On Rational Closure in Description Logics of Typicality
  We define the notion of rational closure in the context of Description Logics
extended with a tipicality operator. We start from ALC+T, an extension of ALC
with a typicality operator T: intuitively allowing to express concepts of the
form T(C), meant to select the "most normal" instances of a concept C. The
semantics we consider is based on rational model. But we further restrict the
semantics to minimal models, that is to say, to models that minimise 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 original one. We also extend the notion of rational closure to
the Abox component. We provide an ExpTime algorithm for computing the rational
closure of an Abox and we show that it is sound and complete with respect to
the minimal model semantics.
