Towards a Rational Closure for Expressive Description Logics: The Case of SHIQ

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.