Formal semantics for mutual belief (Q685541)

The paper proposes a formal semantics for a modal mutual belief operator, within a traditional doxastic logic. The truth set of a mutual belief expression is characterized as the greatest fixpoint of a monotone, continuous set operator. In this way, it is shown that mutual belief can be defined in terms of private beliefs and that, while its definition is in a sense circular, mutual belief need not itself be a non-well-founded mathematical object. It is also shown that if the logic of private beliefs is assumed to be Weak S5, the resulting logic of mutual belief is weaker, in that it does not enforce negative introspection.