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 \. 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. (shrink)