Qualitative simulation of behavior from structure is a valuable method for reasoning about partially known physical systems. Unfortunately, in many realistic situations, a qualitative description of structure is consistent with an intractibly large number of behavioral predictions. We present two complementary methods, representing different trade-offs between generality and power, for taming an important case of intractible branching. The first method applies to the most general case of the problem. It changes the level of the behavioral description to aggregate an exponentially exploding tree of behaviors into a few distinct possibilities The second method draws on additional mathematical knowledge, and assumptions about the smoothness of partially known functional relationships, to derive a correspondingly stronger result. Higher-order derivative constraints are automatically derived by manipulating the structural constraint model algebraically, and applied to eliminate impossible branches These methods have been implemented as extensions to QSIM and tested on a substantial number of examples They move us significantly closer to the goal of reasoning qualitatively about complex physical systems

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...

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