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On the existence of a criterion of model completeness for the classes of 3-valued functions. (English)
Authors: Covalgiu O., Ratsa M.
Abstract
The general 3-valued logic $P_3$ is considerated. A function $F(p_1,$ $\dots, p_n)$ of $P_3$ is called a model of the Boolean function $f(p_1, \dots, p_n)$ if $F(\alpha_1,$ $\dots, \alpha_n) = f(\alpha_1, \dots, \alpha_n)$ for any $\alpha_i \in \{0, 1\}$. A system $\Sigma$ of functions of a closed class $K \subseteq P_3$ is called model complete in $K$ if, for any Boolean function possessing a model in $K$, at least one model of it can be expressed via both variables and functions of $\Sigma$ by means of superpositions. In this paper the existence in principle of a criterion of model completeness for an arbitrary closed class of functions of $P_3$ in proved, and it is based on the existence of only a finite number of so-called model pre-complete classes.Institute of Mathematics Moldavian Academy of Sciences
Academy str. 5, Chisinau, MD-2028 Moldova
Academy str. 5, Chisinau, MD-2028 Moldova
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- On the existence of a criterion of model completeness for the classes of 3-valued functions. (English)
