Abstract
What happens if in the Muddy Children story [22] we drop the assumption that the public announcements (made by the father and by the children) are commonly known to be always true, and instead we simply assume that they are true and commonly believed to be true? More generally, what happens in the long term with a group's beliefs, knowledge and "epistemic states" (fully describable in fact by conditional beliefs), when receiving (or exchanging) a sequence of public announcements of truthful but uncertain information? Do the agents' beliefs (or knowledge, or conditional beliefs, or other doxastic attitudes such as "strong beliefs") reach a fixed point? Or do they exhibit instead a cyclic behavior, oscillating forever?
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