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In the present paper we consider the simplest non-classical extension $GL4$of the well-known propositional provability logic $GL$ together with the notionof expressibility of formulas in a logic proposed by A. V. Kuznetsov.Conditions for expressibility of constants in the 4-valued extension$L\mathfrak{B}_2$ of $GL$ are found out, which were first announced in aauthor's paper in 1996.

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