On Automated Scientific Theory Formation: A Case Study using the AM Program

A program called "AM" is described which carries on simple mathematics research, defining and studying new concepts under the guidance of a large body of heuristic rules. The 250 heuristics communicate via an agenda mechanism, a global priority queue of small tasks for the program to perform, and reasons why each task is plausible (for example, "Find generalizations of'primes', because'primes' turned out to be so useful a concept"). Each concept is represented as an active, structured knowledge module. One hundred very incomplete modules are initially supplied, each one corresponding to an elementary set-theoretic concept (for example, union). This provides a definite but immense space which AM begins to explore.