Existence of Finite Total Equivalence Systems for Certain Closed Classes of 3-Valued Logic Functions

Logica Universalis. 2015. Vol. 9. No. 1. P. 1–26.

Макаров И. А.

The article deals with finding finite total equivalence systems for formulas based on an arbitrary closed class of functions of several variables defined on the set \{0, 1, 2\} and taking values in the set \{0,1\} with the property that the restrictions of its functions to the set \{0, 1\} constitutes a closed class of Boolean functions. We consider all classes whose restriction closure is either the set of all functions of two-valued logic or the set T a of functions preserving a,a\in\{0,1\} . In each of these cases, we find a finite total equivalence system, construct a canonical type for formulas, and present a complete algorithm for determining whether any two formulas are equivalent.

Ключевые слова: замкнутые классы, closed classes, Many-valued logics, finite total equivalence system, Многозначные логики, конечная полная система тождеств