A Stochastic Approach to Qualitative Simulation using Markov Processes

Abstract

Interval based value representation methods constitute a major technical foundation of qualitative reasoning, but they necessarily generate ambiguous situations and spurios solutions. Ambiguity may be reduced by introducing more infonnation and knowlegde: either in the fonn of supplementary quantitative infonnation or by applying general rules, taken from systems theory, on the behavior of dynamic systems. In the second approach concepts as state space diagrams or qualitative cells are exploited. The set of solutions is reduced and general classes of behavior are described. But the concrete behavior still depends on known infonnation, and still too many things cannot be excluded. The application of stochastic concepts could exploit a further type of knowledge: some vague infonnation in the fonn of priorities or the strength of some influence. The concept of Markov processes provides a similar description as the state space approach, but indicates priorities of different behaviors in solution space as well. This paper demonstrates bow existing approaches in qualitative simulation can be transfonned appropriately.