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...

The representation of physical systems using qualitative formalisms are examined in this review, with an emphasis on recent developments in the area. The push to develop reasoning systems incorporating deep knowledge originally focused on naive physical representations, but have now shifted to more formal ones based on qualitative mathematics. The qualitative differential constraint formalism used in systems like QSIM is examined, and current efforts to link this to competing representations like Qualitative Process Theory are noted. Inference and representation are intertwined, and the decision to represent notions like causality explicitly, or infer it from other properties has shifted as the field has developed. The evolution of causal and functional representations are thus examined. Finally, a growing body of work that allows reasoning systems to utilise multiple representations of a system is identified. Dimensions along which multiple model hierarchies could be constructed are e...

We have developed and implemented in the QPORTRAIT progralll a qualitative simulation based method to construct phase portraits for significant class of systems of two coupled first order autonomous differential equations, even in the presence of incomplete, qualitative knowledge.

In diagnosis, when a hypothesis proposes a variable's value, several different lines of evidence may be considered; the different evidence must be arbitrated. The result of this arbitration consists of a single best estimate of the variable value and of a measure of that estimate's plausibility. The plausibility measure reflects the degree of agreement among the lines of evidence. This report describes heatx, a program for model-based diagnosis of nonlinear mechanisms with continuous variables. Previous work in model-based diagnosis has avoided arbitrating numeric evidence, often by representing continuous variables as discrete symbols (e.g., high, cold). Such restricted representation have had difficulty in diagnosing mechanisms with feedback or reconvergent fanout. Heatx represents numerical data explicitly in the hypotheses and in the inferencing procedures; it is thereby able to arbitrate evidence numerically. Heatx uses both nonlinear numerical simulations and approximate linear ...