 It may be the case that some very knowing agent knows all that is distributed knowledge in G, but it is not guaranteed. To capture that all the agents know \(\varphi\), we could use the conjunction of the formulas \(K_{i}\varphi\) for \(\in\mathcal{A}\), i.e., \(\bigwedge_{i\in\mathcal{A}}K_{i}\varphi\). This is a well-defined formula if \(\mathcal{A}\) is finite (which it typically is). If \(\mathcal{A}\) is not finite, then \(\bigwedge_{i\in\mathcal{A}}K_{i}\varphi\) is not a formula in \(\mathcal{L}_{Kn}\), as it has only finite conjunctions. As a shorthand for \(\bigwedge_{i\in\mathcal{A}}K_{i}\varphi\), it is standard to introduce the everybody knows operator, \(E_{G}\):