A Preferential Tableaux Calculus for Circumscriptive ${\mathcal ALCO}$

  • Authors:

  • Stephan Grimm;Pascal Hitzler

  • Affiliations:

  • FZI Research Center for Information Technologies, Univ. of Karlsruhe, Germany;Institute AIFB, University of Karlsruhe, Germany

  • Venue:
  • RR '09 Proceedings of the 3rd International Conference on Web Reasoning and Rule Systems
  • Year:
  • 2009

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Abstract

Nonmonotonic extensions of description logics (DLs) allow for default and local closed-world reasoning and are an acknowledged desired feature for applications, e.g. in the Semantic Web. A recent approach to such an extension is based on McCarthy's circumscription, which rests on the principle of minimising the extension of selected predicates to close off dedicated parts of a domain model. While decidability and complexity results have been established in the literature, no practical algorithmisation for circumscriptive DLs has been proposed so far. In this paper, we present a tableaux calculus that can be used as a decision procedure for concept satisfiability with respect to concept-circumscribed ${\mathcal ALCO}$ knowledge bases. The calculus builds on existing tableaux for classical DLs, extended by the notion of a preference clash to detect the non-minimality of constructed models.