A Tableau Decision Algorithm for Modalized ALC with Constant Domains

The aim of this paper is to construct a tableau decision algorithm for the modal description logic KALC with constant domains. More precisely , we present a tableau procedure that is capable of deciding, given an ALC-formula ' with extra modal operators (which are applied only to concepts and TBox axioms, but not to roles), whether ' is satiss-able in a model with constant domains and arbitrary accessibility relations. Tableau-based algorithms have been shown to bèpractical' even for logics of rather high complexity. This gives us grounds to believe that, although the satissability problem for KALC 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].