用范畴论构建类比，让机器理解知识迁移的逻辑
Types of Relations: Defining Analogies with Category Theory
- 将知识域形式化为范畴，用数学结构定义类比关系
- 通过函子、拉回和推出操作，生成类比的核心与融合态
- 适合对形式化推理与认知建模感兴趣的读者
为使人类和机器能智能行为，必须以恰当方式表征知识。人类常通过类比将知识迁移到新领域，或通过解释帮助他人完成迁移。因此，核心问题在于：何种表征可用于构建、发现与评估类比？本文研究构成类比的关键领域特征，通过将知识域形式化为范畴来实现。以太阳系与氢原子的类比为例，演示如何构建领域范畴，并展示如何利用函子（functors）、拉回（pullbacks）与推出（pushouts）定义类比、描述其核心以及对应领域的融合。该方法为类比的数学建模提供了系统框架。
原文摘要 · Abstract (English)
In order to behave intelligently both humans and machines have to represent their knowledge adequately for how it is used. Humans often use analogies to transfer their knowledge to new domains, or help others with this transfer via explanations. Hence, an important question is: What representation can be used to construct, find, and evaluate analogies? In this paper, we study features of a domain that are important for constructing analogies. We do so by formalizing knowledge domains as categories. We use the well-known example of the analogy between the solar system and the hydrogen atom to demonstrate how to construct domain categories. We also show how functors, pullbacks, and pushouts can be used to define an analogy, describe its core and a corresponding blend of the underlying domains.
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