类比分类器的伽罗瓦理论
Galois theory for analogical classifiers
摘要：
类比比例是4元关系，读作“A对B如同C对D”。最近的研究强调了这样一个事实，即这种关系可以支持一种特定形式的推理，称为类比推理。这种推理机制在几个推理和分类任务中被实证证明是有效的。在后一种情况下，它依赖于类推保全的概念。本文探讨了类比的形式模型与对应的类比保持函数类之间的关系，建立了类比分类器的伽罗瓦理论。我们说明了这个伽罗瓦框架在布尔域上的有用性，我们明确地确定了类比分类器的闭集，即，对于每对布尔类比，与类比推理兼容的分类器。
英文摘要：
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.
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