A criterion for positive completeness in ternary logic
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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.
KeywordsBoolean Function Constant Function Distinct Element Closure Operator Criterion System
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