On copulas, quasicopulas and fuzzy logic. (English) Zbl 1152.03018

The authors discuss the possibility to interpret the conjunction in fuzzy logics by a copula or a quasicopula. In contrast to t-norms, quasicopulas are not necessarily associative, and it is shown that associativity is exactly what makes the difference in logics: The logic of associative copulas and their corresponding residua is BL, the logic of continuous t-norms and their residua. Furthermore, an expansion of Łukasiewicz logic by an additional connective interpreted by a quasicopula is suggested. Strong finite standard completeness is shown. Finally, also the case of a further connective interpreted by the residuum corresponding to the quasicopula is considered.


03B52 Fuzzy logic; logic of vagueness
62H05 Characterization and structure theory for multivariate probability distributions; copulas
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