Typicalities and probabilities of exceptions in nonmotonic Description Logics

We introduce a nonmonotonic procedure for preferential Description Logics in order to reason about typicality by taking probabilities of exceptions into account. We consider an extension, called ALC+T R P , of the logic of typicality ALC+T R by inclusions of the form T(C)⊑ p D with probability p, whose intuitive meaning is that “all the typical Cs are Ds, and the probability that a C is not a D is 1−p”. We consider a notion of extension of an ABox containing only some typicality assertions, then we equip each extension with a probability. We then restrict entailment of a query F to those extensions whose probabilities belong to a given and fixed range. We propose a decision procedure for reasoning in ALC+T R P and we exploit it to show that entailment is EXPTIME-complete as for the underlying ALC.