Fuzzy Logic and Probability

TL;DR

This paper introduces a fuzzy logic framework for probabilistic reasoning, bridging fuzzy logic and probability theory, with completeness results and extensions to conditional probabilities and other uncertainty models.

Contribution

It proposes a novel fuzzy logic of probability that differs from classical probabilistic logics, providing formal completeness results and methods to handle various uncertainty types.

Findings

Established a fuzzy logic of probability with completeness results.

Demonstrated how probability values relate to fuzzy truth-values.

Suggested extensions to conditional probabilities and other uncertainty formalisms.

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.