Boolean proportions

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.