Towards a practical theory of reformulation for reasoning about physical systems

Reformulation is ubiquitous in problem solving and is especially common in modeling physical systems. In this paper we examine reformulation techniques in the context of reasoning about physical systems. This paper does not present a general theory of reformulation, but it studies a number of known reformulation techniques to achieve a broad understanding of the space of available reformulations. In doing so, we present a practical framework for specifying, classifying, and evaluating various reformulation techniques applicable to this class of problems. 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.