Geodesic
On the action of the implicative closure operator on the set of partial functions of the multivalued logic
Diskretnaya Matematika, Tome 32 (2020) no. 1, pp. 60-73

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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. 
@article{DM_2020_32_1_a4,
     author = {S. S. Marchenkov},
     title = {On the action of the implicative closure operator on the set of partial functions of the multivalued logic},
     journal = {Diskretnaya Matematika},
     pages = {60--73},
     publisher = {mathdoc},
     volume = {32},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2020_32_1_a4/}
}
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S. S. Marchenkov. On the action of the implicative closure operator on the set of partial functions of the multivalued logic. Diskretnaya Matematika, Tome 32 (2020) no. 1, pp. 60-73. http://geodesic.mathdoc.fr/item/DM_2020_32_1_a4/