 A subintuitionistic propositional logic can be obtained from \(\mathbf{IPC}\) by restricting the language, or weakening the logic, or both. An extreme example of the first is \(\mathbf{RN},\) intuitionistic logic with a single propositional variable \(P,\) which is named after its discoverers Rieger and Nishimura [1960]. \(\mathbf{RN}\) is characterized by the Rieger-Nishimura lattice of infinitely many nonequivalent formulas \(F_n\) such that every formula whose only propositional variable is \(P\) is equivalent by intuitionistic logic to some \(F_n.\) Nishimura’s version is