 The interval logic \(\mathsf{HS}\) starts from instant-based models over linear time, and intervals are considered defined elements. So let \(\mathcal{T} = \langle T,\prec\rangle\) be a temporal frame and assume that the temporal precedence relation \(\prec\) induces a strict linear order on the set of time instants \(T\). An interval in \(\mathcal{T}\) is defined as an ordered pair \([a,b]\) such that \(a,b\in T\) and \(a\leq b.\) The set of all intervals in \(\mathcal{T}\) is denoted by \(\mathbb{I}(\mathcal{T)}.\) Note that the definition allows for ‘point intervals’ whose beginning and end points coincide, following the original proposal by Halpern and Shoham (1986). Sometimes, only ‘strict’ intervals are considered, excluding point-intervals.