AM: A case study in AI methodology.
Artificial Intelligence
Why AM an EUISKO appear to work.
Artificial Intelligence
Am: an artificial intelligence approach to discovery in mathematics as heuristic search.
Am: an artificial intelligence approach to discovery in mathematics as heuristic search.
Knowledge representation in mathematics: a case study in graph theory
Knowledge representation in mathematics: a case study in graph theory
Graph Theory With Applications
Graph Theory With Applications
Computational Discovery in Pure Mathematics
Computational Discovery of Scientific Knowledge
Managing automatically formed mathematical theories
MKM'06 Proceedings of the 5th international conference on Mathematical Knowledge Management
| Hi-index | 0.00 |
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 of 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).