Substructural Logics and their Algebraic Structures

子结构逻辑及其代数结构

• 批准号: 13640109
• 负责人: ONO Hiroakira
• 金额: $ 2.3万
• 依托单位: Japan Advanced Institute of Science and Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640109/
• 关键词: 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

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 … More 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

本项目的主要目的是利用代数方法促进子结构逻辑的研究。该项目的首席研究员Hiroakira Ono多年来领导了这一研究领域，与来自美国、波兰、捷克、意大利、澳大利亚等国的研究人员合作。该课题不仅吸引了包括多值逻辑和模糊逻辑研究人员在内的逻辑学家，而且也吸引了代数学家。目前，我们的交叉学科“代数与子结构逻辑”项目在逻辑学界得到了很好的认可。我们的项目相当成功，并取得了许多与该项目相关的重要成果。H.Ono曾两次应邀前往意大利，与意大利锡耶纳大学的F.Montagna教授和佛罗伦萨大学的D.Mundici教授进行合作研究，取得了一些重要进展。例如一阶模糊逻辑的标准完备性和剩余格上原子核的一般观察， ...更多信息 嗅觉本课题的其他主要成果如下：1.割消定理的纯代数证明（与F.Berardinelli和P.Jipsen合著），2.子结构逻辑的代数化及其应用（与N.Galatos合著），3. Glivenko型定理的综合研究这些结果在几个国际会议上发表，如“第一届AMS和UMI联合国际会议”，“模态逻辑2002进展”，“软计算逻辑III”和“50年逻辑研究会议II”，其中H.Ono被邀请。我们项目的另一个重要活动是组织一个国际研讨会“代数和子结构逻辑：2002年11月，《两个人》。我们从国外邀请了八位逻辑学和代数学方面的顶尖研究人员。这次研讨会水平很高，因此相当成功。该论文集现由著名的逻辑学期刊Studia Logica编辑成两卷特刊，将于2004年出版。少

项目成果

古森 雄一: "λρ-calculus : A natural deduction for classical logic"Bulletin of the Section of Logic. 31. 65-70 (2002)

小森雄一：“λρ-演算：经典逻辑的自然演绎”逻辑科公告 31. 65-70 (2002)。

T.Shimura: "Kripke incompleteness of predicate extensions of Gabbay-de Jongh's logic of the finite binary trees."Bulletin of the Section of Logic. 31. 111-118 (2002)

T.Shimura：“Gabbay-de Jongh 的有限二叉树逻辑的谓词扩展的 Kripke 不完备性。”逻辑部分公告。

Y.Tanaka: "Model existence in noncompact modal logic."Studia Logica. 67-1. 61-73 (2001)

Y.Tanaka：“非紧模态逻辑中的模型存在。”Studia Logica。

志村 立矢: "Kripke incompleteness of predicate extentions of Gabbay-de Jongh's logic of the finite binary trees"Bulletin of the Section of Logic. 31・2. 111-118 (2002)

Tateya Shimura：“Gabbay-de Jongh 的有限二叉树逻辑的谓词扩展的 Kripke 不完备性”逻辑部分公告 31・2 (2002)。

金子 守: "Map of common knowledge logics"Studia Logica. (受理済).

Mamoru Kaneko：“常识逻辑图”Studia Logica（已接受）。