 Note that in the above, we may replace F by a contradiction such as the propositional constant \(\bot\) for falsehood. Accordingly, an agent who initially believes p is lead by an announcement that p is false to an inconsistent state in which she believes everything, including falsehoods. This trivialization occurs whenever something is announced that contradicts the agent’s beliefs; in particular, it occurs if a contradiction such as \(\bot\) is itself announced: 