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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| 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.
Semisimplicity, EDPC and Discriminator Varieties of Residuated Lattices.Tomasz Kowalski - 2004 - Studia Logica 77 (2):255 - 265.
On Fuzzy Logic II. Enriched Residuated Lattices and Semantics of Propositional Calculi.Jan Pavelka - 1979 - Mathematical Logic Quarterly 25 (7‐12):119-134.
The Variety Of Residuated Lattices Is Generated By Its Finite Simple Members.Tomasz Kowalski & Hiroakira Ono - 2000 - Reports on Mathematical Logic:59-77.
View all 9 references / Add more references
Citations of this work BETA
Stone Duality for Lattice Expansions.Chrysafis Hartonas - 2018 - Logic Journal of the IGPL 26 (5):475-504.
Constructive Logic with Strong Negation is a Substructural Logic. I.Matthew Spinks & Robert Veroff - 2008 - Studia Logica 88 (3):325-348.
Constructive Logic with Strong Negation is a Substructural Logic. II.M. Spinks & R. Veroff - 2008 - Studia Logica 89 (3):401-425.
Modal Translation of Substructural Logics.Chrysafis Hartonas - 2020 - Journal of Applied Non-Classical Logics 30 (1):16-49.
View all 8 citations / Add more citations
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