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Abstract : |
Qualitative simulation predicts the set of possible behaviors consistent with a qualitative differential equation model of the world. Its value comes from the ability to express natural types of incomplete knowledge of the world, and the ability to derive a provably complete set of possible behaviors in spite of the incompleteness of the model. A qualitative dierential equation model (QDE) is an abstraction of an ordinary dierential equation, consisting of a set of real-valued variables and functional, algebraic and dierential constraints among them. A QDE model is qualitative in two senses. First, the values of variables are described in terms of their ordinal relations with a nite set of symbolic landmark values, rather than in terms of real numbers. Second, functional relations may be described as monotonic functions (increasing or decreasing over particular ranges) rather than by specifying a functional form. These purely qualitative descriptions can be augmented with semi-quantitative knowledge in the form of real bounding intervals around unknown real values and real-valued bounding envelope functions around unknown real-valued functions. Qualitative and semi-quantitative models can be derived by composing model fragments and collecting the associated modeling assumptions. Qualitative simulation starts with a QDE and a qualitative description of an initial state. Given, |
