{"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}
引用次数: 10
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.