FORMAL SEMANTICS FOR MUTUAL BELIEF

I propose 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, I show 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. I also show 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