 Each diner knows the condition of the other diners’ faces, but not her own. Suppose the cook makes no announcement, after all. Then none of the diners knows the true state of the world whatever \(\omega \in \Omega\) the actual world turns out to be, but they do know a priori that certain propositions are true at various states of the world. For instance, Cathy’s information system before any announcement is made is depicted in Figure 2.1a: