A differential method for reasoning by analogy
Robert McNaughton, Gilbert B. Porter · 1987
This thesis describes a differential method for conducting reasoning by analogy. It is founded on the idea that some systems of representational symbology such as mathematics come equipped with rules for reducing the search for a problem solution by simplifying the representational expressions and for obtaining a closed form solution. Although the performance of these rules is generally unpredictable, there is still great potential for gain due to the variety of the rules. The utility of this concept is evidenced by our own persistence in the development of mathematics. We have applied this concept to machine reasoning. The goal of our approach is to reduce the complexity of the associated search tasks by such symbolic manipulations. In particular, we apply a differential method for deriving problem formulations in the form of constraint equations. To illustrate this approach, we have chosen two important areas of machine reasoning: automated diagnosis and analogical reasoning. Both of these areas lend themselves to our process since the problem requirements are fundamentally differential in nature. Automated diagnosis has received considerable attention in recent years perhaps due to the fact that diagnosis systems can be built in demonstrable stages and with shallow knowledge bases. Although we have focused on the details of the diagnostic process, our approach is more general in that it is based on causal models of systems. We believe this sort of system should be more easily extended by adding to its general physical knowledge. Specifically in the case of diagnosis systems, the system performance can be improved without impacting other parts of the system since the behavioral and failure models of components are captured in separable models. Our approach to analogical reasoning is based on the notion that the similarity of two situations or objects can be used to extend the knowledge contained in the knowledge base by applying knowledge of one situation to another. In this method, deviations of object characteristics are expressed as equational relations between object models. Again our approach is to transform the reasoning problem into the problem of solving a set of constraint equations.