 Naturally, the question arises how to evaluate the atomic propositions in the model: do the truth values of atomic propositions depend only on the time instant, or do they depend on the history as well? The answer to this question crucially hinges on whether atomic propositions may contain ‘traces of futurity’ or not (Prior 1967, 124). There is no consensus on the treatment of atomic propositions in the literature (cf. Zanardo 1996), and Prior himself entertained the idea of a two-sorted language with two different kinds of atomic propositions that each require a different treatment (Prior 1967, Chapter 7.4). Here we will allow the truth values of atomic propositions to depend on both the time instant and the history. The more specific case of instant-based propositions can be obtained by imposing the additional requirement that the formula \(p \leftrightarrow \Box p\) be valid for \(p \in {PROP}\).