Reasoning in Circumscriptive ALCO

Abstract. Non-monotonic extensions of description logics (DLs) allow for default and local closed-world reasoning and are an acknowledged desired feature for applications, e.g. in the Semantic Web. A recent approach to such an extension is based on McCarthy’s circumscription, which rests on the principle of minimising the extension of selected predicates to locally close off dedicated parts of a domain model. While decidability and complexity results have been established in the literature, no practical algorithmisation for circumscriptive DLs has been proposed so far. In this paper, we present a tableaux calculus that can be used as a sound and complete decision procedure for concept satisfiability with respect to concept-circumscribed ALCO knowledge bases. The calculus builds on existing tableaux for classical DLs, extended by the notion of a preference clash to detect the non-minimality of constructed models.