Indiana University Bloomington

Bongard Problems

Bongard problems are a fascinating microdomain in which each problem consists of a series of graphical examples of things belonging to a category, and other things not belonging to that category. The object is to describe the category elegantly. This is not always trivial.

Harry Foundalis has written an extremely useful overview of Bongard problems and has completed a program which solves many of them. This program starts with bitmapped images, performs pattern recognition on a visual level, and then continues to perform pattern recognition on a conceptual level.

In this simple example Bongard problem, the patterns on the left exhibit a common feature, while those on the right exhibit the negation of that feature. Can you see what the feature is?

If this problem tickles your fancy, go to Harry's page, where you will find a great number of Bongard problems of all levels of difficulty. There are a few which Harry himself has yet to solve. He'd be happy to hear your opinions.