A Note on a Description Logic of Concept and Role Typicality for Defeasible Reasoning Over Ontologies

Abstract

In this work, we propose a meaningful extension of description logics for non-monotonic reasoning. We introduce $$\mathcal {ALCH}^{\bullet }$$ , a logic allowing for the representation of and reasoning about both typical class-membership and typical instances of a relation. We propose a preferential semantics for $$\mathcal {ALCH}^{\bullet }$$ in terms of partially-ordered DL interpretations which intuitively captures the notions of typicality we are interested in. We define a tableau-based algorithm for checking $$\mathcal {ALCH}^{\bullet }$$ knowledge-base consistency that always terminates and we show that it is sound and complete w.r.t. our preferential semantics. The general framework we here propose can serve as the foundation for further exploration of non-monotonic reasoning in description logics and similarly structured logics.