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.

Formal semantics for mutual belief

COLOMBETTI, MARCO
1993-01-01

Abstract

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.
1993
INF
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/518112
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact