@MISC{Kuipers93qualitativesimulation:, author = {Benjamin Kuipers}, title = {Qualitative Simulation: Then and Now}, year = {1993} }

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Abstract

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...