Varieties of Interpersonal Compatibility of Beliefs
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 that neither is A commonly believed nor is it common belief that A is not commonly believed. Indeed Negative Introspection of common belief involves restrictions on individual beliefs of an intersubjective nature. We consider a number of interpersonal restrictions on beliefs and study their relationship. We also characterize Negative Introspection of common belief in terms of interpersonal properties of individual beliefs. All the results are proved syntactically.
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