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Regular version of the site

Article

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.

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.