{"title":"作为拓扑空间逻辑的直观 S4","authors":"Jim de Groot, Ian Shillito","doi":"10.1093/logcom/exae030","DOIUrl":null,"url":null,"abstract":"We design and study various topological semantics for the diamond-free intuitionistic modal logic $\\textsf{iS4}$, an intuitionistic analogue of $\\textsf{S4}$. Ultimately we prove that ordinary topological spaces can be used as semantics, using the specialization order to interpret intuitionistic implication and the interior for the modality. Some of our soundness and completeness results are mechanised in Coq.","PeriodicalId":50162,"journal":{"name":"Journal of Logic and Computation","volume":"6 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Intuitionistic S4 as a logic of topological spaces\",\"authors\":\"Jim de Groot, Ian Shillito\",\"doi\":\"10.1093/logcom/exae030\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We design and study various topological semantics for the diamond-free intuitionistic modal logic $\\\\textsf{iS4}$, an intuitionistic analogue of $\\\\textsf{S4}$. Ultimately we prove that ordinary topological spaces can be used as semantics, using the specialization order to interpret intuitionistic implication and the interior for the modality. Some of our soundness and completeness results are mechanised in Coq.\",\"PeriodicalId\":50162,\"journal\":{\"name\":\"Journal of Logic and Computation\",\"volume\":\"6 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-08-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Logic and Computation\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1093/logcom/exae030\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Logic and Computation","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1093/logcom/exae030","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
Intuitionistic S4 as a logic of topological spaces
We design and study various topological semantics for the diamond-free intuitionistic modal logic $\textsf{iS4}$, an intuitionistic analogue of $\textsf{S4}$. Ultimately we prove that ordinary topological spaces can be used as semantics, using the specialization order to interpret intuitionistic implication and the interior for the modality. Some of our soundness and completeness results are mechanised in Coq.
期刊介绍：
Logic has found application in virtually all aspects of Information Technology, from software engineering and hardware to programming and artificial intelligence. Indeed, logic, artificial intelligence and theoretical computing are influencing each other to the extent that a new interdisciplinary area of Logic and Computation is emerging.
The Journal of Logic and Computation aims to promote the growth of logic and computing, including, among others, the following areas of interest: Logical Systems, such as classical and non-classical logic, constructive logic, categorical logic, modal logic, type theory, feasible maths.... Logical issues in logic programming, knowledge-based systems and automated reasoning; logical issues in knowledge representation, such as non-monotonic reasoning and systems of knowledge and belief; logics and semantics of programming; specification and verification of programs and systems; applications of logic in hardware and VLSI, natural language, concurrent computation, planning, and databases. The bulk of the content is technical scientific papers, although letters, reviews, and discussions, as well as relevant conference reviews, are included.
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