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Diskr. Mat., 2020, Volume 32, Issue 1, Pages 60–73 (Mi dm1574)  

On the action of implicative closure operator on the set of partial functions in many-valued logic

S. S. Marchenkov

Lomonosov Moscow State University

Abstract: On the set $P_k^*$ of partial functions of $k$-valued logic, the implicative closure operator is considered (expansion of the parametric closure operator with the help of the implication connective). It is proved that for any $k\geqslant 2$ the number of implicatively closed classes in $P_k^*$ is finite. For any $k\geqslant 2$ in $P_k^*$, two series of implicatively closed classes are defined and it is established that these two series exhaust all implicatively pre-complete classes. All 8 atoms of the lattice of implicatively closed classes in $P_3^*$ are found.

Keywords: implicative closure operator, partial functions in many-valued logic.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-01-00200


DOI: https://doi.org/10.4213/dm1574

Full text: PDF file (451 kB)
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UDC: 519.716
Received: 07.05.2019

Citation: S. S. Marchenkov, “On the action of implicative closure operator on the set of partial functions in many-valued logic”, Diskr. Mat., 32:1 (2020), 60–73

Citation in format AMSBIB
\Bibitem{Mar20}
\by S.~S.~Marchenkov
\paper On the action of implicative closure operator on the set of partial functions in many-valued logic
\jour Diskr. Mat.
\yr 2020
\vol 32
\issue 1
\pages 60--73
\mathnet{http://mi.mathnet.ru/dm1574}
\crossref{https://doi.org/10.4213/dm1574}


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