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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 ..."
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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...
Comparative Analysis and Qualitative Integral Representations * 1 Introductio n
"... The goal of comparative analysis [Forbus, 1984; Weld, 1987, 1988] is t o determine how a perturbation to one aspect of a system affects the behavio r of other aspects of the system, particularly when the system is incompletel y known and described by a qualitative differential equation (QDE) model. ..."
Abstract
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The goal of comparative analysis [Forbus, 1984; Weld, 1987, 1988] is t o determine how a perturbation to one aspect of a system affects the behavio r of other aspects of the system, particularly when the system is incompletel y known and described by a qualitative differential equation (QDE) model. In terms of the QSIM representation for qualitative structure and behavior [Iiuipers, 1986], a predicted behavior is a sequence of qualitativel y distinct sets of values for the variables in the QDE. The behavior implies a set of relationships among the landmark values of the variables. The goal of comparative analysis is to analyze these relations to determine the directio n of effect of a perturbation to the value associated with a landmark p on th e value associated with the landmark q: 1.1 Our Approach C(p,q) = sign (p). Our approach here is &quot;Qualitative Physics &quot; (or &quot;Qualitative Mathematics &quot;) rather than &quot;Naive Physics. &quot; A qualitative differential equation expresses a