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Advances in Nonstandard Logic

非标准逻辑的进展

基本信息

批准号：
10440027
负责人：
ONO Hiroakira
金额：
$ 3.52万
依托单位：
Japan Advanced Institute of Science and Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B).
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-10440027/
关键词：
nonstandard logic substructural logic modal logic epistemic logic Kripke semantics game theory cut elimination theorem lambda calculi クリプキ完全性自然演繹体系クリプキ・フレーム

项目摘要

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

本项目的主要目的是促进非标准逻辑的研究和应用。在项目开始时，我们选择了以下四个主要的研究主题：1.子结构逻辑的代数方法，2.认知逻辑与博弈论，3.非标准谓词逻辑的研究，4.非标准逻辑的证明论方法。本项目的主要成果如下：1.与T·科瓦尔斯基合作，H.Ono一直在研究各种剩余格作为无收缩规则逻辑的代数语义。他已经完成了四篇联合论文，其中两篇已经在国际期刊上发表。同时，H.Ono曾在1998年波兰托伦、1999年西班牙巴塞罗那、1999年意大利米兰和2000年意大利曼托瓦就这一主题进行了四次特邀演讲。最近，科瓦尔斯基和小野写了一本专著《剩余格子》。金子和铃木一直在对游戏逻辑和常见的k…进行全面的研究更多的知识逻辑作为博弈论的逻辑框架。Shimura和One讨论了情态谓词逻辑的最小扩张的Klipke完备性和不完全性问题，Suzuki为非标准谓词逻辑引入了更强的语义。在与Lambda演算有关的序列演算和自然演绎系统上，Komori、Hirokawa、Takano和Kashima得到了有趣的结果。所有这些成果要么发表在国际期刊上，要么在国际会议上公布。作为我们项目活动的一部分，我们组织了两个小型国际讲习班。1999年，举办了一个题为“代数与子结构逻辑”的讲习班，来自国外的8人作为特邀演讲者参加了讲习班。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嘉宾作演讲。支持第32届、第33届、第34届数理逻辑年会。这次会议被认为是日本关于非标准逻辑的最重要的会议，我们项目的成员多年来一直作为活跃的演讲者参与其中。出版并广泛分发了这三次会议的会议记录。此外，第34届年会的部分论文将作为2001年《逻辑部分公报》的特刊出版。较少