{"title":"连接副协调量子逻辑的自然演绎","authors":"N. Kamide","doi":"10.1109/ISMVL.2017.12","DOIUrl":null,"url":null,"abstract":"In this study, a new logic called the connexive paraconsistent quantum logic is introduced as a common denominator of a paraconsistent logic and a quantum logic. A natural deduction system for this logic is introduced, and the weak normalization theorem for this system is shown. A typed lambda calculus for the implication-negation fragment of this logic is developed on the basis of the Curry-Howard correspondence. The strong normalization theorem for this calculus is proved.","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":"0","resultStr":"{\"title\":\"Natural Deduction for Connexive Paraconsistent Quantum Logic\",\"authors\":\"N. Kamide\",\"doi\":\"10.1109/ISMVL.2017.12\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this study, a new logic called the connexive paraconsistent quantum logic is introduced as a common denominator of a paraconsistent logic and a quantum logic. A natural deduction system for this logic is introduced, and the weak normalization theorem for this system is shown. A typed lambda calculus for the implication-negation fragment of this logic is developed on the basis of the Curry-Howard correspondence. The strong normalization theorem for this calculus is proved.\",\"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\":\"0\",\"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.2017.12\",\"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.2017.12","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Natural Deduction for Connexive Paraconsistent Quantum Logic
In this study, a new logic called the connexive paraconsistent quantum logic is introduced as a common denominator of a paraconsistent logic and a quantum logic. A natural deduction system for this logic is introduced, and the weak normalization theorem for this system is shown. A typed lambda calculus for the implication-negation fragment of this logic is developed on the basis of the Curry-Howard correspondence. The strong normalization theorem for this calculus is proved.