Advances in Nonstandard Logic

该项目的主要目的是促进非标准逻辑的研究及其应用。在开始项目时，我们选择了以下四个作为我们研究的主要主题：1。子结构逻辑的代数方法，2。认知逻辑和博弈论，3。非标准谓词逻辑的研究，4。非标准逻辑的证明理论方法。以下是我们项目的主要成果：在与T.Kowalski的合作中，h.o o一直在研究各种剩余格作为没有收缩规则的逻辑代数语义。他已经完成了四篇合作论文，其中两篇已经在国际期刊上发表。同时，小野洋子在1998年的波兰托伦、1999年的西班牙巴塞罗那、1999年的意大利米兰和2000年的意大利曼托瓦就这一主题进行了四次特邀演讲。最近，Kowalski和Ono撰写了专著《残格》（residual lattice）。Kaneko和Suzuki一直在对博弈论的逻辑框架——游戏逻辑和公共知识逻辑进行全面的研究。Shimura和One讨论了模态谓词逻辑的最小扩展的kripke -完备性和不完备性问题，Suzuki则引入了非标准谓词逻辑的更强语义。关于数列演算和与λ演算相关的自然演绎系统，Komori、Hirokawa、Takano和Kashima等人得到了有趣的结果。所有这些结果都在国际期刊上发表或在国际会议上宣布。作为我们项目活动的一部分，我们组织了两个小型国际研讨会。1999年举办了“代数与亚结构逻辑”研讨会，邀请了8位国外学者作为主讲嘉宾。研讨会的部分论文已发表在2001年的《数理逻辑报告》特刊上。2000年，我们组织了一个名为“代数与逻辑”的研讨会，邀请了三位来自国外的人作为主讲嘉宾。支持第32、33、34届数理逻辑年会。该会议被认为是日本最重要的非标准逻辑会议，我们的项目成员多年来一直积极发言。这三次会议的会议记录已出版并广为分发。第34届年会的论文选集将作为2001年《Section Logic Bulletin》的特刊发表。少

Main aim of this project is to promote the study of nonstandard logic and its application. When starting the project, we have chosen the following four as major subjects of our study :1. algebraic approach to substructural logics,2. epistemic logic and game theory,3. study of nonstandard predicate logics,4. proof-theoretic approach to nonstandard logics.Here are major achievments of our project :1. In collaboration with T.Kowalski, H.Ono has been developing a study of varieties of residuated lattices as algebraic semantics for logics without contraction rule. He has completed four joint papers, two of which have already been published in international journals. At the same time, H.Ono has given four invited talks on this topics at Torun, Poland, 1998, Barcelona, Spain, 1999, Milano, Italy, 1999, and Mantova, Italy, 2000. Recently, Kowalski and Ono have written up a monograph "Residuated Lattices".2. Kaneko and Suzuki have been developing a comprehensive study of game logic and common k … More nowledge logic as logical frameworks of game theory. Kripke-completeness and incompleteness problems of minimum extensions of modal predicate logics are discussed by Shimura and One, while Suzuki introduced stronger semantics for nonstandard predicate logics. On sequent calculi and natural deduction systems in relation to lambda calculi, Komori, Hirokawa, Takano and Kashima obtained interesting results. All of these results have been either published in international journals or announced at international conferences.3. As a part of the activity of our project, we organized two small international workshops. In 1999, a workshop "Algebra ＆ Substructural Logics" was held, where eight people were participated from abroad as invited speakers. Selected papers of the workshop have been published in a special issue of Reports on Mathematical Logic in 2001. In 2000, we organized a workshop "Algebra and Logic" by inviting three people from abroad as guest speakers.4. We supported 32nd, 33rd and 34th Annual Meetings of Mathematical Logic. The Meeting is regarded as the most important meeting on nonstandard logic in Japan, to which members of our project have contributed as active speakers for many years. Proceedings of these three meetings were published and distributed widely. Also, selected papers of the 34th Annual Meeting will be published as a special issue of Bulletin of the Section Logic in 2001. Less