WHITHER QUALITATIVE REASONING?: A RESPONSE TO SACKS AND DOYLE

Ideally, all reasoning would be qualitative. That is, reasoners would refer to exactly those qualities that concern them, making all relevant distinctions and ignoring the rest. Of course, in any knowledge representation effort we strive to design languages expressing the useful distinctions. But when the subject of reasoning involves quantities, there is a great temptation to apply more precision than is needed or wanted for any given task. In particular, numeric precision typically renders the reasoning problem vivid, and thus amenable to a large body of analytic techniques. Indeed, most automated analysis methods developed by engineers require full numeric precision in the specification of mathematical models. A1 researchers in qualitative reasoning are right to resist the temptation of precision. While numeric models may facilitate efficient analysis and produce stronger conclusions, unmotivated distinctions impose an excess burden of specification and degrade the generality of results. Designers of systems that reason about quantities must face this central trade-off and may resolve it in different ways, depending on their objectives. Mathematicians, who are inclined to place a great premium on generality, have-as Sacks and Doyle point out-devoted significant effort to the exploration of qualitative properties of relations among quantities. Engineers, who tend to require strong results and straightforward algorithmic solutions, have typically taken the numeric route. But economy of specification and generality of results are nonetheless significant objectives in engineering problem solving, and to whatever extent we can further these goals without excessively compromising computational tractability and power, we should do so. Therein lies the potential contribution of qualitative reasoning. But we should not deny that there is a compromise involved, at least regarding strength of conclusions.’ There is no avoiding the fact that weaker constraints on a mathematical model lead to weaker entailments. In fact, the limitations are often quite clear. For instance, the incompleteness in qualitative analyses of what Sacks and Doyle call “type 2 SPQR equations” was first noted by Kuipers (1985). Possessing a clear characterization of the limits of a given technique helps us understand where it fits in a comprehensive problemsolving architecture. For example, in decision-theoretic reasoning, qualitative ambiguity is the hallmark of a “trade-off situation” (Wellman 19901, and signals the need for complementary analysis techniques. An important virtue of qualitative representations is that their boundaries often correspond to intuitive problem classes, and thus their scope may often be succinctly characterized. Too often, however, the tendency in research is to deemphasize limitations in favor of more positive capabilities of a proposed new idea. Sacks and Doyle have thus provided