  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.
