{"title":"布尔组的关联逻辑","authors":"Yale Weiss","doi":"10.1093/jigpal/jzab031","DOIUrl":null,"url":null,"abstract":"","PeriodicalId":51114,"journal":{"name":"Logic Journal of the IGPL","volume":"31 1","pages":"96-114"},"PeriodicalIF":0.6000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The relevance logic of Boolean groups\",\"authors\":\"Yale Weiss\",\"doi\":\"10.1093/jigpal/jzab031\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\",\"PeriodicalId\":51114,\"journal\":{\"name\":\"Logic Journal of the IGPL\",\"volume\":\"31 1\",\"pages\":\"96-114\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Logic Journal of the IGPL\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/10057253/\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"LOGIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Logic Journal of the IGPL","FirstCategoryId":"100","ListUrlMain":"https://ieeexplore.ieee.org/document/10057253/","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"LOGIC","Score":null,"Total":0}
引用次数: 0
摘要
在本文中,我考虑布尔群的正逻辑(即每个非单位元素为2阶的阿贝尔群),其中这些被视为操作语义 la Urquhart的框架。我称这种逻辑为BG。证明了最小非平凡布尔群上的逻辑,作为一个框架,与Robles和msamudez开发的拟相关逻辑的正片段相同(还讨论了该结果的扩展,其中包括否定)。证明了BG满足变量共享性质,是halldsamen完全的,但不满足分离性质。声音和完整的下标表提出了BG。提出了一个公理化(用融合扩展的肯定语言),它对于BG是健全的,并且对于相关的三元关系语义是完整的;确定BG本身的完全公理化的问题仍未解决。还讨论了BG与准相关逻辑KR之间的联系。
期刊介绍:
Logic Journal of the IGPL publishes papers in all areas of pure and applied logic, including pure logical systems, proof theory, model theory, recursion theory, type theory, nonclassical logics, nonmonotonic logic, numerical and uncertainty reasoning, logic and AI, foundations of logic programming, logic and computation, logic and language, and logic engineering.
Logic Journal of the IGPL is published under licence from Professor Dov Gabbay as owner of the journal.