On the discovery of mathematical concepts

✍ Scribed by S. L. Epstein

• Publisher: John Wiley and Sons
• Year: 1988
• Tongue: English
• Weight: 684 KB
• Volume: 3
• Category: Article
• ISSN: 0884-8173
• DOI: 10.1002/int.4550030205

✦ Synopsis

The Graph Theorist (GT) is a system intended to perform mathematical research in graph theory. This paper focuses upon GT's ability 10 discover new mathematical concepts by varying the definitions in its input knowledge base. Each new definition is a correct and complete generator for a class of graphs. The new concepts arise from the specialization of an existing concept, the generalization of an existing concept, and the merger of two or more existing concepts. Discovery is driven both by examples (specific graphs) and by definitional form (algorithms). GT explores new concepts either to develop an area of knowledge or to link a newly-acquired concept into a pre-existing knowledge base. From an initial knowledge base containing only the definition of "graph," GT discovers such concepts as acyclic graphs, connected graphs and bipartite graphs. Given an input concept, such as "star," GT discovers "trees" while searching for the appropriate links to integrate star into its knowledge base. The discovery processes construct a semantic net linking frames for all of GT's concepts together.