  Analogical reasoning is a powerful qualitative reasoning tool that enables
humans to connect two situations, and to generalize their knowledge from
familiar to novel situations. Cognitive Science research provides valuable
insights into the richness and complexity of analogical reasoning, together
with implementations of expressive analogical reasoners with limited
scalability. Modern scalable AI techniques with the potential to reason by
analogy have been only applied to the special case of proportional analogy, and
not to understanding higher-order analogies. In this paper, we aim to bridge
the gap by: 1) formalizing six dimensions of analogy based on mature insights
from Cognitive Science research, 2) annotating a corpus of fables with each of
these dimensions, and 3) defining four tasks with increasing complexity that
enable scalable evaluation of AI techniques. Experiments with language models
and neuro-symbolic AI reasoners on these tasks reveal that state-of-the-art
methods can be applied to reason by analogy with a limited success, motivating
the need for further research towards comprehensive and scalable analogical
reasoning by AI. We make all our code and data available.
