 An intermediate propositional logic \(\mathbf{L}\) is structurally complete if every rule which is admissible for \(\mathbf{L}\) is derivable in \(\mathbf{L},\) and hereditarily structurally complete if every intermediate logic extending \(\mathbf{L}\) is also structurally complete. Every intermediate logic \(\mathbf{L}\) has a structural completion \(\mathbf{\overline{L}},\) obtained by adjoining all its admissible rules. \(\mathbf{LC}\) and \(\mathbf{G_n}\) are hereditarily structurally complete. While \(\mathbf{IPC},\) \(\mathbf{RN}\) and \(\mathbf{KC}\) are not structurally complete, their structural completions are hereditarily structurally complete. For these results and more, see Citkin [2016, Other Internet Resources].