Tableaux for temporal description logic with constant domains

Abstract

We show how to combine the standard tableau system for the basic description logic ALC and Wolper's tableau calculus for propositional temporal logic PTL (with the temporal operators 'next-time' and 'until') in order to design a terminating sound and complete tableau-based satisfiability-checking algorithm for the temporal description logic PTLALC of [20] interpreted in models with constant domains. We use the method of quasimodels [18,16] to represent models with infinite domains, and the technique of minimal types [11] to maintain these domains constant. The combination is flexible and can be extended to more expressive description logics or even to decidable fragments of first-order temporal logics. © Springer-Verlag Berlin Heidelberg 2001.