Studia Logica

, Volume 72, Issue 2, pp 199-232

First online:

A Tableau Decision Algorithm for Modalized ALC with Constant Domains

  • Carsten LutzAffiliated withLuFG Theoretical Computer Science, RWTH Aachen
  • , Holger SturmAffiliated withInstitut für Informatik, Universität Leipzig
  • , Frank WolterAffiliated withInstitut für Informatik, Universität Leipzig
  • , Michael ZakharyaschevAffiliated withDepartment of Computer Science, King's College

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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