Semantic foundation for preferential description logics

Abstract

Description logics are a well-established family of knowledge representation formalisms in Artificial Intelligence. Enriching description logics with non-monotonic reasoning capabilities, especially preferential reasoning as developed by Lehmann and colleagues in the 90's, would therefore constitute a natural extension of such KR formalisms. Nevertheless, there is at present no generally accepted semantics, with corresponding syntactic characterization, for preferential consequence in description logics. In this paper the authors fill this gap by providing a natural and intuitive semantics for defeasible subsumption in the description logic ALC. Their semantics replace the propositional valuations used in the models of Lehmann et al. with structures that they refer to as concept models. They present representation results for the description logic ALC for both preferential and rational consequence relations. They argue that their semantics pave the way for extending preferential and rational consequence, and therefore also rational closure, to a whole class of logics that have a semantics defined in terms of first-order relational structures.