 Given a first-order temporal model \(\mathcal{M}= (T, \prec,\mathcal{U},D,\mathcal{I})\), a variable assignment in \(\mathcal{M}\) is a mapping \(v: \mathrm{VAR} \to \mathcal{U}\) that assigns to each variable \(x \in \mathrm{VAR}\) an element \(v(x)\) in the global domain \(\mathcal{U}\) of the model. Each such assignment \(v\) can be uniquely extended to a term valuation \(v: T \times \mathrm{TERM} \to \mathcal{U}\) as follows:   \[v_{t}(x) := v(x), \  v_{t}(c) :=  \mathcal{I}_{t}(c). \]  Note that the variable assignment is defined globally, whereas the valuation of the constant symbols depends on the respective time instant.