 To begin, let us consider a specific example of a more complex communicative action: a completely private announcement. The idea of this action is that one agent, let us call her a, is to receive a message in complete privacy. Accordingly, no other agent should learn the contents of this message, and, furthermore, no other agent should even consider the possibility that agent a received the message in the first place. (Think of agent a traveling unnoticed to a secret and secure location, finding and reading a coded message only she can decode, and then destroying the message then and there.) One way to think about this action is as follows: there are two possible events that might occur. One of these, let us call it event e, is the announcement that p is true; this is the secret message to a. The other event, let us call it f, is the announcement that the propositional constant \(\top\) for truth is true, an action that conveys no new propositional information (since \(\top\) is a tautology). Agent a should know that the message is p and hence that the event that is in fact occurring is e. All other agents should mistakenly believe that it is common knowledge that the message is \(\top\) and not even consider the possibility that the message is p. Accordingly, other agents should consider event f the one and only possibility and mistakenly believe that this is common knowledge. We picture a diagrammatic representation of this setup in Figure 3. 