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Graph Theory

The Graph Theorist (GT) was a successful, implemented system that did original mathematical research in graph theory. It represented knowledge of mathematical concepts with declarative expressions, each of which had a semantic interpretation as a stylized, recursive algorithm that defined a class by generating it correctly and completely. GT generated correct examples, defined and explored new graph theory properties, and conjectured and proved theorems. It was the first system to both generate and prove mathematical hypotheses.

Key references

Epstein, S. L. and Sridharan, N. S. (1991). Knowledge Representation for Mathematical Discovery – Three Experiments in Graph Theory. Applied Intelligence, 1 (1): 7-33.

Epstein, S. L. (1988). Learning and Discovery: One System’s Search for Mathematical Knowledge. Computational Intelligence , 4 (1): 42-53.

Epstein, S. L. (1983). Knowledge Representation in Mathematics: A Case Study in Graph Theory. Ph.D. thesis, Department of Computer Science, Rutgers University.

Additional references

Epstein, S. L. (1988). On the Discovery of Mathematical Concepts. International Journal of Intelligent Systems, 3 (2): 167-178.

Epstein, S. L. (1987). Languages for Problem Solving in Graph Theory. In J. C. Boudreaux, B. W. Hamill, & R. N. Jernigan (Ed.), The Role of Language in Problem Solving 2 (pp. 261-300). New York: North-Holland.

Epstein, S. L. (1987). On the Discovery of Mathematical Theorems. In Proceedings of the Tenth International Joint Conference on Artificial Intelligence, 194-197. Milan: Morgan Kaufmann.

This material is based upon work supported by the National Science Foundation under Grant Nos. 9423085, #IRI-9703475, 9222720, and #9001936, by the New York State Technological Development Graduate Research and Technology Initiative, and by the PSC-CUNY Research Foundation.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation, New York State, or PSC-CUNY.