On sufficient conditions for expressibility of constants in the 4-valued extension of the propositional provability logic $GL$

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 expressibility 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.