A non-monotonic Description Logic for reasoning about typicality Original Research Article

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