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 the robustness and applicability of the general framework.

翻译：作者最近在泛代数的一般设定中引入了一种类比比例的抽象代数框架。本文在该框架内研究由两个元素0和1构成的布尔域中的类比比例。结果表明，我们所提出的布尔比例概念与文献中不同背景下两种著名模型相吻合。这意味着我们能够在单一框架内同时捕捉布尔比例的两种独立建模方式，这在数学上具有吸引力，并进一步证明了该通用框架的稳健性与适用性。