On the Complexity of EL with Defeasible Inclusions

We analyze the complexity of reasoning in EL with defeasible inclusions and extensions thereof. The results by Bonatti et al., 2009a are extended by proving tight lower complexity bounds and by relaxing the syntactic restrictions adopted there. We further extend the old framework by supporting arbitrary priority relations.

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

[2]  Franz Baader,et al.  Embedding defaults into terminological knowledge representation formalisms , 1995, Journal of Automated Reasoning.

[3]  Diego Calvanese,et al.  The Description Logic Handbook: Theory, Implementation, and Applications , 2003, Description Logic Handbook.

[4]  Marco Schaerf,et al.  Closed world reasoning in Hybrid systems , 1990 .

[5]  Gerhard Brewka,et al.  The Logic of Inheritance in Frame Systems , 1987, IJCAI.

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

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

[8]  Jeffrey M. Bradshaw,et al.  Semantic Web Languages for Policy Representation and Reasoning: A Comparison of KAoS, Rei, and Ponder , 2003, SEMWEB.

[9]  Diego Calvanese,et al.  DL-Lite: Tractable Description Logics for Ontologies , 2005, AAAI.

[10]  Laura Giordano,et al.  Reasoning About Typicality in ALC and EL , 2009, Description Logics.

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

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

[13]  Jeffrey M. Bradshaw,et al.  KAoS policy management for semantic Web services , 2004, IEEE Intelligent Systems.

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

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

[16]  Franz Baader The Instance Problem and the Most Specific Concept in the Description Logic EL w.r.t. Terminological Cycles with Descriptive Semantics , 2003, KI.

[17]  Robert Stevens,et al.  Using OWL to model biological knowledge , 2007, Int. J. Hum. Comput. Stud..

[18]  Alan L. Rector Defaults, Context, and Knowledge: Alternatives for OWL-Indexed Knowledge Bases , 2004, Pacific Symposium on Biocomputing.

[19]  Timothy W. Finin,et al.  A policy language for a pervasive computing environment , 2003, Proceedings POLICY 2003. IEEE 4th International Workshop on Policies for Distributed Systems and Networks.

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

[21]  Riccardo Rosati,et al.  Autoepistemic Description Logics , 1997, IJCAI.

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

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