On the discovery of mathematical concepts

S. L. Epstein
1988 International Journal of Intelligent Systems  
The Graph Theorist, GT, is a system which performs mathematical research in graph theory. This paper focuses upon GTs ability to conjecture and prove mathematical theorems from the definitions in its input knowledge base. Each class of graphs is defined in an algebraic notation with a semantic interpretation that is a stylized algorithm to generate the class correctly and completely. From a knowledge base of such concept definitions, GT is able to conjecture and prove such theorems as "The set
more » ... f acyclic, connected graphs is precisely the set of trees" and "There is no odd-regular graph on an odd number of vertices." Conjecture and proof are driven both by examples (specific graphs) and by definitional form (algorithms).
doi:10.1002/int.4550030205 fatcat:2uy7naiytvhillxavopj6y7qee