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.

Slow and Smooth: A Bayesian Theory for the Combination of Local Motion Signals in Human Vision

In order to estimate the motion of an object, the visual system needs to combine multiple local measurements, each of which carries some degree of ambiguity. We present a model of motion perception whereby measurements from different image regions are combined according to a Bayesian estimator --- the estimated motion maximizes the posterior probability assuming a prior favoring slow and smooth velocities. In reviewing a large number of previously published phenomena we find that the Bayesian estimator predicts a wide range of psychophysical results. This suggests that the seemingly complex set of illusions arise from a single computational strategy that is optimal under reasonable assumptions.