{"title":"一些有趣的多值逻辑的规范化","authors":"Nils Kürbis, Y. Petrukhin","doi":"10.12775/llp.2021.009","DOIUrl":null,"url":null,"abstract":"In this paper, we consider a set of quite interesting threeand four-valued logics and prove normalisation theorem for their natural deduction formulations. Among the logics in question are the Logic of Paradox, First Degree Entailment, Strong Kleene logic, and some of their implicative extensions, including RM3 and RM3 . Also, we present a detailed version of Prawitz’s proof of Nelson’s logic N4 and its extension by intuitionist negation.","PeriodicalId":43501,"journal":{"name":"Logic and Logical Philosophy","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Normalisation for Some Quite Interesting Many-Valued Logics\",\"authors\":\"Nils Kürbis, Y. Petrukhin\",\"doi\":\"10.12775/llp.2021.009\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we consider a set of quite interesting threeand four-valued logics and prove normalisation theorem for their natural deduction formulations. Among the logics in question are the Logic of Paradox, First Degree Entailment, Strong Kleene logic, and some of their implicative extensions, including RM3 and RM3 . Also, we present a detailed version of Prawitz’s proof of Nelson’s logic N4 and its extension by intuitionist negation.\",\"PeriodicalId\":43501,\"journal\":{\"name\":\"Logic and Logical Philosophy\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-06-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Logic and Logical Philosophy\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12775/llp.2021.009\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"LOGIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Logic and Logical Philosophy","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12775/llp.2021.009","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"LOGIC","Score":null,"Total":0}
Normalisation for Some Quite Interesting Many-Valued Logics
In this paper, we consider a set of quite interesting threeand four-valued logics and prove normalisation theorem for their natural deduction formulations. Among the logics in question are the Logic of Paradox, First Degree Entailment, Strong Kleene logic, and some of their implicative extensions, including RM3 and RM3 . Also, we present a detailed version of Prawitz’s proof of Nelson’s logic N4 and its extension by intuitionist negation.
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