{"title":"折叠构造模态逻辑和直觉模态逻辑","authors":"Leonardo Pacheco","doi":"arxiv-2408.16428","DOIUrl":null,"url":null,"abstract":"In this note, we prove that the constructive and intuitionistic variants of\nthe modal logic $\\mathsf{KB}$ coincide. This result contrasts with a recent\nresult by Das and Marin, who showed that the constructive and intuitionistic\nvariants of $\\mathsf{K}$ do not prove the same diamond-free formulas.","PeriodicalId":501306,"journal":{"name":"arXiv - MATH - Logic","volume":"26 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Collapsing Constructive and Intuitionistic Modal Logics\",\"authors\":\"Leonardo Pacheco\",\"doi\":\"arxiv-2408.16428\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this note, we prove that the constructive and intuitionistic variants of\\nthe modal logic $\\\\mathsf{KB}$ coincide. This result contrasts with a recent\\nresult by Das and Marin, who showed that the constructive and intuitionistic\\nvariants of $\\\\mathsf{K}$ do not prove the same diamond-free formulas.\",\"PeriodicalId\":501306,\"journal\":{\"name\":\"arXiv - MATH - Logic\",\"volume\":\"26 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.16428\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.16428","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Collapsing Constructive and Intuitionistic Modal Logics
In this note, we prove that the constructive and intuitionistic variants of
the modal logic $\mathsf{KB}$ coincide. This result contrasts with a recent
result by Das and Marin, who showed that the constructive and intuitionistic
variants of $\mathsf{K}$ do not prove the same diamond-free formulas.
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