A non-monotonic Description Logic for reasoning about typicality

In this paper we propose a non-monotonic extension of the Description Logic ALC for reasoning about prototypical properties and inheritance with exceptions. The resulting logic, called ALC + T_min, 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 ) ⊆ D ("T(C ) is subsumed by D "), expressing that typical C -members are instances of concept D . From a knowledge representation point of view, the monotonic logic ALC + T is too weak to perform inheritance reasoning. In ALC + T_min, in order to perform non-monotonic inferences, we define a "minimal model" semantics over ALC + T. The intuition is that preferred or minimal models are those that maximize typical instances of concepts. By means of ALC + T_min we are able to infer defeasible properties of (explicit or implicit) individuals. We also present a tableau calculus for deciding ALC + T_min entailment that allows to give a complexity upper bound for the logic, namely that query entailment is in co-NExp^NP.