Startseite On the action of the implicative closure operator on the set of partial functions of the multivalued logic
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On the action of the implicative closure operator on the set of partial functions of the multivalued logic

  • Sergey S. Marchenkov EMAIL logo
Veröffentlicht/Copyright: 25. Juni 2021
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Abstract

On the set Pk of partial functions of the k-valued logic, we consider the implicative closure operator, which is the extension of the parametric closure operator via the logical implication. It is proved that, for any k ⩾ 2, the number of implicative closed classes in Pk is finite. For any k ⩾ 2, in Pk two series of implicative closed classes are defined. We show that these two series exhaust all implicative precomplete classes. We also identify all 8 atoms of the lattice of implicative closed classes in P3 .


Note: Originally published in Diskretnaya Matematika (2020) 32, №1, 60–73 (in Russian).


  1. Funding: This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 19–01–00200).

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Received: 2019-05-07
Published Online: 2021-06-25
Published in Print: 2021-06-25

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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