Reasoning in description logics with typicalities and probabilities of exceptions

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+TR, of the logic of typicality ALC+TR by inclusions of the form T(C)⊑pD , 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+TR and we exploit it to show that entailment is ExpTime-complete as for the underlying ALC.