{"title":"模态双格逻辑及其扩展","authors":"S. O. Speranski","doi":"10.1007/s10469-022-09667-x","DOIUrl":null,"url":null,"abstract":"<div><div><p>We consider the lattices of extensions of three logics: (1) modal bilattice logic; (2) full Belnap–Dunn bimodal logic; (3) classical bimodal logic. It is proved that these lattices are isomorphic to each other. Furthermore, the isomorphisms constructed preserve various nice properties, such as tabularity, pretabularity, decidability or Craig’s interpolation property.</p></div></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Modal Bilattice Logic and its Extensions\",\"authors\":\"S. O. Speranski\",\"doi\":\"10.1007/s10469-022-09667-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div><p>We consider the lattices of extensions of three logics: (1) modal bilattice logic; (2) full Belnap–Dunn bimodal logic; (3) classical bimodal logic. It is proved that these lattices are isomorphic to each other. Furthermore, the isomorphisms constructed preserve various nice properties, such as tabularity, pretabularity, decidability or Craig’s interpolation property.</p></div></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-04-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10469-022-09667-x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10469-022-09667-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We consider the lattices of extensions of three logics: (1) modal bilattice logic; (2) full Belnap–Dunn bimodal logic; (3) classical bimodal logic. It is proved that these lattices are isomorphic to each other. Furthermore, the isomorphisms constructed preserve various nice properties, such as tabularity, pretabularity, decidability or Craig’s interpolation property.
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