{"title":"哥德尔逻辑的关系序列演算中的切消","authors":"M. Baaz, A. Ciabattoni, C. Fermüller","doi":"10.1109/ISMVL.2001.924570","DOIUrl":null,"url":null,"abstract":"Previously, the analytic calculus RG/sub /spl infin// for Godel logic has been introduced. RG/sub /spl infin// operates on \"sequents of relations\". We show constructively how to eliminate cuts from RG/sub /spl infin//-derivations. The version of the cut rule we consider allows to derive other forms of cut as well as a rule corresponding to the \"communication rule\" of Avron's hypersequent calculus for G/sub /spl infin//. Moreover, we give an explicit description of all the axioms of RG/sub /spl infin// and prove their completeness.","PeriodicalId":297353,"journal":{"name":"Proceedings 31st IEEE International Symposium on Multiple-Valued Logic","volume":"25 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2001-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"24","resultStr":"{\"title\":\"Cut-elimination in a sequents-of-relations calculus for Godel logic\",\"authors\":\"M. Baaz, A. Ciabattoni, C. Fermüller\",\"doi\":\"10.1109/ISMVL.2001.924570\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Previously, the analytic calculus RG/sub /spl infin// for Godel logic has been introduced. RG/sub /spl infin// operates on \\\"sequents of relations\\\". We show constructively how to eliminate cuts from RG/sub /spl infin//-derivations. The version of the cut rule we consider allows to derive other forms of cut as well as a rule corresponding to the \\\"communication rule\\\" of Avron's hypersequent calculus for G/sub /spl infin//. Moreover, we give an explicit description of all the axioms of RG/sub /spl infin// and prove their completeness.\",\"PeriodicalId\":297353,\"journal\":{\"name\":\"Proceedings 31st IEEE International Symposium on Multiple-Valued Logic\",\"volume\":\"25 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-05-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"24\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings 31st IEEE International Symposium on Multiple-Valued Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISMVL.2001.924570\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings 31st IEEE International Symposium on Multiple-Valued Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.2001.924570","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Cut-elimination in a sequents-of-relations calculus for Godel logic
Previously, the analytic calculus RG/sub /spl infin// for Godel logic has been introduced. RG/sub /spl infin// operates on "sequents of relations". We show constructively how to eliminate cuts from RG/sub /spl infin//-derivations. The version of the cut rule we consider allows to derive other forms of cut as well as a rule corresponding to the "communication rule" of Avron's hypersequent calculus for G/sub /spl infin//. Moreover, we give an explicit description of all the axioms of RG/sub /spl infin// and prove their completeness.