 Thus, an Ockhamist tree model is a triple \(\mathcal{M} = \left\langle T, \prec, V \right\rangle\) where \(\mathcal{T} = \langle T,\prec\rangle\) is a tree and \(V\) is a valuation that assigns to every atomic proposition \(p\in {PROP}\) the set of instant-history pairs \(V(p) \subseteq T \times \mathcal{H}(\mathcal{T})\) at which \(p\) is considered true. The truth of an arbitrary formula \(\varphi\) of OBTL at an instant-history pair \((t,h)\) in an Ockhamist tree model \(\mathcal{M}\) is defined inductively as follows: