推翻常识：共同信念并非KD4，而是需额外公理的逻辑系统。
Common Belief Revisited
- 提出新公理以完整刻画共同信念的逻辑结构
- 发现该逻辑依赖于参与者数量，且需额外一个公理
- 解决长期未解的共同信念形式化难题
与普遍认知相反，共同信念并非KD4。若个体信念为KD45，共同信念确实失去5性质而保留D和4性质，且不具有其他常被设想的知识与信念属性。但它具备新性质：$C(Cϕ\rightarrow ϕ)$，对应所谓的移位自反性（前向自反）。这引发疑问：在KD4基础上添加此公理，能否完整刻画KD45情形下的共同信念？本文证明答案是否定的——还存在一个额外公理，且其有效性依赖于参与者的数量。我们最终给出完全刻画共同信念的逻辑体系，解决了这一开放问题。
原文摘要 · Abstract (English)
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: $C(Cϕ\rightarrow ϕ)$ -- 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. We show that the result is a complete characterisation of common belief, settling the open problem.
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