Qualitative simulation is a useful method for predicting the possible qualitatively distinct behaviors of an incompletely known mechanism described by a system of qualitative differential equations (QDEs). Under some circumstances, sparse information about the derivatives of variables can lead to intractable branching (or "chatter") representing uninteresting or even spurious distinctions among qualitative behaviors. The problem of chatter stands in the way of real applications such as qualitative simulation of models in the design or diagnosis of engineered systems. One solution to this problem is to exploit information about higherorder derivatives of the variables. We demonstrate automatic methods for identification of chattering variables, algebraic derivation of expressions for second-order derivatives, and evaluation and application of the sign of second- and third-order derivatives of variables, resulting in tractable simulation of important qualitative models. Caution is requir...

v Table of Contents vii List of Tables xii List of Figures xiii 1. Introduction and Overview 1 1.1 Motivating Overview : : : : : : : : : : : : : : : : : : : : : : : : 1 1.2 Specific Benefits of Qualitative-Quantitative Simulation : : : : : 4 1.3 Previous work : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 1.3.1 Qualitative-quantitative work in VLSI : : : : : : : : : : 7 1.3.2 Qualitative-quantitative spatial reasoning : : : : : : : : : 8 1.3.3 Qualitative-Quantitative work in temporal ordering : : : 8 1.3.4 Interval and inequality reasoning : : : : : : : : : : : : : 9 1.3.5 Qualitative-quantitative simulation work : : : : : : : : : 10 1.4 Outline of Remaining Chapters : : : : : : : : : : : : : : : : : : 14 2. Q2: Adding Interval Information to Qualitative Simulation 15 2.1 Overview : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 15 2.2 Propagation of Incomplete Quantitative Information : : : : : : : 16 2.2.1 Types of quantitative propagation constrain...

Comparative analysis is applied to a qualitative behavior of an incompletely known mechanism, to determine the effect of a given perturbation on the behavior as a whole. This class of inference is useful in diagnosis, design, planning, and generally for understanding the relations among a set of alternate qualitative behaviors. Comparative analysis depends on information which is implicit, and relatively difficult to extract, from qualitative differential equations. By introducing the definite integral as a descriptive term linking qualitative variables and their landmarks, we show that the qualitative integral representation (QIR) makes the required information easily accessible. Inspired by observations of expert physicists, we have adopted an approach to inference that allows global algebraic manipulation of the QIR. Within this approach, comparative analysis can be decomposed into a search and algebraic manipulation problems. Several detailed examples are presented to clarify our m...