Controlling Qualitative Resolution

Jean-Luc Dormoy

We proposed earlier in [Dormoy and Raiman, 1988] a new way of reasoning about a device, we called "Assembling a Device". Starting from a component description (namely confluences), the qualitative resolution rule provides task-oriented global relations which link the physical quantities involved in a device to some selected reference variables. This rule is complete: given any task to be performed (simulation, postdiction,...), it discovers an assemblage, i.e. a set of relations reducing the task to a straightforward propagation. We might thus expect to apply qualitative reasoning to large-scale systems. Unfortunately, the number of potential applications of the resolution rule is likely to increase exponentially as it is being fired. This behavior has to be related to the NP-completeness of the problem which consists of solving a set of confluences. In this paper, we present a heuristic for controlling the resolution rule, i.e. for choosing between its potential applications, and a collection of simple rules for speeding it up. This heuristic has a combinatorial form, but it is based on a simple commonsense idea. At the same time, it is borne out by mathematical results. Theoretically, a qualitative model can be out of its scope, but we have not yet hit upon a physical system with this kind of pathology.

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