 In interval-based temporal logic, formulae are evaluated relative to time intervals rather than instants. An interval model is a triple \(\mathcal{M} = \langle T,\prec,V\rangle\) consisting of a temporal frame \(\mathcal{T} = \langle T,\prec\rangle\) and a valuation \(V\) that assigns to each atomic proposition \(p\in{PROP}\) the set of time intervals \(V(p) \subseteq \mathcal{P}(\mathbb{I}(\mathcal{T}))\) at which \(p\) is considered true. The truth of an arbitrary formula \(\varphi\) with respect to a given interval \([a,b]\) in an interval model \(\mathcal{M}\) is defined by structural induction on formulae as follows: