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 ACC + T_r 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 ACC + T_R~P and we exploit ıt to show that entailment is ExpTiME-complete as for the underlying ALC.
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