A Tableau Calculus for Temporal Description Logic: the Expanding Domain Case

In this paper we present a tableau calculus for a temporal extension of the description logic ALC, called T L ALC. This logic is based on the temporal language with`Until' interpreted over the natural numbers with expanding ALC-domains. The tableau calculus forms an elaborated combination of Wolper's tableau calculus for propositional linear temporal logic, the standard tableau-algorithm for ALC, and the method of quasi-models as it has been introduced by Wolter and Zakharyaschev. Based on those three ingredients the paper provides a new method of how tableau-based decision procedures can be constructed for many-dimensional logics which lack the nite model property. The method can be applied to deal with other temporalized formalisms as well.