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We contribute to the theory of implications and conjunctions related by adjointness, in multiple-valued logics. We suggest their use in Zadeh’s compositional rule of inference, to interpret generalized modus ponens inference schemata. We provide new complete characterizations of implications that distinguish left arguments, implications that satisfy the exchange principle, divisible conjunctions,...
As it is well known the logical material implication is not natural from the point of view of human reasoning; besides, in fuzzy logic, it is possible to classify the ply operators refering either to the boolean implication, or to the boolean conjunction (Mamdani's operator). Combining the aim to modelize human reasoning in a more natural way (subsequently in the spirit of Mamdani) with the necessity...
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