Preferential description logics

  • Authors:

  • Laura Giordano;Valentina Gliozzi;Nicola Olivetti;Gian Luca Pozzato

  • Affiliations:

  • Dip. di Informatica, Univ. Piemonte O. "A. Avogadro";Dip. di Informatica, Università di Torino;LSIS, UMR, CNRS, Univ. "P. Cézanne";Dip. di Informatica, Università di Torino

  • Venue:
  • LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
  • Year:
  • 2007

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Abstract

We extend the Description Logic ALC with a "typicality" operator T that allows us to reason about the prototypical properties and inheritance with exceptions. The resulting logic is called ALC + T. The typicality operator is intended to select the "most normal" or "most typical" instances of a concept. In our framework, knowledge bases may then contain, in addition to ordinary ABoxes and TBoxes, subsumption relations of the form "T(C) is subsumed by P", expressing that typical C-members have the property P. The semantics of a typicality operator is defined by a set of postulates that are strongly related to Kraus-Lehmann-Magidor axioms of preferential logic P. We first show that T enjoys a simple semantics provided by ordinary structures equipped by a preference relation. This allows us to obtain a modal interpretation of the typicality operator. Using such a modal interpretation, we present a tableau calculus for deciding satisfiability of ALC + T knowledge bases. Our calculus gives a nondeterministic-exponential time decision procedure for satisfiability of ALC + T. We then extend ALC + T knowledge bases by a nonmonotonic completion that allows inferring defeasible properties of specific concept instances.