Artificial Intelligence: A New Approach to Modeling and Control

Abstract Recent work in artificial intelligence has produced a collection of methods for qualitative reasoning that may fill an important gap in the modeling and control toolkit. Qualitative reasoning methods provide greater expressive power for states of incomplete knowledge than differential or difference equations, and thus make it possible to build models without incorporating assumptions of linearity or specific values for incompletely known constants. On the other hand, there is enough information in a qualitative description to support qualitative simulation, predicting the possible behaviors of an incompletely described system. We survey results from several approaches to qualitative reasoning, and provide a detailed example of the application of these methods to a simple problem. The mathematical validity of this approach is also assessed. Results with small examples have been encouraging, and we are now taking the steps toward additional mathematical power, hierarchical decomposition, and incremental quantitative constraints, that we believe will make qualitative reasoning into a valuable formal reasoning method.

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