 Note that the Future Barcan scheme \(\mathsf{BF}_{G}\) semantically corresponds to the converse Past Barcan scheme \(\mathsf{CBF}_{H}\), and vice versa. From the above it follows that an augmented temporal frame \(\mathcal{F}\) has locally constant domains iff either of the following formulae is VD-valid in \(\mathcal{F}\): \(\mathsf{BF}_{G} \wedge \mathsf{BF}_{H}\), \(\mathsf{CBF}_{G} \wedge \mathsf{CBF}_{H}\), \(\mathsf{BF}_{G} \wedge \mathsf{CBF}_{G}\), or \(\mathsf{BF}_{H} \wedge \mathsf{CBF}_{H}\).