Arbitrary Ranking of Defeasible Subsumption

In this paper we propose an algorithm that generalises existing procedures for the implementation of defeasible reasoning in the framework of Description Logics (DLs). One of the well-known approaches to defeasible reasoning, the so-called KLM approach, is based on constructing specific rankings of defeasible information, and using these rankings to determine priorities in case of conflicting information. Here we propose a procedure that allows us to input any possible ranking of the defeasible concept inclusions contained in the knowledge base. We analyse and investigate the forms of defeasible reasoning obtained when conclusions drawn are obtained using these rankings.

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

[2]  Thomas Andreas Meyer,et al.  Relevant Closure: A New Form of Defeasible Reasoning for Description Logics , 2014, JELIA.

[3]  Lin Padgham,et al.  A Terminological Logic with Defaults: A Definition and an Application , 1993, IJCAI.

[4]  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..

[5]  P. Bonatti.  The Complexity of Circumscription in Description Logic , 2009 .

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

[7]  Laura Giordano,et al.  Defeasible Reasoning in SROEL: from Rational Entailment to Rational Closure , 2018, Fundam. Informaticae.

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

[9]  Thomas Andreas Meyer,et al.  Preferential Role Restrictions , 2013, Description Logics.

[10]  Piero A. Bonatti,et al.  On the logical properties of the nonmonotonic description logic DLN , 2017, Artif. Intell..

[11]  Joachim Quantz,et al.  Preferential Default Description Logics , 1993 .

[12]  Pascal Hitzler,et al.  Local Closed World Semantics: Grounded Circumscription for OWL , 2011, SEMWEB.

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

[14]  Thomas Andreas Meyer,et al.  Semantic Foundation for Preferential Description Logics , 2011, Australasian Conference on Artificial Intelligence.

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

[16]  Umberto Straccia,et al.  Defeasible Inheritance-Based Description Logics , 2011, IJCAI.

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

[18]  Jianfeng Du,et al.  Extending description logics with uncertainty reasoning in possibilistic logic , 2007, Int. J. Intell. Syst..

[19]  Guido Governatori,et al.  Defeasible Description Logics , 2004, RuleML.

[20]  Stijn Heymans,et al.  A Defeasible Ontology Language , 2002, OTM.

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

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

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

[24]  Gert Smolka,et al.  Attributive Concept Descriptions with Complements , 1991, Artif. Intell..

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

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

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

[28]  Joachim Quantz,et al.  A Preference Semantics for Defaults in Terminological Logics , 1992, International Conference on Principles of Knowledge Representation and Reasoning.

[29]  Ivan Varzinczak,et al.  A Note on a Description Logic of Concept and Role Typicality for Defeasible Reasoning Over Ontologies , 2018, Logica Universalis.

[30]  Thomas Andreas Meyer,et al.  Introducing Defeasibility into OWL Ontologies , 2015, International Semantic Web Conference.

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

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

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

[34]  Franz Baader,et al.  How to Prefer More Specific Defaults in Terminological Default Logic , 1993, IJCAI.

[35]  Thomas Andreas Meyer,et al.  Modelling Object Typicality in Description Logics , 2009, Description Logics.

[36]  Thomas Andreas Meyer,et al.  Towards Practical Defeasible Reasoning for Description Logics , 2013, Description Logics.

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

[38]  Ulrike Sattler,et al.  Theoretical Foundations of Defeasible Description Logics , 2019, ArXiv.

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

[40]  Thomas Andreas Meyer,et al.  Taking Defeasible Entailment Beyond Rational Closure , 2019, JELIA.

[41]  Carsten Lutz,et al.  The Complexity of Conjunctive Query Answering in Expressive Description Logics , 2008, IJCAR.

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

[43]  Laura Giordano,et al.  Towards a Rational Closure for Expressive Description Logics: the Case of 풮풽풾퓆 , 2018, Fundam. Informaticae.

[44]  Gerd Wagner,et al.  Rules and Rule Markup Languages for the Semantic Web , 2003, Lecture Notes in Computer Science.

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