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Probabilistic Description Logics for Subjective Uncertainty

Carsten Lutz; Lutz Schröder
In: Fangzhen Lin; Ulrike Sattler (Hrsg.). Proceedings of the 12th International Conference on Principles of Knowledge Representation and Reasoning. International Conference on Principles of Knowledge Representation and Reasoning (KR-2010), 12th, May 9-13, Toronto, Ontario, Canada, AAAI Press, Menlo, CA, 5/2010.

Abstract

We propose a new family of probabilistic description logics (DLs) that, in contrast to most existing approaches, are derived in a principled way from Halpern's probabilistic first-order logic. The resulting probabilistic DLs have a two-dimensional semantics similar to certain popular combinations of DLs with temporal logic and are well-suited for capturing subjective probabilities. Our main contribution is a detailed study of the complexity of reasoning in the new family of probabilistic DLs, showing that it ranges from PTIME for weak variants based on the lightweight DL EL to undecidable for some expressive variants based on the DL ALC.

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