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Residuated logics based on strict triangular norms with an involutive negation. (English) Zbl 1165.03326
Summary: In general, there is only one fuzzy logic in which the standard interpretation of the strong conjunction is a strict triangular norm, namely, the product logic. We study several equations which are satisfied by some strict t-norms and their dual t-conorms. Adding an involutive negation, these equations allow us to generate countably many logics based on strict t-norms which are different from the product logic.

MSC:
03B52 Fuzzy logic; logic of vagueness
03G25 Other algebras related to logic
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