 Lastly, a few words about the relationship between interval temporal logics and first-order logic. The standard translation of Prior’s basic tense logic TL into first-order logic (presented in  Section 3.3)  extends naturally to interval logics, where atomic propositions are represented in the first-order language by binary relations. It turns out that some fragments of \(\mathsf{HS}\) can be translated into the two-variable fragment FO\(^{2}\) of first-order logic, which eventually implies their decidability. The expressively strongest such interval logic is the neighborhood interval logic, which was proven to be expressively complete for FO\(^{2}\) (Bresolin et al. 2009). Other fragments of \(\mathsf{HS}\) require at least three distinct variables for the standard translation. Still, even the full logic \(\mathsf{HS}\) is less expressive than the three-variable fragment FO\(^{3}\) of first-order logic, for which Venema (1991) showed that the logic CDT is expressively complete.