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. The research that led to the present paper was partially supported by a grant of the group GNCS of INdAM.