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Fuzzy logic is understood as a logic with a comparative and truth-functional notion of truth. Arithmetical complexity of sets of tautologies (identically true sentences) and satisfiable sentences (sentences true in at least one interpretation) as well of sets of provable formulas of the most important systems of fuzzy predicate logic is determined or at least estimated.
We construct a faithful interpretation of Łukasiewicz's logic in product logic (both propositional and predicate). Using known facts it follows that the product predicate logic is not recursively axiomatizable. We prove a completeness theorem for product logic extended by a unary connective δ of Baaz [1]. We show that Gödel's logic is a sublogic of this extended product logic. We also prove NP-completeness...
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