{"title":"对称直观逻辑和混淆直观逻辑","authors":"Norihiro Kamide","doi":"10.1093/jigpal/jzae001","DOIUrl":null,"url":null,"abstract":"Two new propositional non-classical logics, referred to as symmetric intuitionistic logic (SIL) and conflated intuitionistic logic (CIL), are introduced as indexed and non-indexed Gentzen-style sequent calculi. SIL is regarded as a natural hybrid logic combining intuitionistic and dual-intuitionistic logics, whereas CIL is regarded as a variant of intuitionistic paraconsistent logic with conflation and without paraconsistent negation. The cut-elimination theorems for SIL and CIL are proved. CIL is shown to be conservative over SIL.","PeriodicalId":51114,"journal":{"name":"Logic Journal of the IGPL","volume":"39 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Symmetric and conflated intuitionistic logics\",\"authors\":\"Norihiro Kamide\",\"doi\":\"10.1093/jigpal/jzae001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Two new propositional non-classical logics, referred to as symmetric intuitionistic logic (SIL) and conflated intuitionistic logic (CIL), are introduced as indexed and non-indexed Gentzen-style sequent calculi. SIL is regarded as a natural hybrid logic combining intuitionistic and dual-intuitionistic logics, whereas CIL is regarded as a variant of intuitionistic paraconsistent logic with conflation and without paraconsistent negation. The cut-elimination theorems for SIL and CIL are proved. CIL is shown to be conservative over SIL.\",\"PeriodicalId\":51114,\"journal\":{\"name\":\"Logic Journal of the IGPL\",\"volume\":\"39 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-03-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Logic Journal of the IGPL\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1093/jigpal/jzae001\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"LOGIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Logic Journal of the IGPL","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1093/jigpal/jzae001","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"LOGIC","Score":null,"Total":0}
引用次数: 0
摘要
本文介绍了两种新的命题非经典逻辑，分别称为对称直觉逻辑（SIL）和混同直觉逻辑（CIL），作为有索引和无索引的根岑式序列计算。SIL 被视为结合了直观逻辑和双直观逻辑的自然混合逻辑，而 CIL 则被视为直观准一致逻辑的一种变体，具有混淆性，但没有准一致的否定。证明了 SIL 和 CIL 的割除定理。证明了 CIL 比 SIL 保守。
Two new propositional non-classical logics, referred to as symmetric intuitionistic logic (SIL) and conflated intuitionistic logic (CIL), are introduced as indexed and non-indexed Gentzen-style sequent calculi. SIL is regarded as a natural hybrid logic combining intuitionistic and dual-intuitionistic logics, whereas CIL is regarded as a variant of intuitionistic paraconsistent logic with conflation and without paraconsistent negation. The cut-elimination theorems for SIL and CIL are proved. CIL is shown to be conservative over SIL.
期刊介绍：
Logic Journal of the IGPL publishes papers in all areas of pure and applied logic, including pure logical systems, proof theory, model theory, recursion theory, type theory, nonclassical logics, nonmonotonic logic, numerical and uncertainty reasoning, logic and AI, foundations of logic programming, logic and computation, logic and language, and logic engineering.
Logic Journal of the IGPL is published under licence from Professor Dov Gabbay as owner of the journal.
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