Rational closure in SHIQ

ABSTRACT. We propose a nonmonotonic extension of SHIQ, which is at the base of the OWL-DL language and does not enjoy the finite model property. We extend to SHIQ the well established notion of rational closure, a nonmonotonic mechanism introduced by Lehmann and Magidor for propositional logic, built on the top of the rational logic R. We start from an extension of SHIQ with a typicality operator T, whose aim is to select the typical (the most normal) instances of a concept C: T(C) stands for typical Cs. As a further contribution, we provide a semantic characterization of the rational closure for SHIQ, namely a minimal model semantics built upon standard Description Logics models enriched with a preference relation among domain elements.