Qualitative reasoning: Theory and applications

This paper presents a general theory of qualitative reasoning (QR) systems which includes, as special cases, reasoning methods that use representations of qualitative differential equations and qualitative difference equations. Based on set theory, our QR framework describes fundamental concepts such as qualitative models and solutions, and relates them to the quantitative analogues of its underlying quantitative reference system. Our motivation arises from the types of models found in the social sciences. Thus we emphasize the significance of discrete, dynamic models and optimization models in the management and economics fields, both of which have received less attention in current QR research. We discuss in detail rules constraint reasoning, a QR system based on qualitative difference equations. Finally, we extend on theoretical framework to include an approach to qualitative optimization.