I.: Semantic foundation for preferential description logics

Abstract. Description logics are a well-established family of knowledge representation formalisms in Artificial Intelligence. Enriching descrip-tion logics with non-monotonic reasoning capabilities, especially prefer-ential 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 we fill this gap by providing a natu-ral and intuitive semantics for defeasible subsumption in the description logic ALC. Our semantics replaces the propositional valuations used in the models of Lehmann et al. with structures we refer to as concept mod-els. We present representation results for the description logic ALC for both preferential and rational consequence relations. We argue that our semantics paves the way for extending preferential and rational conse-quence, and therefore also rational closure, to a whole class of logics that have a semantics defined in terms of first-order relational structures.