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 and has a simple logical characterization which entails appealing mathematical properties. In a broader sense, this paper is a further step towards a mathematical theory of analogical reasoning.

翻译：作者近期在泛代数的一般框架下引入了一个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，我们对布尔比例的定义与文献中的两个重要模型一致，并具有简单的逻辑表征，该表征蕴含着吸引人的数学性质。从更广泛的意义上讲，本文是迈向类比推理数学理论的又一步骤。