  The ability to recognise and make analogies is often used as a measure or
test of human intelligence. The ability to solve Bongard problems is an example
of such a test. It has also been postulated that the ability to rapidly
construct novel abstractions is critical to being able to solve analogical
problems. Given an image, the ability to construct a program that would
generate that image is one form of abstraction, as exemplified in the
Dreamcoder project. In this paper, we present a preliminary examination of
whether programs constructed by Dreamcoder can be used for analogical reasoning
to solve certain Bongard problems. We use Dreamcoder to discover programs that
generate the images in a Bongard problem and represent each of these as a
sequence of state transitions. We decorate the states using positional
information in an automated manner and then encode the resulting sequence into
logical facts in Prolog. We use inductive logic programming (ILP), to learn an
(interpretable) theory for the abstract concept involved in an instance of a
Bongard problem. Experiments on synthetically created Bongard problems for
concepts such as 'above/below' and 'clockwise/counterclockwise' demonstrate
that our end-to-end system can solve such problems. We study the importance and
completeness of each component of our approach, highlighting its current
limitations and pointing to directions for improvement in our formulation as
well as in elements of any Dreamcoder-like program synthesis system used for
such an approach.
