On complete residuated many-valued logics with t-norm conjunction

In this paper we summarize recent results, both logical and algebraic, about [0,1]-valued logical systems having a t-norm and its residuum as truth functions for conjunction and implication. We describe their axiomatic systems and their algebraic varieties, and we stress that the most general variety generated by residuated structures in [0, 1] defined by (left-continuous) t-norms is the variety of pre-linear residuated lattices.