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[2602.15403] Common Belief Revisited
Summary
The paper 'Common Belief Revisited' challenges existing notions of common belief in knowledge representation, proposing a new axiom for its complete characterization in the KD45 framework.
Why It Matters
This research addresses a significant question in artificial intelligence regarding the logic of common belief, which is crucial for understanding multi-agent systems and knowledge representation. By refining the axioms governing common belief, it enhances our theoretical foundation in AI, influencing future developments in collaborative AI systems.
Key Takeaways
- Common belief is not adequately represented by KD4 in the KD45 framework.
- An additional axiom is necessary for a complete characterization of common belief.
- The new axiom relies on the number of agents involved.
- The findings settle an open problem in the field of knowledge representation.
- This research can influence the design of multi-agent systems in AI.
Computer Science > Artificial Intelligence arXiv:2602.15403 (cs) [Submitted on 17 Feb 2026] Title:Common Belief Revisited Authors:Thomas Ågotnes View a PDF of the paper titled Common Belief Revisited, by Thomas {\AA}gotnes 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. We show that the result is a complete characterisation of common belief, settling the open problem. Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2602.15403 [cs.AI] (or arXiv:2602.15403v1 [cs.AI] for this version) https://doi.org/10.48550/arXiv.2602.15403 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Thomas Ågotnes [view email] [v1] Tue, 17 Feb 2026 07:22:31 UTC (15 KB) Full-text links: Access Paper: View a PDF of the paper titled Common Belief...
