 Hence, though the \(E_{G}\) operator is definable in the language \(\mathcal{L}_{Kn}\), a suitable notion of common knowledge is not. For that, we again need to define a new relation on our model. This time, we are interested in capturing that nobody considers \(\varphi\) epistemically possible anywhere. To build the relation, we therefore first take the union the relations of all the agents in G, but this is not quite enough: to use the standard modal semantic clause, we must also be able to reach all of the worlds in this relation in a single step. Hence, let 