Studia Logica

, Volume 72, Issue 2, pp 199–232 | Cite as

A Tableau Decision Algorithm for Modalized ALC with Constant Domains

  • Carsten Lutz
  • Holger Sturm
  • Frank Wolter
  • Michael Zakharyaschev
Article

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].

modal logics description logics tableaux combining systems decidability complexity 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Carsten Lutz
    • 1
  • Holger Sturm
    • 2
  • Frank Wolter
    • 2
  • Michael Zakharyaschev
    • 3
  1. 1.LuFG Theoretical Computer ScienceRWTH AachenAachenGermany
  2. 2.Institut für InformatikUniversität LeipzigLeipzigGermany
  3. 3.Department of Computer ScienceKing's CollegeStrand, LondonU.K.

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