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Description Logics and Fuzzy Probability

Lutz Schröder; Dirk Pattinson
In: Toby Walsh (Hrsg.). 22nd International Joint Conference on Artificial Intelligence. International Joint Conference on Artificial Intelligence (IJCAI-2011), July 16-22, Barcelona, Spain, AAAI Press, Menlo Park, CA, 2011.


Uncertainty and vagueness are pervasive phenomena in real-life knowledge. They are supported in extended description logics that adapt classical description logics to deal with numerical probabilities or fuzzy truth values. While the two concepts are distinguished for good reasons, they combine in the notion of probably, which is ultimately a fuzzy qualification of probabilities. Here, we develop existing propositional logics of fuzzy probability into a full-blown description logic, and we show decidability of several variants of this logic under Lukasiewicz semantics. We obtain these results in a novel generic framework f fuzzy coalgebraic logic; this enables us to extend our results to logics that combine crisp ingredients including standard crisp roles and crisp numerical probabilities with fuzzy roles and fuzzy probabilities.


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