Implicatively implicit extensions of two-place symmetric functions in <i>P</i> <sub>3</sub>

Abstract We characterize the implicatively implicit extensions of all 27 two-place symmetric functions of the three-valued logic that preserve all three constants. We show that they contain extensions coinciding with the known implicatively closed classes and extensions which are not closed relative to the superposition operation.

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Publication Details

Journal
Discrete Mathematics and Applications
Published
2025-12-01
DOI
https://doi.org/10.1515/dma-2025-0029
Primary Topic
Advanced Algebra and Logic
Type
article
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article

Implicatively implicit extensions of two-place symmetric functions in P 3

Sergey MARCHENKOV
Discrete Mathematics and Applications
Advanced Algebra and Logic
article

Implicatively implicit extensions of two-place symmetric functions in P 3

Sergey MARCHENKOV
article en

Abstract

Abstract We characterize the implicatively implicit extensions of all 27 two-place symmetric functions of the three-valued logic that preserve all three constants. We show that they contain extensions coinciding with the known implicatively closed classes and extensions which are not closed relative to the superposition operation.

Discrete Mathematics and ApplicationsVol. 35(6)
Lomonosov Moscow State University (RU)
Reduced inequalities
Openalex Percentile: Top 21%
Advanced Algebra and Logic
DOISourceOpenAlex
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