IMI/Publicaţii/BASM/Ediţii/BASM n.2 (12), 1993/

Modeling of self-dual Boolean functions commuting with 1 in a 3-valued extension of provability-intuitionistic logic. (Russian)

Authors: Covaljiu O. I., Rata M. F.


The 3-valued extension of provability-intuitionistic logic is studied. It reprezents the logic $L^{\Delta}$ of the $\Delta$-pseudo-boolean algebra $$ Z_3^{\Delta} = < \{0, \tau, 1\}; \&, \lor, \supset, \neg, \Delta > (0 < \tau < 1, \Delta 0 = \tau, \Delta \tau = \Delta 1 = 1). $$ We call a model of a boolean function $f(p_1, \dots, p_n)$ in the logic $L^{\Delta}$ every formula, which express such $\Delta$-pseudo-boolean function $F(p_1, \dots, p_n)$, that for every set $<\alpha_1, \dots, \alpha_n>$ of 0s and 1s the equality $f(\alpha_1, \dots, \alpha_n) = F(\alpha_1, \dots, \alpha_n)$ is true. Let $K$ be a class of formulas, closed with respect to expressibility in logic $L^{\Delta}$. The system $\Sigma$ of formulas of the class $K$ is called model complete in $K$, if for every boolean function, which has a model in $K$, can be expressed via $\Sigma$ at least one model of it in $L^{\Delta}$. The criteria of model completeness in two classes of formulas, which model autodual boolean functions and boolean functions permutable with 1 in the logic $L^{\Delta}$ are istablished . The rezults are expressed in terms of three and thirteen classes of formulas.

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