Reasoning in description logics with typicalities and probabilities of exceptions

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Abstract

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+TPR, of the logic of typicality ALC+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 + TPR and we exploit it to show that entailment is ExpTime-complete as for the underlying ALC.

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Pozzato, G. L. (2017). Reasoning in description logics with typicalities and probabilities of exceptions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10369 LNAI, pp. 409–420). Springer Verlag. https://doi.org/10.1007/978-3-319-61581-3_37

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