 We see that \(\frac12\Pri_a(p)\) satisfies just what we want: the actual event that occurs is the point e (the announcement of the precondition p), agent a knows this, but all other agents consider it possible that either e (the announcement of p) or f (the announcement of \(\lnot p\)) occurred. Furthermore, the other agents know that a knows which event was the case (since at each of the events e and f that they consider possible, agent a knows the event that occurs). This is just what we want of a semi-private announcement. 