Defeasible Reasoning in SROEL: from Rational Entailment to Rational Closure

In this work we study a rational extension $SROEL^R T$ of the low complexity description logic SROEL, which underlies the OWL EL ontology language. The extension involves a typicality operator T, whose semantics is based on Lehmann and Magidor's ranked models and allows for the definition of defeasible inclusions. We consider both rational entailment and minimal entailment. We show that deciding instance checking under minimal entailment is in general $\Pi^P_2$-hard, while, under rational entailment, instance checking can be computed in polynomial time. We develop a Datalog calculus for instance checking under rational entailment and exploit it, with stratified negation, for computing the rational closure of simple KBs in polynomial time.

[1]  Laura Giordano,et al.  Semantic characterization of rational closure: From propositional logic to description logics , 2015, Artif. Intell..

[2]  Matthias Knorr,et al.  Reconciling OWL and Non-monotonic Rules for the Semantic Web , 2012, ECAI.

[3]  Michael Gelfond,et al.  Logic programming and knowledge representation—The A-Prolog perspective , 2002 .

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

[5]  Krysia Broda,et al.  Reasoning in the presence of inconsistency through Preferential ALC , 2015, LPAR.

[6]  Teodor C. Przymusinski Stable semantics for disjunctive programs , 1991, New Generation Computing.

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

[8]  Stijn Heymans,et al.  The DReW System for Nonmonotonic DL-Programs , 2012, CSWS.

[9]  Maurizio Lenzerini,et al.  Inconsistency-tolerant query answering in ontology-based data access , 2015, J. Web Semant..

[10]  Oliver Fernandez Gil,et al.  On the Non-Monotonic Description Logic ALC+Tmin , 2014, ArXiv.

[11]  Richard Booth,et al.  On the Entailment Problem for a Logic of Typicality , 2015, IJCAI.

[12]  Gian Luca Pozzato,et al.  A minimal model semantics for rational closure , 2012, NMR 2012.

[13]  Christoph Beierle,et al.  Skeptical Inference Based on C-Representations and Its Characterization as a Constraint Satisfaction Problem , 2016, FoIKS.

[14]  Thomas Andreas Meyer,et al.  Semantic Preferential Subsumption , 2008, KR.

[15]  Umberto Straccia,et al.  Lexicographic Closure for Defeasible Description Logics , 2012 .

[16]  Georg Gottlob,et al.  Stable Model Semantics for Guarded Existential Rules and Description Logics , 2014, KR.

[17]  Laura Giordano,et al.  ASP for minimal entailment in a rational extension of SROEL , 2016, Theory Pract. Log. Program..

[18]  Sarit Kraus,et al.  Nonmonotonic Reasoning, Preferential Models and Cumulative Logics , 1990, Artif. Intell..

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

[20]  Thomas Andreas Meyer,et al.  Nonmonotonic Reasoning in Description Logics: Rational Closure for the ABox , 2013, Description Logics.

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

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

[23]  Umberto Straccia,et al.  Defeasible Inheritance-Based Description Logics , 2013, J. Artif. Intell. Res..

[24]  Markus Krötzsch,et al.  Effi cient Inferencing for the Description Logic Underlying OWL EL , 2010 .

[25]  Laura Giordano,et al.  Reasoning in a Rational Extension of SROEL , 2016, CILC.

[26]  Piero A. Bonatti,et al.  Optimizing the Computation of Overriding , 2015, International Semantic Web Conference.

[27]  Franz Baader,et al.  Priorities on defaults with prerequisites, and their application in treating specificity in terminological default logic , 1995, Journal of Automated Reasoning.

[28]  Laura Giordano,et al.  Prototypical Reasoning with Low Complexity Description Logics: Preliminary Results , 2009, LPNMR.

[29]  Georg Gottlob,et al.  Disjunctive datalog , 1997, TODS.

[30]  Georg Gottlob,et al.  On the computational cost of disjunctive logic programming: Propositional case , 1995, Annals of Mathematics and Artificial Intelligence.

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

[32]  Boris Motik,et al.  Reconciling description logics and rules , 2010, JACM.

[33]  Carsten Lutz,et al.  The Complexity of Circumscription in DLs , 2009, J. Artif. Intell. Res..

[34]  Daniel Lehmann,et al.  What does a Conditional Knowledge Base Entail? , 1989, Artif. Intell..

[35]  Francesco M. Donini,et al.  Description logics of minimal knowledge and negation as failure , 2002, TOCL.

[36]  Laura Giordano,et al.  Encoding a Preferential Extension of the Description Logic SROIQ into SROIQ , 2015, ISMIS.

[37]  Umberto Straccia Default Inheritance Reasoning in Hybrid KL-ONE-Style Logics , 1993, IJCAI.

[38]  Daniel Lehmann,et al.  Another perspective on default reasoning , 1995, Annals of Mathematics and Artificial Intelligence.

[39]  Kody. Moodley Practical reasoning for defeasable description logics. , 2016 .

[40]  Madalina Croitoru,et al.  Inconsistency-Tolerant Query Answering: Rationality Properties and Computational Complexity Analysis , 2016, JELIA.

[41]  Ulrike Sattler,et al.  Next Steps for Description Logics of Minimal Knowledge and Negation as Failure , 2008, Description Logics.

[42]  Laura Giordano,et al.  ALC + T: a Preferential Extension of Description Logics , 2009, Fundam. Informaticae.

[43]  Laura Giordano,et al.  Preferential Description Logics , 2007, LPAR.

[44]  Hans Tompits,et al.  Well-Founded Semantics for Description Logic Programs in the Semantic Web , 2004, RuleML.

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

[46]  Franz Baader,et al.  Pushing the EL Envelope , 2005, IJCAI.

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