A Tableau Calculus for a Nonmonotonic Extension of the Description Logic $\mbox{\em DL-Lite}_{\mathit{core}}$

In this paper we introduce a tableau calculus for a nonmonotonic extension of the low complexity Description Logic DL-Litecore of the DL-Litecore family. The extension, called DL-LitecTmin, can be used to reason about typicality and defeasible properties. The calculus performs a two-phase computation to check whether a query is minimally entailed from the initial knowledge base. It is sound, complete and terminating. Furthermore, it is a decision procedure for DL-LitecTmin knowledge bases, whose complexity matches the known results for the logic, namely that entailment is in Π2p.

[1]  Ian Horrocks,et al.  The Semantic Web – ISWC 2010: 9th International Semantic Web Conference, ISWC 2010, Shanghai, China, November 7-11, 2010, Revised Selected Papers, Part I , 2010, SEMWEB.

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

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

[4]  Francesco M. Donini,et al.  Decidable reasoning in terminological knowledge representation systems , 1993 .

[5]  Piero A. Bonatti,et al.  EL with default attributes and overriding , 2010, ISWC 2010.

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

[7]  Frank Wolter,et al.  Semi-qualitative Reasoning about Distances: A Preliminary Report , 2000, JELIA.

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

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

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

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

[12]  Roy Dyckhoff.  Automated Reasoning with Analytic Tableaux and Related Methods , 2000, Lecture Notes in Computer Science.

[13]  Piero A. Bonatti,et al.  Defeasible Inclusions in Low-Complexity DLs: Preliminary Notes , 2009, IJCAI.

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

[15]  Piero A. Bonatti,et al.  EL\mathcal{EL} with Default Attributes and Overriding , 2010, International Semantic Web Conference.

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

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

[18]  Laura Giordano,et al.  A Tableau Calculus for a Nonmonotonic Extension of EL^\mathcal{EL}^\bot , 2011, TABLEAUX.

[19]  Sanghamitra Bandyopadhyay,et al.  Mining the Largest Dense Vertexlet in a Weighted Scale-free Graph , 2009, Fundam. Informaticae.

[20]  Laura Giordano,et al.  Reasoning about Typicality in Preferential Description Logics , 2008, JELIA.