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21
Causal Ordering in a Mixed Structure
 In Proceedings of AAAI '88
, 1988
"... This paper describes a computational approach, based on the theory ofcausal ordering, for inferring causality from an acausal, formal description of a phenomena. Causal ordering is an asymmetric relation among the variables in a selfcontained equilibrium and dynamic structure, which seems to reflec ..."
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Cited by 28 (1 self)
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This paper describes a computational approach, based on the theory ofcausal ordering, for inferring causality from an acausal, formal description of a phenomena. Causal ordering is an asymmetric relation among the variables in a selfcontained equilibrium and dynamic structure, which seems to reflect people's intuitive notion of causal dependency relations among variables in a system. This paper extends the theory to cover models consisting of mixture ofdynamic and equilibrium equations. When people's intuitive causal understanding ofasituation isbased on a mixed description, the causal ordering produced by the extension reflects this intuititve understanding better than that ofan equilibrium description. The paper also discusses the view ofa mixed model asan approximation to acompletely dynamic model.
The Composition and Validation of Heterogeneous Control Laws
, 1993
"... We present a method for creating and validating a nonlinear controller by the composition of heterogeneous local control laws appropriate to different operating regions. Like fuzzy logic control, these methods apply even in the presence of incomplete knowledge of the structure of the system, the bou ..."
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Cited by 19 (9 self)
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We present a method for creating and validating a nonlinear controller by the composition of heterogeneous local control laws appropriate to different operating regions. Like fuzzy logic control, these methods apply even in the presence of incomplete knowledge of the structure of the system, the boundaries of the operating regions, or even the control action to take. Unlike fuzzy logic control, these methods can be analyzed by a combination of classical and qualitative methods. Each operating region of the system has a classical control law, which provides highresolution control and can be analyzed by classical methods. Operating regions are defined by fuzzy set membership functions. The global control law is the weighted average of the local control laws, where the weights are provided by the operating region membership functions. A heterogeneous control law can be analyzed, even in the presence of incomplete knowledge, by representing it as a qualitative differential equation and usi...
Qualitative Simulation: Then and Now
, 1993
"... ion, Soundness, and Incompleteness Once the abstraction relations from ODEs to QDEs, and from continuously differentiable functions to qualitative behaviors, are carefully defined 1 , the mathematical results are relatively straightforward. We can view an ordinary differential equation solver as ..."
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Cited by 17 (1 self)
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ion, Soundness, and Incompleteness Once the abstraction relations from ODEs to QDEs, and from continuously differentiable functions to qualitative behaviors, are carefully defined 1 , the mathematical results are relatively straightforward. We can view an ordinary differential equation solver as a theoremprover for theorems of a special form: DiffEqs ` ODE State(t 0 ) ! Beh: (1) A qualitative simulation algorithm can also be viewed as a specialpurpose theoremprover: QSIM ` QDE QState(t 0 ) ! or(QBeh 1 ; : : : QBeh n ): (2) The soundness theorem says that when QSIM proves a theorem of form (2), it is true: that is, for any ODE described by the QDE, and State(t 0 ) described by QState(t 0 ), the solution Beh to the ODE is described by one of the qualitative behaviors, QBeh 1 ; : : : QBeh n . The constraint filtering algorithm makes the proof very simple: all possible real transitions from one qualitative state to the next are proposed, and only impossible ones are filtered out...
Building Qualitative Models of Thermodynamic Processes
"... This paper describes a qualitative domain theory for core phenomena in engineering thermodynamics, expressed in Qualitative Process theory. It represents many of the best features of domain models developed by our group over the past five years. It focuses on supporting systemlevel qualitative anal ..."
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Cited by 14 (1 self)
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This paper describes a qualitative domain theory for core phenomena in engineering thermodynamics, expressed in Qualitative Process theory. It represents many of the best features of domain models developed by our group over the past five years. It focuses on supporting systemlevel qualitative analyses of typical fluid and thermal systems, such as refrigerators and power plants. We use explicit modeling assumptions [3] to control the level of detail used in building models of specific scenarios. We begin by outlining the primitives of the specific QP modeling language. The bulk of the paper describes the domain model itself, highlighting our design choices, simplifications, and use of modeling assumptions. Next we demonstrate how this domain model can be used to build models of a variety of specific scenarios, including simplified versions of a refrigerator, a steam plant, and a thermal control system. Finally, we describe some planned extensions to the model. Contents 1 Introducti...
Qualitative reasoning about fluids and mechanics
 UNIVERSITY
, 1993
"... Understanding people's commonsense knowledge about physical world is a fundamental problem in building intelligent systems. If this knowledge can be represented and used by computers, they can duplicate people's ability to understand and interact with the world. Qualitative physics is the attempt t ..."
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Cited by 9 (0 self)
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Understanding people's commonsense knowledge about physical world is a fundamental problem in building intelligent systems. If this knowledge can be represented and used by computers, they can duplicate people's ability to understand and interact with the world. Qualitative physics is the attempt to capture and formalize this knowledge. An important aspect of qualitative reasoning is the ability to derive the possible behaviors of a given physical system from the structure of the system, using minimal initial information. This thesis investigates qualitative domain theories and reasoning techniques which will enable computers to analyze the qualitative behaviors of physical systems which include both mechanical mechanisms and fluids, such as internal combustion engines and hydraulic lift pumps. We have developed a domain theory which integrates richer models of mechanics, fluids, and geometry than previous research in qualitative physics. These theories and inference techniques are embodied in QSA, a program that produces possible behaviors of physical systems.
Order of Magnitude Reasoning in Qualitative Differential Equations
, 1987
"... We present a theory that combines order of magnitude reasoning with envisionment of qualitative differential equations. Such a theory can be used to reason qualitatively about dynamical systems containing parameters of widely varying magnitudes. We present an a mathematical analysis of envisionment ..."
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Cited by 8 (2 self)
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We present a theory that combines order of magnitude reasoning with envisionment of qualitative differential equations. Such a theory can be used to reason qualitatively about dynamical systems containing parameters of widely varying magnitudes. We present an a mathematical analysis of envisionment over orders of magnitude, including a complete categorization of adjacent pairs of qualitative states. We show how this theory can be applied to simple problems, we give an algorithm for generating a complete envisionment graph, and we discuss the implementation of this algorithm in a running program.
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 ..."
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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...
The Qualitative Representation of Physical Systems
, 1992
"... 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 ..."
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Cited by 6 (1 self)
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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...
Caveats for Causal Reasoning with Equilibrium Models
, 2003
"... Abstract. In this paper 1 we examine the ability to perform causal reasoning with recursive equilibrium models. We identify a critical postulate, which we term the Manipulation Postulate, that is required in order to perform causal inference, and we prove that there exists a general class F of recur ..."
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Cited by 5 (2 self)
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Abstract. In this paper 1 we examine the ability to perform causal reasoning with recursive equilibrium models. We identify a critical postulate, which we term the Manipulation Postulate, that is required in order to perform causal inference, and we prove that there exists a general class F of recursive equilibrium models that violate the Manipulation Postulate. We relate this class to the existing phenomenon of reversibility and show that all models in F display reversible behavior, thereby providing an explanation for reversibility and suggesting that it is a special case of a more general and perhaps widespread problem. We also show that all models in F possess a set of variables V ′ whose manipulation will cause an instability such that no equilibrium model will exist for the system. We define the Structural Stability Principle which provides a graphical criterion for stability in causal models. Our theorems suggest that drastically incorrect inferences may be obtained when applying the Manipulation Postulate to equilibrium models, a result which has implications for current work on causal modeling, especially causal discovery from data. 1