连立逻辑和双推理多网格逻辑的代数完备性

IF 0.7 3区数学 Q4 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Journal of Logic Language and Information Pub Date : 2024-05-03 DOI:10.1007/s10849-024-09415-7

Yaroslav Petrukhin

{"title":"连立逻辑和双推理多网格逻辑的代数完备性","authors":"Yaroslav Petrukhin","doi":"10.1007/s10849-024-09415-7","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we introduce the notions of connexive and bi-intuitionistic multilattices and develop on their base the algebraic semantics for Kamide, Shramko, and Wansing’s connexive and bi-intuitionistic multilattice logics which were previously known in the form of sequent calculi and Kripke semantics. We prove that these logics are sound and complete with respect to the presented algebraic structures.</p>","PeriodicalId":48732,"journal":{"name":"Journal of Logic Language and Information","volume":"4 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Algebraic Completeness of Connexive and Bi-Intuitionistic Multilattice Logics\",\"authors\":\"Yaroslav Petrukhin\",\"doi\":\"10.1007/s10849-024-09415-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we introduce the notions of connexive and bi-intuitionistic multilattices and develop on their base the algebraic semantics for Kamide, Shramko, and Wansing’s connexive and bi-intuitionistic multilattice logics which were previously known in the form of sequent calculi and Kripke semantics. We prove that these logics are sound and complete with respect to the presented algebraic structures.</p>\",\"PeriodicalId\":48732,\"journal\":{\"name\":\"Journal of Logic Language and Information\",\"volume\":\"4 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-05-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Logic Language and Information\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1007/s10849-024-09415-7\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Logic Language and Information","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s10849-024-09415-7","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们引入了连生多格法和双直觉多格法的概念，并在其基础上发展了 Kamide、Shramko 和 Wansing 的连生多格法和双直觉多格法逻辑的代数语义，这些逻辑以前是以序列计算和克里普克语义的形式为人所知的。我们证明这些逻辑在所提出的代数结构方面是健全和完整的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

摘要图片

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Algebraic Completeness of Connexive and Bi-Intuitionistic Multilattice Logics

In this paper, we introduce the notions of connexive and bi-intuitionistic multilattices and develop on their base the algebraic semantics for Kamide, Shramko, and Wansing’s connexive and bi-intuitionistic multilattice logics which were previously known in the form of sequent calculi and Kripke semantics. We prove that these logics are sound and complete with respect to the presented algebraic structures.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Logic Language and Information COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCEL-LOGIC

CiteScore

1.70

自引率

12.50%

发文量

期刊介绍： The scope of the journal is the logical and computational foundations of natural, formal, and programming languages, as well as the different forms of human and mechanized inference. It covers the logical, linguistic, and information-theoretic parts of the cognitive sciences. Examples of main subareas are Intentional Logics including Dynamic Logic; Nonmonotonic Logic and Belief Revision; Constructive Logics; Complexity Issues in Logic and Linguistics; Theoretical Problems of Logic Programming and Resolution; Categorial Grammar and Type Theory; Generalized Quantification; Information-Oriented Theories of Semantic Structure like Situation Semantics, Discourse Representation Theory, and Dynamic Semantics; Connectionist Models of Logical and Linguistic Structures. The emphasis is on the theoretical aspects of these areas.

期刊最新文献

Why Sometimes the King of France is Not Bald: Presupposition Denial Without Ambiguity Logical Models of Mathematical Texts: The Case of Conventions for Division by Zero Propositional Logic for Infinitive Sentences Syllogistic Relevance and Term Logic Algebraic Completeness of Connexive and Bi-Intuitionistic Multilattice Logics