Issues on adjointness in multiple-valued logics

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, commutative conjunctions, associative conjunctions and triangular norms. We also introduce and characterize pseudo-strict and pseudo-continuous implications and conjunctions, and we explore the close relationship between these two notions.