On the action of the implicative closure operator on the set of partial functions of the multivalued logic. (English. Russian original) Zbl 1524.03020
Discrete Math. Appl. 31, No. 3, 155-164 (2021); translation from Diskretn. Mat. 32, No. 1, 60-73 (2020).
Summary: 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 \(k \geq 2\), the number of implicative closed classes in \(P_k^*\) is finite. For any \(k \geq 2\), 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 \(P_3^*\).
MSC:
| 03B50 | Many-valued logic |
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