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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/10119/4988
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| タイトル: | Algebraic aspects of cut elimination |
| 著者: | Belardinelli, Francesco
Jipsen, Peter
Ono, Hiroakira |
| キーワード: | Algebraic Gentzen systems
cut elimination
substructural logics
residuated lattices
finite model property |
| 発行日: | 2004-07 |
| 出版者: | Springer |
| 誌名: | Studia Logica |
| 巻: | 77 |
| 号: | 2 |
| 開始ページ: | 209 |
| 終了ページ: | 240 |
| DOI: | 10.1023/B:STUD.0000037127.15182.2a |
| 抄録: | We will give here a purely algebraic proof of the cut elimination theorem for various sequent systems. Our basic idea is to introduce mathematical structures, called Gentzen structures, for a given sequent system without cut, and then to show the completeness of the sequent system without cut with respect to the class of algebras for the sequent system with cut, by using the quasi-completion of these Gentzen structures. It is shown that the quasi-completion is a generalization of the MacNeille completion. Moreover, the finite model property is obtained for many cases, by modifying our completeness proof. This is an algebraic presentation of the proof of the finite model property discussed by Lafont [12] and Okada-Terui [17]. |
| Rights: | This is the author-created version of Springer, Francesco Belardinelli, Peter Jipsen and Hiroakira Ono, Studia Logica, 77(2), 2004, 209-240. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1023/B:STUD.0000037127.15182.2a |
| URI: | http://hdl.handle.net/10119/4988 |
| 資料タイプ: | author |
| 出現コレクション: | i10-1. 雑誌掲載論文 (Journal Articles)
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このアイテムのファイル:
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記述 |
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| C3747.pdf | | 288Kb | Adobe PDF | 見る/開く |
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