Reasoning in Qualitatively Defined Systems using Interval-Based Difference Equations

Quantitative research and statistical techniques have long been regarded as superior ways of analyzing knowledge in social sciences. To deal with incomplete or imprecise knowledge while modeling systems, traditional approaches in social sciences (i.e., management science, operations research) have attempted to measure social facts by making approximations of the problem under analysis. Recent Artificial Intelligence (AI) research on qualitative reasoning which focuses on using qualitative knowledge to reason about the everyday physical world, suggests an opportunity to extend the capability of current logicomathematical instruments used by social scientists. This paper proposes an interval propagation difference equation method, a type of qualitative-quantitative simulation method, to model dynamic systems by abstracting from the underlying true model. The proposed difference equation method can be used to model problems requiring discrete-time analysis, such as applications involving time-lag relationships. Moreover, the method does not require the exact functional form of the problem under analysis to be known with certainty. The incomplete or imprecise knowledge available about the functional form of the true model, and the values of its variables, are represented with bounding functions and interval values respectively.