 Let us write \(\llbracket\phi\rrbracket_m\) for the set \(\left\{h \in H_m : (h,m) \models \phi\right\}\), that is, the set of histories agreeing with \(h\) at least up to \(m\) and such that \(\phi\) is true with respect to the index consisting of that history and \(m\). Defining formal truth-conditions for the stit operator there are at least two possibilities to be considered: