Using Incomplete Quantitative Knowledge In Qualitative Reasoning

Abstract

Incomplete knowledge of the structure of mechanisms is an important fact of life in reasoning, commonsense or expert, about the physical world. Qualitative simulation captures an important kind of incomplete, ordinal, knowledge, and predicts the set of qualitatively possible behaviors of a mechanism, given a qualitative description of its structure and initial state. However, one frequently has quantitative knowledge as well as qualitative, though seldom enough to specify a numerical simulation. We present a method for incrementally exploiting incomplete quantitative knowledge, by using it to refine the predictions of a qualitative reasoner. Incomplete quantitative descriptions (currently ranges within which unknown values are assumed to lie) are asserted about some landmark values in the quantity spaces of qualitative parameters. Unknown monotonic function constraints may be bounded by numerically computable envelope functions. Implications are derived by local propagation across the constraints in the model. When this refinement process produces a contradiction, a qualitatively plausible behavior is shown to conflict with the quantitative knowledge. When all predicted behaviors of a given model are contradicted, the model is refuted. If a behavior is not refuted, propagation of quantitative information results in a mixed quantitative/qualitative description of behavior that can be compared with other surviving predictions for differential diagnosis.