Department
of 

Susan L. EpsteinThe CUNY Graduate School, Department
of Computer Science and 





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Graph TheoryThe
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. Key
references Epstein, S. L.
and Sridharan, N. S. (1991). Knowledge Representation for Mathematical
Discovery  Three Experiments in Graph Theory. Applied Intelligence, 1 (1):
733. 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): 167178. 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. 261300). New York: NorthHolland. Epstein, S. L.
(1987). On the Discovery of Mathematical Theorems. In Proceedings of the
Tenth International Joint Conference on Artificial Intelligence, 194197. Milan: Morgan
Kaufmann. This
material is based upon work supported by the National Science Foundation
under Grant Nos. 9423085, #IRI9703475, 9222720, and #9001936, by the
New York State Technological Development Graduate Research and Technology
Initiative, and by the PSCCUNY 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 PSCCUNY. 