On copulas, quasicopulas and fuzzy logic

We investigate (quasi)copulas as possible truth functions of fuzzy conjunction which is not necessarily associative and present some axiom systems for such fuzzy logics. In particular, we study an expansion of Łukasiewicz (infinite valued propositional) logic by a new connective interpreted as an arbitrary quasicopula (and also by a new connective interpreted as the residuum of the copula). Main results concern standard completeness.