{"title":"扩展理想副协调四值逻辑","authors":"N. Kamide","doi":"10.1109/ISMVL.2017.14","DOIUrl":null,"url":null,"abstract":"We introduce a Gentzen-type sequent calculus PL for a modified extension of Arieli, Avron and Zamansky's ideal paraconsistent four-valued logic 4CC. The calculus PL, which is also regarded as a paradefinite four-valued logic, is formalized based on the idea of connexive logic. Theorems for syntactically and semantically embedding PL into a Gentzen-type sequent calculus LK for classical logic and vice versa are proved. The cut-elimination and completeness theorems for PL are obtained via these embedding theorems. Moreover, we introduce an extension EPL of both PL and a Gentzen-type sequent calculus for 4CC, and show the cut-elimination theorem for EPL. The calculus EPL has a novel characteristic property of negative symmetry.","PeriodicalId":393724,"journal":{"name":"2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2017-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Extending Ideal Paraconsistent Four-Valued Logic\",\"authors\":\"N. Kamide\",\"doi\":\"10.1109/ISMVL.2017.14\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce a Gentzen-type sequent calculus PL for a modified extension of Arieli, Avron and Zamansky's ideal paraconsistent four-valued logic 4CC. The calculus PL, which is also regarded as a paradefinite four-valued logic, is formalized based on the idea of connexive logic. Theorems for syntactically and semantically embedding PL into a Gentzen-type sequent calculus LK for classical logic and vice versa are proved. The cut-elimination and completeness theorems for PL are obtained via these embedding theorems. Moreover, we introduce an extension EPL of both PL and a Gentzen-type sequent calculus for 4CC, and show the cut-elimination theorem for EPL. The calculus EPL has a novel characteristic property of negative symmetry.\",\"PeriodicalId\":393724,\"journal\":{\"name\":\"2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-05-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISMVL.2017.14\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.2017.14","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We introduce a Gentzen-type sequent calculus PL for a modified extension of Arieli, Avron and Zamansky's ideal paraconsistent four-valued logic 4CC. The calculus PL, which is also regarded as a paradefinite four-valued logic, is formalized based on the idea of connexive logic. Theorems for syntactically and semantically embedding PL into a Gentzen-type sequent calculus LK for classical logic and vice versa are proved. The cut-elimination and completeness theorems for PL are obtained via these embedding theorems. Moreover, we introduce an extension EPL of both PL and a Gentzen-type sequent calculus for 4CC, and show the cut-elimination theorem for EPL. The calculus EPL has a novel characteristic property of negative symmetry.