FROM QUALITATIVE TO QUANTITATIVE PHYSICS

Sacks and Doyle have done the A1 community a service by spelling out the limitations of the qualitative physics/reasoning/simulation approach (SPQR). SPQR is one of those approaches that initially looked neat, but did not pan out in practice. Sacks and Doyle note that “. . . there are other simple and common systems that SPQR still cannot comprehend after IS years of investigation.” I believe these meager achievements are largely a result of an artificial distinction between qualitative and quantitative reasoning built into the SPQR approach. This distinction inhibits smooth mixing of qualitative to quantitative reasoning as needed. An alternative approach is to regard a qualitative prediction (e.g., pressure P1 will increase) as a weakly informative quantitative prediction, by representing our knowledge of P1 as a flat probability density between the minimum and maximum pressure. Such a representation says in effect that we know nothing about P1 other than that it is positive. Better knowledge about the value of P1 can be expressed as a peaked distribution around some mean value-the better the knowledge, the sharper the peak. Such a probabilistic representation allows reasoning at a level of detail appropriate to the problem at hand, and in effect claims that all system knowledge is quantitative to some degree. As Sacks and Doyle point out, an expert trying to design/diagnose/understand/controVmodeY . . . a complex system uses an intimate mixture of both qualitative and quantitative reasoning. However, instead of further SPQR bashing, I want to expand on the method of combining both quantitative and qualitative reasoning into a coherent whole, as a constructive extension of Sacks and Doyle’s critique. Attempts have been made to graft quantitative knowledge onto basically qualitative systems using ranges and inequalities (e.g., Simmons 1986; Kuipers and Berleant 1988). While this is clearly an improvement over purely qualitative approaches, it has a number of problems. For example, the all-or-nothing nature of a range means that a slight change in the range associated with say a pressure variable can lead to qualitatively different predictions (e.g., that a relief valve will open)-brittle behavior that is purely the result of using ranges and logical inference where it is not appropriate. In a smooth probabilistic representation of the same situation, a11 that changes is the probability that the relief valve will open. A desirable criterion for any system that represents and reasons about complex situations is that the system should be able to smoothly adjust the accuracy of its reasoning to one that is appropriate for answering the current question. Unfortunately, even SPQR augmented with ranges does not meet this criterion, because if the ranges are reduced to points (no uncertainty) the SPQR system is still doing range arithmetic, not numerical simulation. In other words, when uncertainty is added to a standard differential equation system model, SPQR requires an abrupt change in the type of inference performed. Much more serious is that the proposed inference procedures for these quantitative ranges can lead to erroneous conclusions. For any set of mutually constrained variables