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On implicit extensions in many-valued logic

  • Sergey S. Marchenkov EMAIL logo
Veröffentlicht/Copyright: 17. Oktober 2024
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Abstract

We consider Kuznetsov’s implicit expressibility and its generalizations, when the implicit expressibility language is augmented with the additional disjunction, implication, and negation logical connectives. It is shown that, for each k ⩾ 3, the implicit extensions in Pk have the cardinality of the continuum. For each k ⩾ 3, we also prove that each of the sets of positively implicit, implicatively implicit, and negatively implicit extensions in Pk contains, respectively, as a proper subset, the set of positively implicit, implicatively implicit, and negatively implicit closed classes. We verify that, for k ⩾ 2, the functions of the set Hk of homogeneous functions preserving the set Ek−1 can be used for producing implicatively implicit and negatively implicit extensions without changing the result.


Originally published in Diskretnaya Matematika (2023) 35, №2, 34–41 (in Russian).


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Received: 2023-01-23
Published Online: 2024-10-17
Published in Print: 2024-10-28

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 30.11.2025 von https://www.degruyterbrill.com/document/doi/10.1515/dma-2024-0024/pdf?lang=de
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