Decidable Temporal Dynamic Description Logic

Abstract

The dynamic description logic DDL (dynamic description logic) provides a kind of action theory based on description logics. It is a useful representation of the dynamic application domains in the environment of the Semantic Web. In order to bring the representation capability of the branching temporal logic into the dynamic description logic, this paper treats the time slices of temporal logics as the executions of atomic actions, so that the temporal dimension and the dynamic dimension can be unified. Based on this idea, constructed over the description logic ALCQIO, a temporal dynamic description logic, named TDALCQIO, is presented. Tableau decision algorithm is provided for TDALCQIO. Both the termination and the correctness of this algorithm have been proved. The logic TDALCQIO not only inherits the representation capability provided by the dynamic description logic constructed over ALCQIO (attributive language with complements, qualified number restrictions, inverse roles and nominals), but it also has the ability to describe and reason about some temporal features such as the reachability property and the safety property of the whole dynamic application domains. Therefore, TDALCQIO provides further support for knowledge representation and reasoning in the environment of the Semantic Web.