{"title":"确定多值命题微积分中演绎问题的一种代数方法","authors":"Jin-Zhao Wu, Hongyan Tan","doi":"10.1109/ISMVL.1994.302191","DOIUrl":null,"url":null,"abstract":"We show that there is a polynomial over the rational number field Q corresponding to a given propositional formula in a given many-valued logic. Then, to decide whether a propositional formula can be deduced from a finite set of such formulas (deduction problem), we only need to decide whether the polynomial vanishes on an algebraic variety which is related to this formula set. By decomposing this algebraic variety, an algorithm to decide this problem is given.<<ETX>>","PeriodicalId":137138,"journal":{"name":"Proceedings of 24th International Symposium on Multiple-Valued Logic (ISMVL'94)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1994-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"An algebraic method to decide the deduction problem in many-valued propositional calculus\",\"authors\":\"Jin-Zhao Wu, Hongyan Tan\",\"doi\":\"10.1109/ISMVL.1994.302191\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that there is a polynomial over the rational number field Q corresponding to a given propositional formula in a given many-valued logic. Then, to decide whether a propositional formula can be deduced from a finite set of such formulas (deduction problem), we only need to decide whether the polynomial vanishes on an algebraic variety which is related to this formula set. By decomposing this algebraic variety, an algorithm to decide this problem is given.<<ETX>>\",\"PeriodicalId\":137138,\"journal\":{\"name\":\"Proceedings of 24th International Symposium on Multiple-Valued Logic (ISMVL'94)\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1994-05-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of 24th International Symposium on Multiple-Valued Logic (ISMVL'94)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISMVL.1994.302191\",\"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 of 24th International Symposium on Multiple-Valued Logic (ISMVL'94)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.1994.302191","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
An algebraic method to decide the deduction problem in many-valued propositional calculus
We show that there is a polynomial over the rational number field Q corresponding to a given propositional formula in a given many-valued logic. Then, to decide whether a propositional formula can be deduced from a finite set of such formulas (deduction problem), we only need to decide whether the polynomial vanishes on an algebraic variety which is related to this formula set. By decomposing this algebraic variety, an algorithm to decide this problem is given.<>
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