Fuzzy Logic and Probability
This work addresses the integration of fuzzy logic and probability theory for researchers in logic and uncertainty modeling, though it appears incremental as it builds on existing frameworks.
The paper tackles the problem of probabilistic reasoning by proposing a fuzzy logic of probability, where probability values of crisp propositions are interpreted as truth-values of fuzzy propositions, and provides completeness results for this approach.
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.