Minimal Model Semantics and Rational Closure in Description Logics

We define the notion of rational closure in the context of Description Logics. We start from an extension of ALC with a typicality operator T allowing to express concepts of the form T(C), whose meaning is to select the “most normal” instances of a concept C. The semantics we consider is based on rational models and exploits a minimal models mechanism based on the minimization of the rank of domain elements. We show that this semantics captures exactly a notion of rational closure which is a natural extension to Description Logics of Lehmann and Magidor’s one. We also extend the notion of rational closure to the ABox, by providing an EXPTIME algorithm for computing it that is sound and complete with respect to the minimal model semantics.

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