Fuzzy Logic and Markov Kernels

Fuzzy logic is a way to argue with boolean predicates for which we only have a confidence value between 0 and 1 rather than a well defined truth value. It is tempting to interpret such a confidence as a probability. We use Markov kernels, parametrised probability distributions, to do just that. As a...

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Bibliographic Details
Main Author Brussee, Rogier
Format Journal Article
LanguageEnglish
Published 07.03.2023
Subjects
Computer Science - Logic in Computer Science
Mathematics - Logic
Mathematics - Probability
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Summary:Fuzzy logic is a way to argue with boolean predicates for which we only have a confidence value between 0 and 1 rather than a well defined truth value. It is tempting to interpret such a confidence as a probability. We use Markov kernels, parametrised probability distributions, to do just that. As a consequence we get general fuzzy logic connectives from probabilistic computations on products of the booleans, stressing the importance of joint confidence functions. We discuss binary logic connectives in detail and recover the "classic" fuzzy connectives as bounds for the confidence for general connectives. We push multivariable logic formulas as far as being able to define fuzzy quantifiers and estimate the confidence.
DOI:10.48550/arxiv.2303.03725