Comparative Analysis

Comparative analysis answers questions about how and why a system will react to perturbations of its parameters. For example, comparative analysis can explain why the period of a spring/block system would increase if the mass of the block were larger. This paper formalizes the problem of comparative analysis and describes a solution technique, differential qualitative analysis; the technique only works if the system can dynamically change perspectives when it compares the values of parameters over intervals. This paper shows how perspectives can be used for comparative analysis, summarizes a soundness proof for the technique, demonstrates incompleteness, describes a working implementation , and presents experimental results. 1 Introduction The problem of symbolic analysis of real-world systems is central to many problems in artificial intelligence. In order to cope with a changing world one must be able to understand its behavior. Recently, considerable emphasis has been put on a specific kind of analysis: qualitative simulation[l,3,10,5,8]. Qualitative simulation seeks to produce a description of the behavior of a system over time, often in the form of a tree of histories of the system's qualitatively interesting changes over time [9]. This paper discusses the problem of comparative analysis , in many ways the complement of qualitative simulation. Whereas qualitative simulation takes a structural description of a system and predicts its behavior, comparative analysis takes as input this behavior and a perturbation and outputs a description of how the behavior would change as a result of the pertubation. For example, given the structural description of a horizontal , frictionless spring/block system (i.e., Hooke's law), a qualitative simulator would say that the block would first move one direction, stop, then reverse, etc. A description of oscillation would be produced. Comparative analysis, on the other hand, should take this description of oscillation and evaluate the effects of perturbations. For example , comparative analysis should deduce that if the mass of the block were increased, the period of oscillation would lengthen and explain why (figure 1). In this paper, I describe differential qualitative analysis, 2 which solves comparative analysis problems in much the same way as 1. Just as qualitative simulation works without explicit equations for the value of each parameter as a function of time, differential analysis does not need a formula for the period of oscillation. Since force is inversely proportional to position , the force on the block will remain the same when the mass …