Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative justification-based notion of similarity based on the observation that sets of generalizations encode important properties of elements. We show that similarity defined in this way has appealing mathematical properties. As we construct our notion of similarity from first principles using only elementary concepts of universal algebra, to convince the reader of its plausibility, we show that it can be naturally embedded into first-order logic via model-theoretic types.

翻译：检测并利用看似遥远对象之间的相似性无疑是人类的一项重要能力。本文从头开始构建了一种基于泛化集合编码元素重要性质这一观察的抽象代数和定性理由驱动的相似性概念。我们证明，以这种方式定义的相似性具有令人满意的数学性质。由于我们仅使用泛代数的基本概念从第一原理构建相似性概念，为了向读者证明其合理性，我们展示了它可以自然地通过模型论类型嵌入一阶逻辑中。