Advances in Logics by Algebraic Methods

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Algebraic approaches to logics are attracting much attention in recent year. One can see this tendency in particular in the study of modal logics and substructural logics, which accelerates collaborations among logicians and algebraists. The head investigator Ono has made a certain contribution to this. In fact, he organized the workshop "Algebra and Substructural Logics" (AsubL) twice before at JAIST in 1999 and 2002.During the term of the present project, Ono organized the 2nd International Conference "Algebraic and Topological Methods in Nonclassical Logics" (TANCL) at Barcelona in 2005 as the chair. The conference was quite successful, and therefore international conferences of this kind have been organized often, after this. During the 3rd TANCL conference held in 2007 at Oxford, it was decided to have the conference biennially, and Ono was elected as a member of its steering committee. Also, together with A. Wronski, he organized the 3rd AsubL workshop in Krakow of Poland in 2006 … More , which was small but of high level. The collection of selected papers presented there was published already as a special issue of Reports on Mathematical Logic.Ono gave tutorial talks in two international conferences "Ordered Structures in Many-Valued Logics" in 2006 and "Order, Algebra and Logics" in 2007. In the latter, also N. Galatos, an investigator of the project, gave an invited talk. These talks are based on two joint papers with Ono and Galatos, in which some of fundamental results on substructural logics and residuated lattices are shown.The most important contribution of our project is that we have finally completed a book with the help of both T. Kowalski and P. Jipsen. The book "Residuated Lattices: an algebraic glimpse at substructural logics" consists of more than 500 pages, which was published in 2007 from Elsevier as a volume in the prestigious series "Studies in Logic and the Foundations of Mathematics". It has already had a reputation as a seminal work in this research field. Less