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The Liar paradox and fuzzy logic. (English) Zbl 0945.03031
Summary: Can one extend crisp Peano arithmetic PA by a possibly many-valued predicate $$\text{Tr}(x)$$ saying “$$x$$ is true” and satisfying the “dequotation schema” $$\varphi\equiv \text{Tr}(\overline\varphi)$$ for all sentences $$\varphi$$? This problem is investigated in the frame of Łukasiewicz infinitely valued logic.

##### MSC:
 03B50 Many-valued logic 03F30 First-order arithmetic and fragments 03B52 Fuzzy logic; logic of vagueness
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##### References:
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