Advances in Logics by Algebraic Methods

近年来，逻辑的代数方法引起了人们的广泛关注。人们可以看到这种趋势，特别是在模态逻辑和子结构逻辑的研究中，这加速了逻辑学家和代数学家之间的合作。首席调查员小野对此做出了一定的贡献。事实上，他在1999年和2002年两次在JAIST组织了“代数和子结构逻辑”（AsubL）研讨会。在本项目期间，小野于2005年在巴塞罗那组织了第二届国际会议“非经典逻辑中的代数和拓扑方法”（TANCL）。这次会议相当成功，因此此后经常组织这样的国际会议。在2007年于牛津举行的第三届TANCL会议期间，决定每两年举行一次会议，小野当选为指导委员会成员。此外，与A. 2006年在波兰克拉科夫组织了第三届AsubL研讨会 ...更多信息 规模虽小，但水平很高。小野在2006年和2007年的两次国际会议上分别发表了题为“多值逻辑中的有序结构”和“秩序、代数和逻辑”的演讲。在后者中，N. Galatos是该项目的调查员，他应邀做了一次演讲。这些演讲是基于与Ono和Galatos的两篇联合论文，其中展示了关于子结构逻辑和剩余格的一些基本结果。Kowalski和P. Jipsen。这本书“剩余晶格：代数一瞥子结构逻辑”由500多页组成，这是在2007年出版的爱思唯尔作为一个卷在著名的系列“研究逻辑和数学的基础”。它已经在这一研究领域作为一个开创性的工作的声誉。少

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