The author has recently introduced an abstract algebraic framework of analogical proportions within the general setting of universal algebra. This paper studies analogical proportions in the boolean domain consisting of two elements 0 and 1 within his framework. It turns out that our notion of boolean proportions coincides with two prominent models from the literature in different settings. This means that we can capture two separate modellings of boolean proportions within a single framework which is mathematically appealing and provides further evidence for its robustness and applicability.

翻译：作者近期在泛代数的一般框架下提出了一个关于类比比例的抽象代数框架。本文在其框架内研究由两个元素0和1组成的布尔域中的类比比例。结果表明，我们提出的布尔比例概念与文献中不同场景下的两个著名模型一致。这意味着我们可以在单一框架内捕获两种独立的布尔比例建模方式，这在数学上颇具吸引力，并进一步证明了该框架的稳健性和适用性。