  Analogical proportions compare pairs of items (a, b) and (c, d) in terms of
their differences and similarities. They play a key role in the formalization
of analogical inference. The paper first discusses how to improve analogical
inference in terms of accuracy and in terms of computational cost. Then it
indicates the potential of analogical proportions for explanation. Finally, it
highlights the close relationship between analogical proportions and
multi-valued dependencies, which reveals an unsuspected aspect of the former.
