The logic of common belief does not always reflect the logic of individual beliefs. In particular, the Negative Introspection property fails at the common belief level, that is, it can happen than either is A commonly believed nor is it common belief that A is not commonly believed. Indeed...

When we make a non-trivial prediction about the future we select, among the conceivable future descriptions of the world, those that appear to us to be most likely. Within a branching-time framework we capture this by means of two binary relations, less than c and less than p. If t1 and t2 are...

Aumann (1976) put forward a formal definition of common knowledge and used it to prove that two "like minded" individuals cannot "agree to disagree" in the following sense. If they start from a common prior and update the probability of an event E (using Bayes' rule) on the basis of private...

We provide an introduction to interactive belief systems from a qualitative and semantic point of view. Properties of belief hierarchies are formulated locally. Among the properties considered are "Common belief in no error" (which has been shown to have important game theoretic applications),...