Residuated logics based on strict triangular norms with an involutive negation

Mathematical Logic Quarterly 52 (3):269-282 (2006)
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Abstract

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

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