  More than 50 years ago Bongard introduced 100 visual concept learning
problems as a testbed for intelligent vision systems. These problems are now
known as Bongard problems. Although they are well known in the cognitive
science and AI communities only moderate progress has been made towards
building systems that can solve a substantial subset of them. In the system
presented here, visual features are extracted through image processing and then
translated into a symbolic visual vocabulary. We introduce a formal language
that allows representing complex visual concepts based on this vocabulary.
Using this language and Bayesian inference, complex visual concepts can be
induced from the examples that are provided in each Bongard problem. Contrary
to other concept learning problems the examples from which concepts are induced
are not random in Bongard problems, instead they are carefully chosen to
communicate the concept, hence requiring pragmatic reasoning. Taking pragmatic
reasoning into account we find good agreement between the concepts with high
posterior probability and the solutions formulated by Bongard himself. While
this approach is far from solving all Bongard problems, it solves the biggest
fraction yet.
