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 straight-forward. We can view an ordinary differential equation solver as a theorem-prover for theorems of a special form: DiffEqs ` ODE State(t 0 ) ! Beh: (1) A qualitative simulation algorithm can also be viewed as a special-purpose theorem-prover: 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...

Diagnostic monitoring systems track disease hypotheses over time, symbolically interpreting the time-varying patient data produced by medical instrumentation. The need to track multiple interacting diseases recommends a hypothesize, test and refine reasoning architecture which incorporates a robust knowledge representation. Rule-based systems are often inadequate for this task, and deep or model based representations capable of first principles reasoning are currently favoured. However the model based approach may be too low level for many monitoring tasks. While disease interactions may present novel patterns to a monitor, usually the diseases themselves will be familiar. It is proposed that disease histories generated from pathophysiological models are at an appropriate level of abstraction for many monitoring tasks. Histories lie between disease models and rules in depth. Using the QSIM representation, results are presented for modelgenerated histories that define some limits of the...

This article describes a method for monitoring and diagnosis of process systems based on three foundational technologies: semi-quantitative simulation, measurement interpretation (tracking), and model-based diagnosis. Compared to existing methods based on fixed-threshold alarms, fault dictionaries, decision trees, and expert systems, several advantages accrue: ffl the physical system is represented in a semi-quantitative model which, unlike a pure numeric model, predicts all possible behaviors that are consistent with the incomplete/imprecise knowledge of the system's devices and processes, ensuring, for example, that a hazardous-but-infrequent behavior will not be overlooked; ffl imprecise knowledge of parameter values and functional relationships (both linear and non-linear) can be expressed in the semi-quantitative model and used during simulation, producing a valid range for each variable; ffl incremental simulation of the model in step with incoming sensor readings, with subseq...

ion for Tractable Simulation Daniel J. Clancy and Benjamin Kuipers Department of Computer Sciences University of Texas at Austin Austin, Texas 78712 clancy@cs.utexas.edu and kuipers@cs.utexas.edu Abstract Most qualitative simulation techniques perform simulation at a single level of detail highlighting a fixed set of distinctions. This can lead to intractable branching within the behavioral description. The complexity of the simulation can be reduced by eliminating uninteresting distinctions. Behavior abstraction provides a hierarchy of behavioral descriptions allowing the modeler to select the appropriate level of description highlighting the relevant distinctions. Two abstraction techniques are presented. Behavior aggregation eliminates occurrence branching by providing a hybrid between a behavior tree representation and a history based description. Chatter box abstraction uses attainable envisionment to eliminate intractable branching due to chatter within a behavior tree simulat...

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 en-able computers to analyze the qualitative behaviors of physical systems which include both me-chanical 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. iii To My Parents iv I would like to thank: ACKNOWLEDGMENTS • Professor Kenneth Forbus, my advisor, for initiating and directing this research, for stim-ulating me to think creatively and to stand on my own legs, and for giving me a great example of researcher.

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.

structural description : : : : : : : : : : : : : : : : : : : : 31 4.7 FR templates : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 31 4.8 Component class hierarchy : : : : : : : : : : : : : : : : : : : : : : 32 4.9 Organizing SFFs : : : : : : : : : : : : : : : : : : : : : : : : : : : : 33 4.10 Additional component features : : : : : : : : : : : : : : : : : : : : 33 4.11 The Task Definition : : : : : : : : : : : : : : : : : : : : : : : : : : 34 V The Algorithm : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 35 5.1 Simplify the structural description : : : : : : : : : : : : : : : : : : 35 5.2 Analyze the structural description : : : : : : : : : : : : : : : : : : 36 5.2.1 Special-method : : : : : : : : : : : : : : : : : : : : : : : : : 37 5.2.2 Fetch-match-sff-method : : : : : : : : : : : : : : : : : : : : 39 5.2.3 Consolidate-analyze-method : : : : : : : : : : : : : : : : : : 44 5.2.4 Partition-method : : : : : : : : : : : : : : : : : : : : : : : : 45 5.2.5 Co...

Qualitative modeling and simulation make it feasible to predict the possible behaviors of a mechanism consistent with an incomplete state of knowledge. Though qualitative simulation predicts all possible behaviors of a system, it can also produce spurious behaviors, i.e., behaviors that correspond to no solution of any ordinary differential equation consistent with the qualitative model. A method for reasoning about energy is presented that eliminates an important source of spurious behaviors. This method is applied to an industrially significant mechanism--a nonlinear, proportional-integral controllermand show that qualitative simulation capSures the main qualitative properties of such a system, such as stability and zero-offset control. It is believed that this is a significant step toward the application of qualitative simulation to model-based monitoring, diagnosis, and design of realistic mechanisms.