The Use of Equality in Deduction and Knowledge Representation

This report describes a system which maintains canonical expressions for designators under a set of equalities. Substitution is used to maintain all knowledge in terms of these canonical expressions. A partial order on designators, termed the better-name relation, is used in the choice of canonical expressions. It is shown that with an appropriate better-name relation an important engineering reasoning technique, propagation of constraints, can be implemented as a special case of this substitution process. Special purpose algebraic simplification procedures are embedded such that they interact effectively with the equality system. An electrical circuit analysis system is developed which relies upon constraint propagation and algebraic simplification as primary reasoning techniques. The reasoning is guided by a better-name relation in which referentially transparent terms are preferred to referentially opaque ones. Multiple description of subcircuits are shown to interact strongly with the reasoning mechanism.

The Use of Grouping in Visual Object Recognition.

The report describes a recognition system called GROPER, which performs grouping by using distance and relative orientation constraints that estimate the likelihood of different edges in an image coming from the same object. The thesis presents both a theoretical analysis of the grouping problem and a practical implementation of a grouping system. GROPER also uses an indexing module to allow it to make use of knowledge of different objects, any of which might appear in an image. We test GROPER by comparing it to a similar recognition system that does not use grouping.

The Role of Programming in the Formulation of Ideas

Classical mechanics is deceptively simple. It is surprisingly easy to get the right answer with fallacious reasoning or without real understanding. To address this problem we use computational techniques to communicate a deeper understanding of Classical Mechanics. Computational algorithms are used to express the methods used in the analysis of dynamical phenomena. Expressing the methods in a computer language forces them to be unambiguous and computationally effective. The task of formulating a method as a computer-executable program and debugging that program is a powerful exercise in the learning process. Also, once formalized procedurally, a mathematical idea becomes a tool that can be used directly to compute results.