{"title":"3值逻辑中部分Sheffer函数的表征","authors":"L. Haddad, D. Lau","doi":"10.1109/ISMVL.2007.12","DOIUrl":null,"url":null,"abstract":"partial function f on a k-element set k is a partial Sheffer function if every partial function on k is definable in terms of f. Since this holds if and only if f belongs to no maximal partial clone on k, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on k. We present minimal coverings of maximal partial clones on k for k = 2 and k = 3 and deduce criteria for partial Sheffer functions on a 2-element and a 3-element set.","PeriodicalId":368339,"journal":{"name":"37th International Symposium on Multiple-Valued Logic (ISMVL'07)","volume":"40 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Characterization of Partial Sheffer Functions in 3-Valued Logic\",\"authors\":\"L. Haddad, D. Lau\",\"doi\":\"10.1109/ISMVL.2007.12\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"partial function f on a k-element set k is a partial Sheffer function if every partial function on k is definable in terms of f. Since this holds if and only if f belongs to no maximal partial clone on k, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on k. We present minimal coverings of maximal partial clones on k for k = 2 and k = 3 and deduce criteria for partial Sheffer functions on a 2-element and a 3-element set.\",\"PeriodicalId\":368339,\"journal\":{\"name\":\"37th International Symposium on Multiple-Valued Logic (ISMVL'07)\",\"volume\":\"40 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2007-05-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"37th International Symposium on Multiple-Valued Logic (ISMVL'07)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISMVL.2007.12\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"37th International Symposium on Multiple-Valued Logic (ISMVL'07)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.2007.12","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
摘要
部分函数f k-element k是一组部分Sheffer函数如果每个部分函数k是可定义的。因为这成立当且仅当f属于没有极大部分克隆k,部分Sheffer函数的特性减少了寻找家庭最小的覆盖物的极大部分克隆k。我们现在最大的最小覆盖物部分克隆k k = 2 k = 3和推断标准部分Sheffer 2-element和一组转换功能。
Characterization of Partial Sheffer Functions in 3-Valued Logic
partial function f on a k-element set k is a partial Sheffer function if every partial function on k is definable in terms of f. Since this holds if and only if f belongs to no maximal partial clone on k, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on k. We present minimal coverings of maximal partial clones on k for k = 2 and k = 3 and deduce criteria for partial Sheffer functions on a 2-element and a 3-element set.