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arXiv:1302.4953cs.AI

Fuzzy Logic and Probability

Petr Hajek, Lluis Godo, Francesc Esteva

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Abstract

In this paper we deal with a new approach to probabilistic reasoning in a logical framework. Nearly almost all logics of probability that have been proposed in the literature are based on classical two-valued logic. After making clear the differences between fuzzy logic and probability theory, here we propose a {em fuzzy} logic of probability for which completeness results (in a probabilistic sense) are provided. The main idea behind this approach is that probability values of crisp propositions can be understood as truth-values of some suitable fuzzy propositions associated to the crisp ones. Moreover, suggestions and examples of how to extend the formalism to cope with conditional probabilities and with other uncertainty formalisms are also provided.

arXiv comments
Appears in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI1995)
Journal reference
DOI
Subjects
cs.AIArtificial Intelligence

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  1. Ranked programming: Probabilistic programming without probabilities 1 comment

    • That's fascinating! > This type of uncertainty is better addressed using fuzzy measures other than probability (which is only a subset of more general fuzzy theory). Do you mean that both probability theory and possibility theory are subsumed by fuzzy logic? What about works…

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