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We define the notion of rational closure in the context of Description Logicsextended with a tipicality operator. We start from ALC+T, an extension of ALCwith a typicality operator T: intuitively allowing to express concepts of theform T(C), meant to select the "most normal" instances of a concept C. Thesemantics we consider is based on rational model. But we further restrict thesemantics to minimal models, that is to say, to models that minimise the rankof domain elements. We show that this semantics captures exactly a notion ofrational closure which is a natural extension to Description Logics of Lehmannand Magidor's original one. We also extend the notion of rational closure tothe Abox component. We provide an ExpTime algorithm for computing the rationalclosure of an Abox and we show that it is sound and complete with respect tothe minimal model semantics.

On Rational Closure in Description Logics of Typicality