Reasoning in Description Logics with Typicalities and Probabilities of Exceptions

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10369)

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 \(\mathcal {ALC}+\mathbf{T}_\mathbf{R}^{ \textsf {P} }\), of the logic of typicality \(\mathcal {ALC}+\mathbf{T}_\mathbf{R}\) by inclusions of the form \(\mathbf{T}(C) \sqsubseteq _p D\), 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 \(\mathcal {ALC}+\mathbf{T}_\mathbf{R}^{ \textsf {P} }\) and we exploit it to show that entailment is ExpTime-complete as for the underlying \(\mathcal {ALC}\).

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversità di TorinoTurinItaly

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