ONTIC: A Knowledge Representation System for Mathematics

Ontic is an interactive system for developing and verifying mathematics. Ontic's verification mechanism is capable of automatically finding and applying information from a library containing hundreds of mathematical facts. Starting with only the axioms of Zermelo-Fraenkel set theory, the Ontic system has been used to build a data base of definitions and lemmas leading to a proof of the Stone representation theorem for Boolean lattices. The Ontic system has been used to explore issues in knowledge representation, automated deduction, and the automatic use of large data bases.

Automated Reasoning About Classical Mechanics

In recent years, researchers in artificial intelligence have become interested in replicating human physical reasoning talents in computers. One of the most important skills in this area is predicting how physical systems will behave. This thesis discusses an implemented program that generates algebraic descriptions of how systems of rigid bodies evolve over time. Discussion about the design of this program identifies a physical reasoning paradigm and knowledge representation approach based on mathematical model construction and algebraic reasoning. This paradigm offers several advantages over methods that have become popular in the field, and seems promising for reasoning about a wide variety of classical mechanics problems.