• Computer Science > Artificial Intelligence [Submitted on 17 Feb 2026] Title:Common Belief Revisited View PDF HTML (experimental)Abstract:Contrary to common belief, common belief is not KD4. • If individual belief is KD45, common belief does indeed lose the 5 property and keep the D and 4 properties – and it has none of the other commonly considered properties of knowledge and belief. • But it has another property: $C(C\phi \rightarrow \phi)$ – corresponding to so-called shift-reflexivity (reflexivity one step ahead). • This observation begs the question: is KD4 extended with this axiom a complete characterisation of common belief in the KD45 case? • If not, what \emph{is} the logic of common belief? • In this paper we show that the answer to the first question is ``no’’: there is one additional axiom, and, furthermore, it relies on the number of agents.
Article Summaries:
- Computer Science > Artificial Intelligence [Submitted on 17 Feb 2026] Title:Common Belief Revisited View PDF HTML (experimental)Abstract:Contrary to common belief, common belief is not KD4. If individual belief is KD45, common belief does indeed lose the 5 property and keep the D and 4 properties – and it has none of the other commonly considered properties of knowledge and belief. But it has another property: $C(C\phi \rightarrow \phi)$ – corresponding to so-called shift-reflexivity (reflexivity one step ahead). This observation begs the question: is KD4 extended with this axiom a complete
Sources: