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 ALC+T R by inclusions of the form T(C)⊑ p D with probability p, whose intuitive meaning is that “all the typical Cs are Ds, and the probability that a C is not a D is 1−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+T R P and we exploit it to show that entailment is EXPTIME-complete as for the underlying ALC.

Typicalities and probabilities of exceptions in nonmotonic Description Logics

Pozzato, Gian Luca
2019-01-01

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+T R P , of the logic of typicality ALC+T R by inclusions of the form T(C)⊑ p D with probability p, whose intuitive meaning is that “all the typical Cs are Ds, and the probability that a C is not a D is 1−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+T R P and we exploit it to show that entailment is EXPTIME-complete as for the underlying ALC.
2019
107
81
100
https://www.sciencedirect.com/science/article/pii/S0888613X17305741?dgcid=author
Description Logics; Nonmonotonic Reasoning; Probabilities of exceptions; Typicality; Software; Theoretical Computer Science; Artificial Intelligence; Applied Mathematics
Pozzato, Gian Luca
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1694148
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