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A criterion for positive completeness in ternary logic

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Abstract

The operator of positive closure is considered on the set P k of functions of k-valued logic. Some positive complete systems of functions are defined. It is proved that every positive complete class of functions from P k is positive generated by the set of all functions depending on at most k variables. For each k ⩾ 3, the three families of positive precomplete classes are defined. It is shown that, for k = 3, the 10 classes of these families constitute a criterion system.

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Authors and Affiliations

  1. Department of Mathematical Cybernetics, Moscow State University, Vorob’ovy gory, Moscow, 119992, 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, 2006, published in Diskretnyi Analiz i Issledovanie Operatsii, Ser. 1, 2006, Vol. 13, No. 3, pp. 27–39.

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Marchenkov, S.S. A criterion for positive completeness in ternary logic. J. Appl. Ind. Math. 1, 481–488 (2007). https://doi.org/10.1134/S1990478907040114

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