Preliminary Thoughts Towards a Practical Theory of Reformulation for Reasoning about Physical Systems

Papers 1

In this paper, we provide a practical framework for characterizing, evaluating and selecting reformulation techniques for reasoning about physical systems, with the long-term goal of automating the selection and application of these techniques. We view reformulation as a mapping from one encoding of a problem to another. A problem solving task is in turn accomplished by the application of a sequence of reformulations to an initial problem encoding to produce a final encoding that addresses the task. Our framework provides the terminology to specify the conditions under which a particular reformulation technique is applicable, the cost associated with performing the reformulation, and the effects of the reformulation with respect to the problem encoding. As such it provides the vocabulary to characterize the selection of a sequence of reformulation techniques as a planning problem. Our framework is sufficiently flexible to accommodate previously proposed properties and metrics for reformulation. We have used the framework to characterize a variety of reformulation techniques, three of which are presented in this paper.