Fuzzy logic Glossary
Definition
Fuzzy logic is an alternative to the classical logical paradigm, based on the idea that truth is not all-or-nothing, but slides on some sort of scale, allowing propositions to be more or less true.
Comments
There are many varieties of fuzzy logic, but the one considered here shares with relevant logic the idea that the logical rules for introducing and eliminating connectives and quantifiers are all fine, but the underlying structure of what counts as a proof should be amended. In the case of fuzzy logic, we want to avoid claiming that multiple assumptions of the same formula (or multiple uses of the same assumption) can be discharged in one step as though the multiplicity made no difference.
Fuzzy logic is designed to accommodate reasoning with vague descriptions, and is intended to provide a solution to the sorites paradox.
See the first link below for an introduction.