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 PTL ALC of [19] interpreted in models with constant domains. We use the method of quasimodels [17, 15] 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 do decidable fragments of first-order temporal logics.

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