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A Tableau Decision Algorithm for Modalized ALC with Constant Domains

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Abstract

The aim of this paper is to construct a tableau decision algorithm for the modal description logic K ALC with constant domains. More precisely, we present a tableau procedure that is capable of deciding, given an ALC-formula ϕ with extra modal operators (which are applied only to concepts and TBox axioms, but not to roles), whether ϕ is satisfiable in a model with constant domains and arbitrary accessibility relations. Tableau-based algorithms have been shown to be 'practical' even for logics of rather high complexity. This gives us grounds to believe that, although the satisfiability problem for K ALC is known to be NEXPTIME-complete, by providing a tableau decision algorithm we demonstrate that highly expressive description logics with modal operators have a chance to be implementable. The paper gives a solution to an open problem of Baader and Laux [5].

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Authors and Affiliations

  1. LuFG Theoretical Computer Science, RWTH Aachen, Ahornstraße 55, 52074, Aachen, Germany

    Carsten Lutz

  2. Institut für Informatik, Universität Leipzig, Augustus-Platz 10-11, 04109, Leipzig, Germany

    Holger Sturm & Frank Wolter

  3. Department of Computer Science, King's College, Strand, London, WC2R 2LS, U.K.

    Michael Zakharyaschev

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  1. Carsten Lutz
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  2. Holger Sturm
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  3. Frank Wolter
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  4. Michael Zakharyaschev
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Lutz, C., Sturm, H., Wolter, F. et al. A Tableau Decision Algorithm for Modalized ALC with Constant Domains. Studia Logica 72, 199–232 (2002). https://doi.org/10.1023/A:1021308527417

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