 A formula \(\varphi\) of a modal language \(\Delta\): holds at a state \(w\) of model \(M\) whenever \(M,w \models \varphi\); is valid in a model \(M\), denoted \(\models_{M} \varphi\), if and only if \(M,w \models \varphi\) for every \(w \in W\), where \(W\) is the domain of \(M\); is valid in a class of models \(\mathcal{M}\), denoted \(\models_{\mathcal{M}} \varphi\), if and only if it is valid in every \(M \in \mathcal{M}\); is valid in a frame \({F}\), denoted \(\models_{{F}} \varphi\), if and only if for every valuation \(V\) we have that \(\models_{(F,V)} \varphi\); is valid in a class of frames \(\mathcal{F}\), denoted \(\models_{\mathcal{F}} \varphi\), if and only if it is valid in every \(F \in \mathcal{F}\).