  Letter-string analogy is an important analogy learning task which seems to be
easy for humans but very challenging for machines. The main idea behind current
approaches to solving letter-string analogies is to design heuristic rules for
extracting analogy structures and constructing analogy mappings. However, one
key problem is that it is difficult to build a comprehensive and exhaustive set
of analogy structures which can fully describe the subtlety of analogies. This
problem makes current approaches unable to handle complicated letter-string
analogy problems. In this paper, we propose Neural logic analogy learning
(Noan), which is a dynamic neural architecture driven by differentiable logic
reasoning to solve analogy problems. Each analogy problem is converted into
logical expressions consisting of logical variables and basic logical
operations (AND, OR, and NOT). More specifically, Noan learns the logical
variables as vector embeddings and learns each logical operation as a neural
module. In this way, the model builds computational graph integrating neural
network with logical reasoning to capture the internal logical structure of the
input letter strings. The analogy learning problem then becomes a True/False
evaluation problem of the logical expressions. Experiments show that our
machine learning-based Noan approach outperforms state-of-the-art approaches on
standard letter-string analogy benchmark datasets.
