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# A Tableau Decision Algorithm for Modalized ALC with Constant Domains

Carsten Lutz, Holger Sturm, Frank Wolter and Michael Zakharyaschev
Studia Logica: An International Journal for Symbolic Logic
Vol. 72, No. 2, Many-Dimensional Logical Systems (Nov., 2002), pp. 199-232
Stable URL: http://www.jstor.org/stable/20016461
Page Count: 34
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## Abstract

The aim of this paper is to construct a tableau decision algorithm for the modal description logic $\text{K}_{\scr{ALC}}$ with constant domains. More precisely, we present a tableau procedure that is capable of deciding, given an $\scr{ALC}$-formula ψ with extra modal operators (which are applied only to concepts and TBox axioms, but not to roles), whether ψ 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 $\text{K}_{\scr{ALC}}$ 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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