Substructural Logics and their Algebraic Structures

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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