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On the enumeration closure operator in multivalued logic

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Abstract

The operator of closure with respect to enumeration (the Π-operator) is defined in multivalued logic. The finiteness of the number of Π-closed classes in k-valued logic is proved. All six Π-closed classes of Boolean functions are specified. Sufficient conditions for presenting Π-closed classes in the form of classes of functions that retain certain relations are determined. The Π-closed classes are compared to positively closed classes. All Π-closed classes of homogeneous functions are described.

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Authors and Affiliations

  1. Department of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia

    S. S. Marchenkov

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  1. S. S. Marchenkov
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Correspondence to S. S. Marchenkov.

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Original Russian Text © S.S. Marchenkov, 2015, published in Vestnik Moskovskogo Universiteta. Vychislitel’naya Matematika i Kibernetika, 2015, No. 2, pp. 33–39.

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Marchenkov, S.S. On the enumeration closure operator in multivalued logic. MoscowUniv.Comput.Math.Cybern. 39, 81–87 (2015). https://doi.org/10.3103/S0278641915020053

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