Title T-norm based fuzzy logics preserving degrees of truth Publication Type Conference Paper Year of Publication 2008 Authors Bou F, Esteva F, Font JMaria, Gil A, Godo L, Torrens A, Verdú V Editor Conference Name IPMU 2008 Pagination 1053-1060 Abstract T-norm based fuzzy logics are usually considered as {\it truth preserving}, that is, taking $1$ as the only truth value to be preserved in inferences. In this paper we study t-norm based fuzzy logics \textit{preserving degrees of truth}, that is, preserving the lower bounds of the truth degrees of the premises. These logics are axiomatizable by using a restricted form of Modus Ponens together with the rule of Adjunction for $\wedge$ and their properties turn out to be very diferent from the ones satisfied by the \textit{truth preserving logics}. For instance, they are selfextensional (but not Fregean) and with few exceptions they are not algebraizable (not even protoalgebraic).