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.

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