Qualitative reasoning about approximations in quantitative modeling

Quantitative models are frequently used to analyze physical systems. A central problem in using quantitative models to reason about physical systems is that the complexity of the reasoning process increases drastically with the size and complexity of the model. Human modelers solve this complexity problem by introducing simplifying approximations. The resultant changes in the model tractability and behavior influence a modeler's choice of approximations. This paper addresses the question of how the behavior of a quantitative model changes when approximations to the model are introduced. We present results that show that model behavior changes in many modeling contexts can be derived by analyzing the model structure, the approximation, and the query to be answered. Our experience with a prototype implementation suggests that the techniques can be useful in the design of modeling support systems.