Analogical proportions are 4-ary relations that read "A is to B as C is to D". Recent works have highlighted the fact that such relations can support a specific form of inference, called analogical inference. This inference mechanism was empirically proved to be efficient in several reasoning and classification tasks. In the latter case, it relies on the notion of analogy preservation. In this paper, we explore this relation between formal models of analogy and the corresponding classes of analogy preserving functions, and we establish a Galois theory of analogical classifiers. We illustrate the usefulness of this Galois framework over Boolean domains, and we explicitly determine the closed sets of analogical classifiers, i.e., classifiers that are compatible with the analogical inference, for each pair of Boolean analogies.

翻译：分析比例是4-关系,读作“A是B,C是D”。 最近的著作强调,这种关系可以支持一种特定形式的推论,称为模拟推论。这种推论机制在几个推理和分类任务中被经验证明是有效的。在后一种情况下,这种推论机制依靠类比保全的概念。在本文中,我们探讨正式的类比模型与相应的类比保全功能类别之间的关系,我们建立了模拟分类学的伽罗瓦理论。我们说明了这个加洛瓦框架对布林域的用处,我们明确确定了与模拟推论相符的闭合类比分类器,即对布林类的每对类比来说,与模拟推论相兼容的分类师。