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Fuzzy Logic and Probability

By Petr Hajek, Lluis Godo and Francesc Esteva


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 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 truthvalues 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. 1 Introduction Discussions about the relation between fuzzy logic and probability are still numerous and sometimes rather controversial. In particular, using fuzzy logic to reason in a probabilistic way may be a priori considered as a "danger..

Year: 1995
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