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このアイテムの引用には次の識別子を使用してください:
http://hdl.handle.net/10119/8554
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| タイトル: | Glivenko theorems for substructural logics over FL |
| 著者: | Galatos, Nikolaos
Ono, Hiroakira |
| 発行日: | 2006-12 |
| 出版者: | Association for Symbolic Logic |
| 誌名: | The Journal of Symbolic Logic |
| 巻: | 71 |
| 号: | 4 |
| 開始ページ: | 1353 |
| 終了ページ: | 1384 |
| 抄録: | 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 |
| 資料タイプ: | publisher |
| 出現コレクション: | z4-10-1. 雑誌掲載論文 (Journal Articles)
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このアイテムのファイル:
| ファイル |
記述 |
サイズ | 形式 |
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| 9278.pdf | | 287Kb | Adobe PDF | 見る/開く |
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