模态遇见蕴涵逻辑

Jim de Groot, D. Pattinson
{"title":"模态遇见蕴涵逻辑","authors":"Jim de Groot, D. Pattinson","doi":"10.46298/lmcs-18(3:1)2022","DOIUrl":null,"url":null,"abstract":"We extend the meet-implication fragment of propositional intuitionistic logic\nwith a meet-preserving modality. We give semantics based on semilattices and a\nduality result with a suitable notion of descriptive frame. As a consequence we\nobtain completeness and identify a common (modal) fragment of a large class of\nmodal intuitionistic logics. We recognise this logic as a dialgebraic logic,\nand as a consequence obtain expressivity-somewhere-else. Within the dialgebraic\nframework, we then investigate the extension of the meet-implication fragment\nof propositional intuitionistic logic with a monotone modality and prove\ncompleteness and expressivity-somewhere-else for it.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"18 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Modal meet-implication logic\",\"authors\":\"Jim de Groot, D. Pattinson\",\"doi\":\"10.46298/lmcs-18(3:1)2022\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We extend the meet-implication fragment of propositional intuitionistic logic\\nwith a meet-preserving modality. We give semantics based on semilattices and a\\nduality result with a suitable notion of descriptive frame. As a consequence we\\nobtain completeness and identify a common (modal) fragment of a large class of\\nmodal intuitionistic logics. We recognise this logic as a dialgebraic logic,\\nand as a consequence obtain expressivity-somewhere-else. Within the dialgebraic\\nframework, we then investigate the extension of the meet-implication fragment\\nof propositional intuitionistic logic with a monotone modality and prove\\ncompleteness and expressivity-somewhere-else for it.\",\"PeriodicalId\":314387,\"journal\":{\"name\":\"Log. Methods Comput. Sci.\",\"volume\":\"18 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-12-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Log. Methods Comput. Sci.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46298/lmcs-18(3:1)2022\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Log. Methods Comput. Sci.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/lmcs-18(3:1)2022","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

我们用满足保持模态扩展了命题直觉逻辑的满足蕴涵片段。给出了基于半格的语义,并给出了适当的描述框架概念的对偶结果。因此,我们获得了完备性,并确定了一大类模态直觉逻辑的公共(模态)片段。我们承认这种逻辑是一种对话性逻辑,并因此在别处获得了表达性。在对话性框架内,我们研究了具有单调模态的命题直觉逻辑的满足-蕴涵片段的扩展,并证明了它的完全性和表达性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Modal meet-implication logic
We extend the meet-implication fragment of propositional intuitionistic logic with a meet-preserving modality. We give semantics based on semilattices and a duality result with a suitable notion of descriptive frame. As a consequence we obtain completeness and identify a common (modal) fragment of a large class of modal intuitionistic logics. We recognise this logic as a dialgebraic logic, and as a consequence obtain expressivity-somewhere-else. Within the dialgebraic framework, we then investigate the extension of the meet-implication fragment of propositional intuitionistic logic with a monotone modality and prove completeness and expressivity-somewhere-else for it.
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
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信