Qualitative Reasoning at Multiple Resolutions

In this paper we describe an approach to unify the various quantity spaces that have been proposed in qualitative reasoning with numbers. We work in the domain of physical devices, such as electrical circuits using lumped parameter models. We show how changing the quantity space can be achieved in the course of analysis and how this is similar to dynamically changing the resolution in analysis. We demonstrate the utility of this approach with two examples in the domain of circuit analysis.