超越分布性的正模态逻辑

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2023-09-26 DOI:10.1016/j.apal.2023.103374

Nick Bezhanishvili , Anna Dmitrieva , Jim de Groot , Tommaso Moraschini

{"title":"超越分布性的正模态逻辑","authors":"Nick Bezhanishvili , Anna Dmitrieva , Jim de Groot , Tommaso Moraschini","doi":"10.1016/j.apal.2023.103374","DOIUrl":null,"url":null,"abstract":"<div>We develop a duality for (modal) lattices that need not be distributive, and use it to study positive (modal) logic beyond distributivity, which we call weak positive (modal) logic. This duality builds on the Hofmann, Mislove and Stralka duality for meet-semilattices. We introduce the notion of <math><msub><mrow><mi>Π</mi></mrow><mrow><mn>1</mn></mrow></msub></math>-persistence and show that every weak positive modal logic is <math><msub><mrow><mi>Π</mi></mrow><mrow><mn>1</mn></mrow></msub></math>-persistent. This approach leads to a new relational semantics for weak positive modal logic, for which we prove an analogue of Sahlqvist's correspondence result.1</div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Positive modal logic beyond distributivity\",\"authors\":\"Nick Bezhanishvili , Anna Dmitrieva , Jim de Groot , Tommaso Moraschini\",\"doi\":\"10.1016/j.apal.2023.103374\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>We develop a duality for (modal) lattices that need not be distributive, and use it to study positive (modal) logic beyond distributivity, which we call weak positive (modal) logic. This duality builds on the Hofmann, Mislove and Stralka duality for meet-semilattices. We introduce the notion of <math><msub><mrow><mi>Π</mi></mrow><mrow><mn>1</mn></mrow></msub></math>-persistence and show that every weak positive modal logic is <math><msub><mrow><mi>Π</mi></mrow><mrow><mn>1</mn></mrow></msub></math>-persistent. This approach leads to a new relational semantics for weak positive modal logic, for which we prove an analogue of Sahlqvist's correspondence result.1</div>\",\"PeriodicalId\":50762,\"journal\":{\"name\":\"Annals of Pure and Applied Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-09-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Pure and Applied Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0168007223001318\",\"RegionNum\":2,\"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":"Annals of Pure and Applied Logic","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168007223001318","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"LOGIC","Score":null,"Total":0}

引用次数: 4

摘要

我们为不需要分配的（模态）格发展了对偶性，并用它来研究超越分配性的正（模态）逻辑，我们称之为弱正（模式）逻辑。这种对偶建立在满足半格的Hofmann、Mislove和Stralka对偶的基础上。我们引入了π1-持久性的概念，并证明了每一个弱正模态逻辑都是π1-持久的。这种方法为弱正模态逻辑带来了一种新的关系语义，我们证明了其类似于Sahlqvist的对应结果。1

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Positive modal logic beyond distributivity

We develop a duality for (modal) lattices that need not be distributive, and use it to study positive (modal) logic beyond distributivity, which we call weak positive (modal) logic. This duality builds on the Hofmann, Mislove and Stralka duality for meet-semilattices. We introduce the notion of $Π_{1}$ -persistence and show that every weak positive modal logic is $Π_{1}$ -persistent. This approach leads to a new relational semantics for weak positive modal logic, for which we prove an analogue of Sahlqvist's correspondence result.¹

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

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.