Qualitative Reasoning at Multiple Resolutions

1 . Introduction IBM T.J. TVatson Research 1n 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 . One of the chief aims of Qualitative Reasoning is to provide a broad picture of the functioning of the world by taking a step back from the details . In this paper we show that in reasoning with numbers the aim is to break the real number line into broad, qualitatively distinct classes and describe the working of a device in terms of these classes . [Johag5a] defines the qualitative values a variable can have Ao . . . A, as representing disjoint abutting intervals that cover the entire number line . I define the set of values (A, . . . A,} as the Q-space.' The aim of Qualitative Reasoning is to reduce the cardinality of the Q-space while still retaining the information available from doing the analysis using quantitative values . This has two benefits . omplete quantitative information is not always available about the variables being analyzed . For example in design, one may not know the exact values of all parameters in the design . Yet one has to make decisions using this partial information . In this case the partial information can be used by representing the variables in a qualitative form . By using the smallest possible Q-space in which to perform the analysis we are able to deal better with incomplete information . " By using a qualitative description of the variables we can form a description of the working of a device that has a smaller number of states . Thus one can get a Qualitative Reasoning at Multiple Resolutions Seshashayee S. Murthy