@inbook { IIIA-2003-759, title = {On the Hierarchy of t-norm Based Residuated Fuzzy Logics}, booktitle = {Beyond Two: Theory and Applications of Multiple-Valued Logic}, editor = {Fitting, M. Orlowska, E.}, year = {2003}, pages = {251-272}, publisher = {Physica-Verlag}, abstract = {In this paper we overview 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 algebraic varieties and show they can be suitably placed in a hierarchy of logics depending on their characteristic axioms. We stress that the most general variety generated by residuated structures in [0,1], which are defined by left-continuous t-norms, is not the variety of residuated lattices but the variety of pre-linear residuated lattices, also known as MTL-algebras. Finally, we also relate t-norm based logics to substructural logics to substructural logics, in particular to Ono's hierarchy of extensions of the Full Lambek Calculus.}, author = {Francesc Esteva and Llu\'{\i}s Godo and Angel Garc\'{\i}a-Cerda\~na} }