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HigherOrder Derivative Constraints in Qualitative Simulation
 Artificial Intelligence
, 1991
"... 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 in ..."
Abstract

Cited by 7 (3 self)
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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 secondorder derivatives, and evaluation and application of the sign of second and thirdorder derivatives of variables, resulting in tractable simulation of important qualitative models. Caution is requir...
Comparative Analysis and Qualitative Integral Representations
 Workshop on Qualitative Reasoning
, 1991
"... 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 alt ..."
Abstract

Cited by 2 (1 self)
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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...