization method gives rise to a complete reasoning procedure for instance checking in DL-LiteR with defeasible axioms. Under consideration in Theory and Practice of Logic Programming (TPLP).1

[1]  Thomas Eiter,et al.  Enhancing context knowledge repositories with justifiable exceptions , 2018, Artif. Intell..

[2]  Luciano Serafini,et al.  Towards More Effective Tableaux Reasoning for CKR , 2012, Description Logics.

[3]  David Pearce,et al.  Strongly equivalent logic programs , 2001, ACM Trans. Comput. Log..

[4]  Piero A. Bonatti,et al.  A new semantics for overriding in description logics , 2015, Artif. Intell..

[5]  Mario Alviano,et al.  Aggregates in Answer Set Programming , 2018, KI - Künstliche Intelligenz.

[6]  Diego Calvanese,et al.  Tractable Reasoning and Efficient Query Answering in Description Logics: The DL-Lite Family , 2007, Journal of Automated Reasoning.

[7]  Wolfgang Faber,et al.  Disjunctive Logic Programs with Inheritance , 1999, ICLP.

[8]  Anni-Yasmin Turhan,et al.  Reasoning in the Defeasible Description Logic εℒ - computing standard inferences under rational and relevant semantics , 2018, Int. J. Approx. Reason..

[9]  Bernardo Cuenca Grau,et al.  OWL 2 Web Ontology Language: Profiles , 2009 .

[10]  Michael Gelfond,et al.  Classical negation in logic programs and disjunctive databases , 1991, New Generation Computing.

[11]  Thomas Eiter,et al.  Contextualized Knowledge Repositories with Justifiable Exceptions , 2014, Description Logics.

[12]  Ian Horrocks,et al.  Description logic programs: combining logic programs with description logic , 2003, WWW '03.

[13]  Jos de Bruijn,et al.  Embedding Approaches to Combining Rules and Ontologies into Autoepistemic Logic , 2008, KR.

[14]  Maurizio Lenzerini,et al.  The Complexity of Propositional Closed World Reasoning and Circumscription , 1994, J. Comput. Syst. Sci..

[15]  Umberto Straccia,et al.  Rational Closure for Defeasible Description Logics , 2010, JELIA.

[16]  Anni-Yasmin Turhan,et al.  Including Quantification in Defeasible Reasoning for the Description Logic EL⊥ , 2017, LPNMR.

[17]  Thomas Eiter,et al.  Reasoning with Justifiable Exceptions in Contextual Hierarchies , 2018, KR.

[18]  Laura Giordano,et al.  Reasoning about Typicality in Low Complexity DLs: The Logics EL⊥Tmin and DL-Litec Tmin , 2011, IJCAI.

[19]  Piero A. Bonatti,et al.  Defeasible Inclusions in Low-Complexity DLs , 2011, J. Artif. Intell. Res..

[20]  Jos de Bruijn,et al.  Embedding nonground logic programs into autoepistemic logic for knowledge-base combination , 2007, TOCL.

[21]  Luciano Serafini,et al.  Materialization Calculus for Contexts in the Semantic Web , 2013, Description Logics.

[22]  Carsten Lutz,et al.  Description Logics with Circumscription , 2006, KR.

[23]  Hans Tompits,et al.  Combining answer set programming with description logics for the Semantic Web , 2004, Artif. Intell..

[24]  Markus Krötzsch.  Efficient Inferencing for OWL EL , 2010, JELIA.

[25]  Umberto Straccia,et al.  A Polynomial Time Subsumption Algorithm for Nominal Safe ELO⊥ under Rational Closure , 2018, Inf. Sci..

[26]  Diego Calvanese,et al.  The Description Logic Handbook , 2007 .

[27]  Stefan Woltran,et al.  A common view on strong, uniform, and other notions of equivalence in answer-set programming* , 2007, Theory and Practice of Logic Programming.

[28]  Katarina Britz,et al.  Introducing Role Defeasibility in Description Logics , 2016, JELIA.

[29]  Stefan Woltran,et al.  The power of non-ground rules in Answer Set Programming , 2016, Theory and Practice of Logic Programming.

[30]  Thomas Lukasiewicz,et al.  Generalized Consistent Query Answering under Existential Rules , 2016, KR.

[31]  Maurizio Lenzerini,et al.  Inconsistency-Tolerant Semantics for Description Logics , 2010, RR.

[32]  Luciano Serafini,et al.  Contextualized knowledge repositories for the Semantic Web , 2012, J. Web Semant..

[33]  Laura Giordano,et al.  A non-monotonic Description Logic for reasoning about typicality , 2013, Artif. Intell..

[34]  Andrea Calì,et al.  A general datalog-based framework for tractable query answering over ontologies , 2009, SEBD.