Affiliations: [a] University of Michigan, Schools of Medicine and Business Administration, Ann Arbor, MI 48109-1234, USA | [b] MIT Artificial Intelligence Laboratory, Cambridge, MA 02139, USA
Abstract: Given a knowledge base that is sufficiently large, organized, and relevant, a few simple and powerful ideas can capture much of the effectiveness of inductive mathematical reasoning. This claim is supported by PM, a program written in a frame-based language. Given a goal, such as ‘Find a relation among the side lengths of a right triangle,’ PM is designed to generate conjectures and to improve its ability to do so. The program repeatedly uses generalization, specialization, and analogy in patterns of plausible inference suggested by Polya. Knowledge is organized by links between entities in the knowledge base so that it need only be searched locally. The point of this paper is to raise the issue of how we should prepare now to manage systems capable of discovery by computer to serve human ends, should it be proved possible.
