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.
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Notes
- 1.
In Theorem 10 in [10] the authors have shown that for any consistent KB there exists a finite minimal canonical model of KB.
- 2.
As mentioned, at this point of the presentation we only want to give an intuition of inferences characterizing \(\mathcal {ALC}+\mathbf{T}_\mathbf{R}^{ \textsf {P} }\). Technical details and definitions will be provided in Definition 5.
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Pozzato, G.L. (2017). Reasoning in Description Logics with Typicalities and Probabilities of Exceptions. In: Antonucci, A., Cholvy, L., Papini, O. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2017. Lecture Notes in Computer Science(), vol 10369. Springer, Cham. https://doi.org/10.1007/978-3-319-61581-3_37
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