 Using a slightly different notion of successfulness wherein a formula F is said to be successful if and only if we have that \(M,w\models F\land \may{a}F\) implies \(M[F!],w\models F\) for each pointed Kripke model \((M,w)\) coming from a given class \(\sC\), Holliday and Icard (2010) provide a comprehensive analysis of (un)successfulness with respect to the class of single-agent \(\mathsf{S5}\) Kripke models and with respect to the class of single-agent \(\mathsf{KD45}\) Kripke models. In particular, they provide a syntactic characterization of the successful formulas over these classes of Kripke models. This analysis was extended in part to a multi-agent setting by Saraf and Sourabh (2012). The highly technical details of these works are beyond the scope of the present article. 