Substructural Logics and their Algebraic Structures

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， 关于我们 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

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