| Project/Area Number |
13640109
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Japan Advanced Institute of Science and Technology |
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Principal Investigator |
ONO Hiroakira JAIST, School of Information Science, Professor, 情報科学研究科, 教授 (90055319)
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| Co-Investigator(Kenkyū-buntansha) |
TANAKA Yoshihito Kyushu Sangyo University, Faculty of Economics, Associate Professor, 経済学部, 助教授 (70320132)
SHIMURA Tatsuya Nihon University, College of Science and Technology, Associate Professor, 理工学部, 助教授 (90246835)
KOMORI Yuichi Chiba Univeristy, Faculty of Science, Professor, 総合メディア基盤センター, 教授 (10022302)
HAMANO Masahiro JAIST, School of Information Science, Research Associate, 情報科学研究科, 助手 (50313705)
TOJO Satoshi JAIST, School of Information Science, Professor, 情報科学研究科, 教授 (90272989)
コワルスキ トマシュ 北陸先端科学技術大学院大学, 情報科学研究科, 助手 (70303336)
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| Project Period (FY) |
2001 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2003: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2002: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2001: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Keywords | substructural logics / universal algebra / residuated lattices / many-valued logics / fuzzy logic / 有限モデル性 / クリプキ意味論 / 剰余構造 |
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| Research Abstract |
Main aim of this project is to promote the study of substructural logics by using algebraic methods.Hiroakira Ono, who is the head investigator of this project, has led this research field for these years, in collaboration with researchers from United States, Poland, Czech, Italy, Australia and so on. The subject attracts not only logicians, including researchers of many-valued logics and fuzzy logic, but also algebraists. Now, our interdisciplinary project of "Algebra and Substructural Logics" is getting recognized well in the community of logicians.
Our project was quite successful and many of important results are obtained related to this project.H.Ono was invited twice to Italy to pursue cooperative researches with Italian logicians, including Prof.F.Montagna of University of Siena and Prof.D.Mundici of University of Florence.Some important progress, e.g. standard completeness of a first-order fuzzy logic and a general observation on nuclei on residuated lattices, was made by this c
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ollaboration. Other major achievements in our project are as follows :
1.purely algebraic proof of cut elimination theorem(with F.Berardinelli and P.Jipsen),
2.algebraization of substructural logics and application(with N.Galatos),
3.comprehensive study of Glivenko-type theorems(with N.Galatos).
These results were presented at several international conferences like "The First Joint International Conference of AMS and UMI, "Advances in Modal Logic 2002", "The Logic of Soft Computing III" and "50 Years of Studia Logica, Conference II", where H.Ono was invited.
Another important activity of our project we have done was to organize an international workshop "Algebra & Substructural Logics : Take Two" in November, 2002. We invited eight leading researchers, both from logic and algebra, from abroad. The workshop was of high level and therefore quite successful. The proceedings is now edited as two volumes of special issue of Studia Logica, one of most prestigious journals of logic, and will be published in 2004. Less
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