 Formulae of PBTL are evaluated in a temporal model \(\mathcal{M} = \langle T,\prec,V\rangle\) on a tree \(\mathcal{T} = \langle T,\prec\rangle\), called a Peircean tree model. As usual, \(V\) is a valuation that assigns to every atomic proposition \(p \in {PROP}\) the set of time instants \(V(p) \subseteq T\) at which \(p\) is considered true, and the truth of an arbitrary formula \(\varphi\) of PBTL at a given time instant \(t\) in a Peircean tree model \(\mathcal{M}\) is defined inductively. The semantic clauses for the truth-functional connectives and for the past operator \(P\) (and its dual \(H\)) are as in TL (see  Section 3.2),  and we only provide here the semantic clauses for the future operators \(F\) and \(G\):