A Canonical Fuzzy Logic

TL;DR

This paper introduces canonical fuzzy logic (CFL), detailing its propositional calculus and fuzzy set theory, showing how classical logic and set theory are special cases within CFL based on a parameter.

Contribution

It presents the foundational notions and operations of CFL, a variant of fuzzy logic, and demonstrates its relation to classical logic and set theory.

Findings

CFL generalizes classical logic and set theory.

CFL's propositional calculus and fuzzy set theory are systematically developed.

Classical theories are special cases of CFL when a parameter w is 0 or 1.

Abstract

A presentation is provided of the basic notions and operations of a) the propositional calculus of a variant of fuzzy logic -- canonical fuzzy logic, CFL -- and in a more succinct and introductory way, of b) the theory of fuzzy sets according to that same logic. The propositional calculus of bivalent classical logic and classical set theory can be considered as particular cases of the corresponding theories of CFL if the numerical value of a specific parameter $w$ is restricted to only two possibilities, 0 and 1.