{"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}
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.