 This logic is the logic in the language of intuitionistic logic that has to the least normal modal logic \(K\) the same relation that intuitionistic logic has to the normal modal logic \(S4\). It was introduced in Visser 1981 (under the name Basic Propositional Logic) and has been studied by several authors, such as Ardeshir, Alizadeh, and Ruitenburg. It is not protoalgebraic, it is truth-equational and it is Fregean (hence also selfextensional).