Authors
Hiroakira Ono
Japan Advanced Institute of Science and Technology
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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Reprint years 2010, 2011
DOI 10.26686/ajl.v8i0.1813
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References found in this work BETA

Logics Without the Contraction Rule.Hiroakira Ono & Yuichi Komori - 1985 - Journal of Symbolic Logic 50 (1):169-201.
The Lattice of Modal Logics: An Algebraic Investigation.W. J. Blok - 1980 - Journal of Symbolic Logic 45 (2):221-236.

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Citations of this work BETA

Stone Duality for Lattice Expansions.Chrysafis Hartonas - 2018 - Logic Journal of the IGPL 26 (5):475-504.
Proof Theory and Algebra in Logic.Hiroakira Ono - 2019 - Singapore: Springer Singapore.
Modal Translation of Substructural Logics.Chrysafis Hartonas - 2020 - Journal of Applied Non-Classical Logics 30 (1):16-49.

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