T-norm based fuzzy logics preserving degrees of truth
Publication Type:
Conference PaperSource:
IPMU 2008, p.1053-1060 (2008)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).