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

摘要

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