布尔函数复合下多值集合逻辑的完备性准则

Proceedings of 24th International Symposium on Multiple-Valued Logic (ISMVL'94) Pub Date : 1994-05-25 DOI:10.1109/ISMVL.1994.302203

I. Stojmenovic

{"title":"布尔函数复合下多值集合逻辑的完备性准则","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":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1994-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"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\":null,\"pages\":null},\"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}","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

摘要

讨论了r值集合逻辑中的函数完备性问题，r值集合逻辑是函数将子集的n元组映射到r值上的子集的逻辑。布尔函数是设计集合逻辑函数的方便选择。如果把所有的布尔函数加到F上，F可以组成任何一个集逻辑函数，则函数集F是布尔完全的。本文证明了在r值集逻辑中存在2/sup r/ 2个布尔极大集，并用等价关系给出了它们的描述。如果一个集合F不是这2/sup r/-2个布尔极大集的子集，则它是布尔完备的，这是布尔函数复合下多值集合逻辑中的完备性准则。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Completeness criteria in many-valued set logic under compositions with Boolean functions

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.<>

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Proceedings of 24th International Symposium on Multiple-Valued Logic (ISMVL'94)

自引率

0.00%

发文量