HP Labs Technical Reports
Qualitative Superposition of Unmodelled Systems
Abstract: Qualitative superposition is a form of inference that allows predictions about behavioral interactions to be made even when a system is not characterized. Normally one must assume that one of the behaviors dominates the superposition. Failure to do so results in unconstrained generation of superposition states which may be spurious. Superposition on unmodelled systems is also difficult because one must take a system identity assumption i.e the two behaviors being summed come from the same physical mechanism. To circumvent these difficulties, it is recognized that one can use system behaviors to learn a qualitative model of a system. By applying machine learning techniques a model is induced, and then used to constrain the superposition. A consequence of this approach is that one can also develop tests for system identity. Unlike most machine learning problems in which examples are preclassified, this problem asks the system to decide whilst learning, whether positive examples truly belong to the concept being learned, or whether they have been misclassified by the trainer. Establishing system identity is cast as a problem in machine learning, and a solution proposed based on the introduction of integrity constraints and detection of contradictions between the QDE state spaces induced from two behaviors. The paper concludes with observations about the similarity of this problem to current work in diagnosis..
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