Abstract

We present a theory that combines order of magnitude reasoning with envisionment of qualitative differential equations. Such a theory can be used to reason qualitatively about dynamical systems containing parameters of widely varying magnitudes. We present an a mathematical analysis of envisionment over orders of magnitude, including a complete categorization of adjacent pairs of qualitative states. We show how this theory can be applied to simple problems, we give an algorithm for generating a complete envisionment graph, and we discuss the implementation of this algorithm in a running program.

Citations