Towards a Rational Closure for Expressive Description Logics: the Case of 𝒮𝒽𝒾𝓆

Abstract

We explore the extension of the notion of rational closure to logics lacking the finite model property, considering the logic 𝒮𝒽𝒾𝓆. We provide a semantic characterization of rational closure in 𝒮𝒽𝒾𝓆 in terms of a preferential semantics, based on a finite rank characterization of minimal models. We show that the rational closure of a KB can be computed in EXPTIME based on a polynomial encoding of the rational extension of 𝒮𝒽𝒾𝓆 into entailment in 𝒮𝒽𝒾𝓆. We discuss the extension of rational closure to more expressive description logics.