AI 中文总结
本文定义不可信与不可知公式，证明其源于Moore不动点，在S5中统一静态与动态概念，并推广至多智能体及分析Brandenburger-Keisler悖论。
AI 中文摘要
在本文中，我们定义一个公式$\varphi$为不可信的，如果$\Box\varphi$不可满足；并定义为不可知的，如果$\Box\varphi\land\varphi$不可满足。然后我们分析了在框架类K、KD、KD45和S5中不可知性和不可信性的来源。我们首先证明任何不可信公式都是Moore函数$f(\varphi)=\varphi\land\lnot\Box\varphi$的不动点。我们的主要结果表明，在S5中，认知逻辑中的静态不可知性和不可信性概念，以及动态认知逻辑中的动态总是信息性和最终自我反驳概念，都等价于“Moore现象”。我们还将该结果推广到多智能体情形，表明尽管所有不可知公式仍然体现Moore现象，但由于其交互性质，出现了新的机制。最后，我们简要分析认知博弈论中的Brandenburger-Keisler悖论是否可以被视为Moore式的。
英文摘要
In this paper, we define a formula $φ$ to be unbelievable if $\Boxφ$ is unsatisfiable, and unknowable if $\Boxφ\landφ$ is unsatisfiable. We then analyze the sources of unknowability and unbelievability in different classes of frames K, KD, KD45, and S5. We first show that any unbelievable formula is a fixed point of the Moore function defined by $f(φ)=φ\land\lnot\Boxφ.$ Our main result shows that in S5, the static notions of unknowability and unbelievability in epistemic logic, and the dynamic notions of always informativeness and eventual self-refutation in dynamic epistemic logic are all equivalent to ``Moorean phenomena.'' We also generalize the result to the multi-agent case, showing that although all unknowable formulas still manifest Moorean phenomena, new mechanisms arise due to their interactive nature. Finally, we briefly analyze whether the Brandenburger-Keisler paradox in epistemic game theory can be considered Moorean.
Comments13 pages, no figures, accepted for presentation and presented at the Asian Workshop on Philosophical Logic (AWPL 2026)
