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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

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UDC: 519.716

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}