 An intermediate propositional logic is any consistent collection of propositional formulas containing all the axioms of \(\mathbf{IPC}\) and closed under modus ponens and substitution of arbitrary formulas for proposition letters. Each intermediate propositional logic is contained in \(\mathbf{CPC}.\) Some particular intermediate propositional logics, characterized by adding one or more classically correct but intuitionistically unprovable axiom schemas to \(\mathbf{IPC},\) have been studied extensively.