用数学公理重新定义智能，揭示其结构与时间本质。
Toward the Axiomatization of Intelligence: Structure, Time, and Existence
- 以集合论构建智能存在框架，将智能视为动态演化结构。
- 通过三类系统对比，揭示神经网络与生物反射的智能差异。
- 提出时间与行为概念，为智能分类提供新视角，适合理论研究者。
本研究旨在在元框架下构建智能的公理化定义，解决智能作为本质模糊且多义概念的难题。首先，我们形式化宇宙的集合论表示，将智能定义为涉及时间演化与外部互动的结构。基于智能是‘具备输入、处理、输出信息或物质结构的实体’这一朴素定义，在该集合论框架中进行公理重构。应用此定义，比较并解析三类系统：未优化的赫布型神经网络、反向传播优化的神经网络及生物反射系统，分析其智能水平、结构特性与生物合理性。进一步，通过范畴论扩展，引入‘时间范畴’与‘智能范畴’，建立二者间的函子关系，抽象表达智能系统的演化与模仿关系。由于智能依赖于时间交互，本文提出‘活动’概念，探讨活动条件对智能分类的影响。最后，主张该定义方法可推广至意识、情感等概念，建议采用统一步骤：构建普适表征、选取朴素定义、进行公理化形式化。
原文摘要 · Abstract (English)
This study aims to construct an axiomatic definition of intelligence within a meta-framework that defines the method of definition, addressing intelligence as an inherently naive and polysemous concept. Initially, we formalize a set-theoretic representation of the universe as the domain wherein intelligence exists and characterize intelligence as a structure that involves temporal evolution and interaction with other sets. Starting from a naive definition of intelligence as "an entity possessing structures for externally inputting, internally processing, and externally outputting information or matter," we axiomatically reformulate it within this set-theoretical depiction of the universe. Applying this axiomatic definition, we compare and interpret three examples -- Hebbian non-optimized neural networks (NNs), backpropagation-optimized NNs, and biological reflexive systems -- in terms of their intelligence, structural properties, and biological plausibility. Furthermore, by extending our definition into a categorical framework, we introduce two categories, "Time Category" and "Intelligence Category," along with the functorial relationships between them, demonstrating the potential to represent changes and mimicry relationships among intelligent systems abstractly. Additionally, since intelligence, as defined herein, functions effectively only when accompanied by temporal interactions, we introduce the concept of "activity" and explore how activity-based conditions influence classifications and interpretations of intelligence. Finally, we suggest that our definitional methodology is not limited to intelligence alone, but can be similarly applied to other concepts, such as consciousness and emotion, advocating for their formal reinterpretation through the same procedural steps: defining a universal representation, selecting naive definitions, and axiomatic formalization.
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