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Semantic Foundation for Preferential Description Logics

  • Katarina Britz
  • Thomas Meyer
  • Ivan Varzinczak
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7106)

Abstract

Description logics are a well-established family of knowledge representation formalisms in Artificial Intelligence. Enriching description logics with non-monotonic reasoning capabilities, especially preferential reasoning as developed by Lehmann and colleagues in the 90’s, would therefore constitute a natural extension of such KR formalisms. Nevertheless, there is at present no generally accepted semantics, with corresponding syntactic characterization, for preferential consequence in description logics. In this paper we fill this gap by providing a natural and intuitive semantics for defeasible subsumption in the description logic \(\mathcal{ALC}\). Our semantics replaces the propositional valuations used in the models of Lehmann et al.. with structures we refer to as concept models. We present representation results for the description logic \(\mathcal{ALC}\) for both preferential and rational consequence relations. We argue that our semantics paves the way for extending preferential and rational consequence, and therefore also rational closure, to a whole class of logics that have a semantics defined in terms of first-order relational structures.

Keywords

Description Logic Preferential Model Rational Closure Viral Meningitis Nonmonotonic Reasoning 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Katarina Britz
    • 1
  • Thomas Meyer
    • 1
  • Ivan Varzinczak
    • 1
  1. 1.Centre for Artificial Intelligence ResearchCSIR Meraka Institute and University of KwaZulu-NatalSouth Africa

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