PROCEEDINGS IPMU '08
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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