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The sorites paradox and fuzzy logic. (English) Zbl 1044.03017
The authors describe two interesting, slightly different ways to use fuzzy logic to discuss and explain the sorites paradox. Both approaches refer to an extended version of the Peano arithmetic: the extension being provided by a new unary predicate “feasible”, subject to some rather natural conditions.
One way is to use Hájek’s fuzzy logic BL and to extend it by a unary connective “almost true” with two suitable axioms
The other way is to refer to a “Pavelka-style” extension of infinite-valued Łukasiewicz logic, which allows for a graded notion of provability.

MSC:
03B52 Fuzzy logic; logic of vagueness
03F30 First-order arithmetic and fragments
03A05 Philosophical and critical aspects of logic and foundations
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