In the present paper we consider the simplest non-classical extension $GL4$ of the well-known propositional provability logic $GL$ together with the notion of expressibility of formulas in a logic proposed by A. V. Kuznetsov. Conditions for expressib
ility of constants in the 4-valued extension $Lmathfrak{B}_2$ of $GL$ are found out, which were first announced in a authors paper in 1996.
In the present paper we show that there are infinitely many classes of term functions in the free-void generated diagonalizable algebra, which are precomplete with respect to parametrical expressibility of functions.
