{"title":"部分动态De Morgan代数的集合表示","authors":"I. Chajda, Jan Paseka","doi":"10.1109/ISMVL.2013.56.","DOIUrl":null,"url":null,"abstract":"By a De Morgan algebra is meant a bounded poset equipped with an antitone involution considered as negation. Such an algebra can be considered as an algebraic axiomatization of a propositional logic satisfying the double negation law. Our aim is to introduce the so-called tense operators in every De Morgan algebra for to get an algebraic counterpart of a tense logic with negation satisfying the double negation law which need not be Boolean. Following the standard construction of tense operators G and H by a frame we solve the following question: if a dynamic De Morgan algebra is given, how to find a frame such that its tense operators G and H can be reached by this construction.","PeriodicalId":246194,"journal":{"name":"2016 IEEE 46th International Symposium on Multiple-Valued Logic (ISMVL)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2016-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Set Representation of Partial Dynamic De Morgan Algebras\",\"authors\":\"I. Chajda, Jan Paseka\",\"doi\":\"10.1109/ISMVL.2013.56.\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"By a De Morgan algebra is meant a bounded poset equipped with an antitone involution considered as negation. Such an algebra can be considered as an algebraic axiomatization of a propositional logic satisfying the double negation law. Our aim is to introduce the so-called tense operators in every De Morgan algebra for to get an algebraic counterpart of a tense logic with negation satisfying the double negation law which need not be Boolean. Following the standard construction of tense operators G and H by a frame we solve the following question: if a dynamic De Morgan algebra is given, how to find a frame such that its tense operators G and H can be reached by this construction.\",\"PeriodicalId\":246194,\"journal\":{\"name\":\"2016 IEEE 46th International Symposium on Multiple-Valued Logic (ISMVL)\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-05-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2016 IEEE 46th International Symposium on Multiple-Valued Logic (ISMVL)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISMVL.2013.56.\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2016 IEEE 46th International Symposium on Multiple-Valued Logic (ISMVL)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.2013.56.","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Set Representation of Partial Dynamic De Morgan Algebras
By a De Morgan algebra is meant a bounded poset equipped with an antitone involution considered as negation. Such an algebra can be considered as an algebraic axiomatization of a propositional logic satisfying the double negation law. Our aim is to introduce the so-called tense operators in every De Morgan algebra for to get an algebraic counterpart of a tense logic with negation satisfying the double negation law which need not be Boolean. Following the standard construction of tense operators G and H by a frame we solve the following question: if a dynamic De Morgan algebra is given, how to find a frame such that its tense operators G and H can be reached by this construction.
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