Logics without the contraction rule and residuated lattices

Australasian Journal of Logic 8:50-81 (2011)
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Abstract

In this paper, we will develop an algebraic study of substructural propositional logics over FLew, i.e. the logic which is obtained from intuitionistic logics by eliminating the contraction rule. Our main technical tool is to use residuated lattices as the algebraic semantics for them. This enables us to study different kinds of nonclassical logics, including intermediate logics, BCK-logics, Lukasiewicz’s many-valued logics and fuzzy logics, within a uniform framework.

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Hiroakira Ono
Japan Advanced Institute of Science and Technology