PROCEEDINGS IPMU '08
A first approach to the Deduction-Detachment Theorem in logics preserving degrees of truth
Félix Bou
This paper studies the Deduction-
Detachment Theorem (DDT) in
the realm of logics associated with
bounded, commutative and integral
residuated lattices whose consequence
relation preserves degrees
of truth (strictly speaking, it preserves
the lower bounds of truth values
of the premises). It is given some
necessary conditions that must enjoy
the varieties with a logic having the
DDT. In two particular cases these
conditions are indeed sufficient to
characterize the DDT. In the paper
it is also considered the case where
the Delta operator is added to the
language, and the case of a kind of
local version of the DDT.
 | PDF full paper |