 The formula \(\neg A \neg \varphi\) will be abbreviated \(E\varphi\). The symbol \(E\) is the existential dual of \(A\) and it indicates that a certain formula holds at some state in the model. With the global modality we have a genuine addition of expressivity (together with further costs and further gains, as shown in Goranko &amp; Passy 1992), therefore we can express validity in a model by means of expressing truth in a world, witness the fact that \(M,w \models A \varphi\) holds if and only if \( \models_M \varphi\) does.