{"title":"Completeness criteria in many-valued set logic under compositions with Boolean functions","authors":"I. Stojmenovic","doi":"10.1109/ISMVL.1994.302203","DOIUrl":null,"url":null,"abstract":"Discusses the functional completeness problems in r-valued set logic, which is the logic of functions mapping n-tuples of subsets into subsets over r values. Boolean functions are convenient choice as building blocks in the design of set logic functions. A set of functions F is Boolean complete if any set logic function can be composed from F once all Boolean functions are added to F. The paper proves that there are 2/sup r/-2 Boolean maximal sets in r-valued set logic and gives their description using equivalence relations. A set F is then Boolean complete if it is not a subset of any of these 2/sup r/-2 Boolean maximal sets, which is a completeness criteria in many-valued set logic under compositions with Boolean functions.<<ETX>>","PeriodicalId":137138,"journal":{"name":"Proceedings of 24th International Symposium on Multiple-Valued Logic (ISMVL'94)","volume":"22 4","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1994-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","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.1994.302203","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 9
Abstract
Discusses the functional completeness problems in r-valued set logic, which is the logic of functions mapping n-tuples of subsets into subsets over r values. Boolean functions are convenient choice as building blocks in the design of set logic functions. A set of functions F is Boolean complete if any set logic function can be composed from F once all Boolean functions are added to F. The paper proves that there are 2/sup r/-2 Boolean maximal sets in r-valued set logic and gives their description using equivalence relations. A set F is then Boolean complete if it is not a subset of any of these 2/sup r/-2 Boolean maximal sets, which is a completeness criteria in many-valued set logic under compositions with Boolean functions.<>
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