{"title":"Implicatively Implicit Extensions in Three-Valued Logic","authors":"","doi":"10.3103/s0278641924010035","DOIUrl":null,"url":null,"abstract":"<span> <h3>Abstract</h3> <p>Implicatively implicit extensions of all 27 one-place functions of three-valued logic are characterized. It is found they include both extensions coinciding with known implicatively closed classes and extensions that are not closed with respect to the operation of superposition. It is also shown that any implicatively implicit extension in <span> <span>\\(P_{k}\\)</span> </span> contains class <span> <span>\\(H_{k}\\)</span> </span> of all homogeneous functions from <span> <span>\\(P_{k}\\)</span> </span> for any <span> <span>\\(k\\geqslant 3\\)</span> </span>.</p> </span>","PeriodicalId":501582,"journal":{"name":"Moscow University Computational Mathematics and Cybernetics","volume":"82 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Moscow University Computational Mathematics and Cybernetics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s0278641924010035","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Implicatively implicit extensions of all 27 one-place functions of three-valued logic are characterized. It is found they include both extensions coinciding with known implicatively closed classes and extensions that are not closed with respect to the operation of superposition. It is also shown that any implicatively implicit extension in \(P_{k}\) contains class \(H_{k}\) of all homogeneous functions from \(P_{k}\) for any \(k\geqslant 3\).
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