A Semantics for Rational Closure: Preliminary Results

We provide a semantical reconstruction of rational closure. We first consider rational closure as defined by Lehman and Magidor for propositional logic, and we provide a semantical characterization based on minimal models mechanism on rational models. Then, we extend the whole formalism and semantics to Description Logics focusing our attention to the standard ALC: we first naturally adapt to Description Logics Lehman and Magidor’s propositional rational closure, starting from an extension of ALC with a typicality operator T that selects the most typical instances of a concept C (hence T(C) stands for typical Cs). Then, we provide for ALC plus T a semantical characterization similar to the one for propositional logic. Last, we extend the notion of rational closure to the ABox.