This article is cited in 2 papers

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

S. S. Marchenkov

Lomonosov Moscow State University

Abstract: On the set $P_k^*$ 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 $k\geqslant 2$, the number of implicative closed classes in $P_k^*$ is finite. For any $k\geqslant 2$, in $P_k^*$ 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 $P_3^*$.

Keywords: implicative closure operator, partial functions of multivalued logic.

UDC: 519.716

Received: 07.05.2019

DOI: 10.4213/dm1574

 English version: Discrete Mathematics and Applications, 2021, 31:3, 155–164

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