论文标题
类似分类器的Galois理论
Galois theory for analogical classifiers
论文作者
论文摘要
类比比例是4个亲戚关系，读为“ a为b作为c为d”。最近的作品强调了这样一个事实，即这种关系可以支持一种称为类似推断的特定形式的推论。从经验上证明，这种推论机制在几个推理和分类任务中是有效的。在后一种情况下，它依赖于类比保存的概念。 在本文中，我们探讨了类比的形式模型与相应的类比保留函数类别之间的关系，并建立了类似分类器的Galois理论。我们说明了该GALOIS框架对布尔域的有用性，并明确确定了类似分类器的封闭集，即与类似推断兼容的分类器对每对布尔类似物的分类器。
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.
