{"title":"三值逻辑中自对偶函数克隆的格","authors":"Dmitriy Zhuk","doi":"10.1109/ISMVL.2011.16","DOIUrl":null,"url":null,"abstract":"The lattice of all clones of self-dual functions in three-valued logic is described in the paper. Even though this lattice contains a continuum of clones, a simple description was found. Using this description different properties of the lattice and of the clones were derived. Pair wise inclusion of the clones into each other was described, and all finitely generated clones were found. Also, for each clone the relation degree, the cardinality of the set of all clones containing this clone, and the cardinality of the set of all clones that are contained in this clone were determined.","PeriodicalId":234611,"journal":{"name":"2011 41st IEEE International Symposium on Multiple-Valued Logic","volume":"258 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"17","resultStr":"{\"title\":\"The Lattice of the Clones of Self-Dual Functions in Three-Valued Logic\",\"authors\":\"Dmitriy Zhuk\",\"doi\":\"10.1109/ISMVL.2011.16\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The lattice of all clones of self-dual functions in three-valued logic is described in the paper. Even though this lattice contains a continuum of clones, a simple description was found. Using this description different properties of the lattice and of the clones were derived. Pair wise inclusion of the clones into each other was described, and all finitely generated clones were found. Also, for each clone the relation degree, the cardinality of the set of all clones containing this clone, and the cardinality of the set of all clones that are contained in this clone were determined.\",\"PeriodicalId\":234611,\"journal\":{\"name\":\"2011 41st IEEE International Symposium on Multiple-Valued Logic\",\"volume\":\"258 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-05-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"17\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2011 41st IEEE International Symposium on Multiple-Valued Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISMVL.2011.16\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2011 41st IEEE International Symposium on Multiple-Valued Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.2011.16","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Lattice of the Clones of Self-Dual Functions in Three-Valued Logic
The lattice of all clones of self-dual functions in three-valued logic is described in the paper. Even though this lattice contains a continuum of clones, a simple description was found. Using this description different properties of the lattice and of the clones were derived. Pair wise inclusion of the clones into each other was described, and all finitely generated clones were found. Also, for each clone the relation degree, the cardinality of the set of all clones containing this clone, and the cardinality of the set of all clones that are contained in this clone were determined.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
