智能系统在推理与预测中存在两大根本局限。
Dual Computational Horizons: Incompleteness and Unpredictability in Intelligent Systems
- 从逻辑完备性与动态不可预测性两方面界定智能算法的计算极限。
- 证明智能体无法普遍验证自身最大预测能力，存在结构性约束。
- 适合研究人工智能本质、认知边界或形式化系统的学者参考。
我们形式化了两种独立的计算限制，它们制约着算法智能：形式不完备性和动态不可预测性。前者限制一致推理系统的演绎能力，后者在有限精度下限制长期预测。我们表明，这两种极端共同对智能体理解自身预测能力的能力施加结构性约束。特别地，一个算法智能体无法普遍验证其自身的最大预测时域。这一视角阐明了智能系统中推理、预测与自我分析之间的内在权衡。本文提出的构造是此类更广泛逻辑限制的一个代表性实例。
原文摘要 · Abstract (English)
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.
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