Reasoning in Description Logics with Typicalities and Probabilities of Exceptions

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 $\mathcal {ALC}$.

G.L. Pozzato—Partially supported by the project “ExceptionOWL”, Università di Torino and Compagnia di San Paolo, call 2014 “Excellent (young) PI”, project ID: Torino_call2014_L1_111.