{"title":"有限值逻辑代数积的完备性问题","authors":"B. A. Romov","doi":"10.1109/ISMVL.1994.302202","DOIUrl":null,"url":null,"abstract":"Gives a general completeness criterion for the arity-calibrated product P/sub k/xP/sub m/ of the algebras of all functions of the k-valued and m-valued logics (k,m/spl ges/2). The Galois connection between the lattice of subalgebras P/sub k/xP/sub m/ and the lattice of subalgebras of the double-base invariant relations algebra (with operations of restricted first order calculus) is established. This is used to obtain a Slupecki type criterion for P/sub k/xP/sub m/ and to solve the completeness problem in P/sub k/xP/sub m/ (m/spl ges/2).<<ETX>>","PeriodicalId":137138,"journal":{"name":"Proceedings of 24th International Symposium on Multiple-Valued Logic (ISMVL'94)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1994-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"The completeness problem on the product of algebras of finite-valued logic\",\"authors\":\"B. A. Romov\",\"doi\":\"10.1109/ISMVL.1994.302202\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Gives a general completeness criterion for the arity-calibrated product P/sub k/xP/sub m/ of the algebras of all functions of the k-valued and m-valued logics (k,m/spl ges/2). The Galois connection between the lattice of subalgebras P/sub k/xP/sub m/ and the lattice of subalgebras of the double-base invariant relations algebra (with operations of restricted first order calculus) is established. This is used to obtain a Slupecki type criterion for P/sub k/xP/sub m/ and to solve the completeness problem in P/sub k/xP/sub m/ (m/spl ges/2).<<ETX>>\",\"PeriodicalId\":137138,\"journal\":{\"name\":\"Proceedings of 24th International Symposium on Multiple-Valued Logic (ISMVL'94)\",\"volume\":\"9 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1994-05-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"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.1994.302202\",\"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.1994.302202","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The completeness problem on the product of algebras of finite-valued logic
Gives a general completeness criterion for the arity-calibrated product P/sub k/xP/sub m/ of the algebras of all functions of the k-valued and m-valued logics (k,m/spl ges/2). The Galois connection between the lattice of subalgebras P/sub k/xP/sub m/ and the lattice of subalgebras of the double-base invariant relations algebra (with operations of restricted first order calculus) is established. This is used to obtain a Slupecki type criterion for P/sub k/xP/sub m/ and to solve the completeness problem in P/sub k/xP/sub m/ (m/spl ges/2).<>
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