We formalize two independent computational limitations that constrain algorithmic intelligence: formal incompleteness and dynamical unpredictability. The former limits the deductive power of consistent reasoning systems while the latter bounds long-term prediction under finite precision. We show that these two extrema together impose structural bounds on an agent's ability to reason about its own predictive capabilities. In particular, an algorithmic agent cannot verify its own maximal prediction horizon universally. This perspective clarifies inherent trade-offs between reasoning, prediction, and self-analysis in intelligent systems. The construction presented here constitutes one representative instance of a broader logical class of such limitations.

翻译：我们形式化了制约算法智能的两个独立计算局限：形式不完备性与动态不可预测性。前者限制了一致推理系统的演绎能力，后者则约束了有限精度下的长期预测能力。我们证明这两种极端情形共同构成了智能体对其自身预测能力进行推理的结构性边界。具体而言，算法智能体无法普遍验证其自身的最大预测视界。这一视角阐明了智能系统中推理、预测与自我分析之间固有的权衡关系。本文提出的构造构成了此类局限更广泛逻辑范畴中的一个代表性实例。