On generalization of expressibility in 5-valued logic

Abstract

Let us consider the pseudo-Boolean algebra (M; ∧, ∨, ⊃, ¬), where ⊃ is relative pseudo-complement, and ¬ is pseudo-complement. We say that the system of pseudo-Boolean terms on the set of variables X (Ω – words over X ) is parametrically complete in algebra (M; Ω), if we can parametrically express the operations from Ω via functions expressed by terms over Σ. The function f (x1, ..., xn) of M preserves the predicate (relation) R (x1, ..., xm) if for any possible values xij ∈ M (i = 1, ..., m; j = 1, ..., n) from the truth of R (x11, x21, ..., xn1), ..., R (x1n, x2n, ..., xmn) follows the truth of R (f (x11, x12, ..., x1n), ..., f (xn1, xn2, ..., xnm)).