This article is cited in 14 papers

A criterion for positive completeness in ternary logic

S. S. Marchenkov

M. V. Lomonosov Moscow State University

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 $k\geqslant 3$, 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.

Received: 14.02.2006

 English version: Journal of Applied and Industrial Mathematics, 2007, 1:4, 481–488

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