T-norm based fuzzy logics preserving degrees of truth

F. Bou, F. Esteva, J.M. Font, A. Gil, L. Godo, A. Torrens, V. Verdú.

T-norm based fuzzy logics are usually considered as 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 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 ^ and their properties turn out to be very diferent from the ones satisfied by the truth preserving logics. For instance, they are selfextensional (but not Fregean) and with few exceptions they are not algebraizable (not even protoalgebraic).

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