Bongard problem

A Bongard problem is a kind of puzzle invented by the Soviet computer scientist Mikhail Moiseevich Bongard, probably in the mid-1960s. They were published in his eponymous 1967 book on pattern recognition, which became known in English translation from 1970. Bongard, in the introduction of the book (which deals with a number of topics including perceptrons) credits the ideas in it to a group including M. N. Vainstvaig, V. V. Maksimov, and M. S. Smirnov.

The idea of a Bongard problem is to present two sets of relatively simple diagrams, say "A" and "B". All the diagrams from set "A" have a common factor or attribute, which is lacking in all the diagrams of set "B". The problem is to find, or to formulate, convincingly, the common factor.

Many computational architectures have been devised to solve Bongard problems, the most extensive of which being Phaeaco, by Dr. Harry Foundalis. Such task was relevant to the early days of machine learning and is still unsolved to this date. The problems were popularised by their occurrence in the 1979 book "Gödel, Escher, Bach" by Douglas Hofstadter, himself a composer of Bongard problems. Bongard problems are also at the heart of the game Zendo.

cientific works on Bongard problems

* Bongard, M. M. (1970). Pattern Recognition. Rochelle Park, N.J.: Hayden Book Co., Spartan Books. (Original publication: Проблема Узнавания, Nauka Press, Moscow, 1967)
* Maksimov, V. V. (1975). Система, обучающаяся классификации геометрических изображений (A system capable of learning to classify geometric images; as translated from the Russian by Marina Eskina), in Моделирование Обучения и Поведения (Modeling of Learning and Behavior, in Russian), M.S. Smirnov, V.V. Maksimov (eds.), Nauka, Moskva.
* Hofstadter, D. R. (1979). Gödel, Escher, Bach: an Eternal Golden Braid. New York: Basic Books.
* Montalvo, F. S. (1985). Diagram Understanding: the Intersection of Computer Vision and Graphics. M.I.T. Artificial Intelligence Laboratory, A. I. Memo 873, November 1985.
* Saito, K., and Nakano, R. (1993) A Concept Learning Algorithm with Adaptive Search. Proceedings of Machine Intelligence 14 Workshop. Oxford University Press. See pp. 347–363.
* Hofstadter, D. R. and the Fluid Analogies Research Group (1995). . New York: Basic Books.
* Hofstadter, D. R. (1995). On Seeing A’s and Seeing As. Stanford Humanities Review 4/2 pp. 109–121.
* Hofstadter, D. R. (1997). Le Ton beau de Marot. New York: Basic Books.
* Linhares, A. (2000). A glimpse at the metaphysics of Bongard problems. Artificial Intelligence, Volume 121, Issue 1-2, pp. 251–270.
* Foundalis, H. (2006). Phaeaco: A Cognitive Architecture Inspired by Bongard’s Problems. Doctoral dissertation, Indiana University, Center for Research on Concepts and Cognition (CRCC), Bloomington, Indiana.

External links

* [http://www.foundalis.com/res/bps/bpidx.htm Index of Bongard problems]