Reasoning about Typicality in Preferential Description Logics

In this paper we propose a nonmonotonic extension ALC + Tmin of the Description Logic ALC for reasoning about prototypical properties and inheritance with exception. The logic ALC + Tmin is built upon a previously introduced (monotonic) logic ALC + T, that is obtained by adding a typicality operator T to ALC. The operator T is intended to select the “most normal” or “most typical” instances of a concept, so that knowledge bases may contain subsumption relations of the form “T(C) is subsumed by P”, expressing that typical C-members have the property P. In order to perform nonmonotonic inferences, we define a “minimal model” semantics ALC + Tmin for ALC + T. The intuition is that preferred, or minimal models are those that maximise typical instances of concepts. By means of ALC + Tmin we are able to infer defeasible properties of (explicit or implicit) individuals. We also present a tableau calculus for deciding ALC + Tmin entailment.