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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/8554

Title: Glivenko theorems for substructural logics over FL
Authors: Galatos, Nikolaos
Ono, Hiroakira
Issue Date: 2006-12
Publisher: Association for Symbolic Logic
Magazine name: The Journal of Symbolic Logic
Volume: 71
Number: 4
Start page: 1353
End page: 1384
Abstract: It is well known that classical propositional logic can be interpreted in intuitionistic propositional logic. In particular Glivenko's theorem states that a formula is provable in the former iff its double negation is provable in the latter. We extend Glivenko's theorem and show that for every involutive substructural logic there exists a minimum substructural logic that contains the first via a double negation interpretation. Our presentation is algebraic and is formulated in the context of residuated lattices. In the last part of the paper, we also discuss some extended forms of the Kolmogorov translation and we compare it to the Glivenko translation.
Rights: Copyright (C) 2006 Association for Symbolic Logic. It is posted here by permission of Association for Symbolic Logic. Nikolaos Galatos and Hiroakira Ono, The Journal of Symbolic Logic, 71(4), 2006, 1353-1384.
URI: http://hdl.handle.net/10119/8554
Material Type: publisher
Appears in Collections:z4-10-1. 雑誌掲載論文 (Journal Articles)

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