Controlling Qualitative Resolution

We proposed earlier in [Dormoy & Raiman, 19881 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. In [Dormoy & Raiman, 19881, we proposed a new way of reasoning about a device, 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. All this is developed in detail in the above mentioned paper [Dormoy & Raiman, 19881 (this issue), and we strongly recommend that the reader consult it before reading the following. Solving a set of confluences turns out to be an NP-complete problem [Dormoy, 19871. Hence, the number of potential applications of the resolution rule is likely to increase exponentially as it is being fired. In practical terms, combinatorial explosion happens even when dealing with very simple models. In the second section, we present a heuristic, which we call the “joining rule”, for controlling the resolution rule, i.e. for choosing between its potential applications. It is based on the simple commonsense idea of consolidation [Bylander, 19871. At the same time, it is borne out by mathematical results. In theory, a qualitative model may be out of the scope of this heuristic. We justify why we have not yet hit upon a physical system with this kind of pathology. Though the joining heuristic is self-sufficient, some rules can be added to the basic machinery in order to speed up the assembling step. We present them in the third section and we show how the whole system works through the use of a simple example. In conclusion, we think that the assembling technique, controlled by the joining heuristic, can assemble large artefacts. We are currently working on a model for a large-scale plant.