  In this work we describe preferential Description Logics of typicality, a
nonmonotonic extension of standard Description Logics by means of a typicality
operator T allowing to extend a knowledge base with inclusions of the form T(C)
v D, whose intuitive meaning is that normally/typically Cs are also Ds. This
extension is based on a minimal model semantics corresponding to a notion of
rational closure, built upon preferential models. We recall the basic concepts
underlying preferential Description Logics. We also present two extensions of
the preferential semantics: on the one hand, we consider probabilistic
extensions, based on a distributed semantics that is suitable for tackling the
problem of commonsense concept combination, on the other hand, we consider
other strengthening of the rational closure semantics and construction to avoid
the so-called blocking of property inheritance problem.
