On probabilities of exceptions in description logics of typicality

We describe 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 ACC+TP R, of the logic of typicality ACC + TR by inclusions of the form T(C) ⊆p D, whose intuitive meaning is that "typical Cs are Ds with a probability 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 + TP R and we exploit it to show that entailment is EXPTIME-complete as for the underlying ALC.