Qualitative modeling

Qualitative modeling concerns the representations and reasoning that people use to understand continuous aspects of the world. Qualitative models formalize everyday notions of causality and provide accounts of how to ground symbolic, relational representations in perceptual processes. This article surveys the basic ideas of qualitative modeling and their applications from a cognitive science perspective. It describes the basic principles of qualitative modeling, and a variety of qualitative representations that have been developed for quantities and for relationships between them, providing a kind of qualitative mathematics. Three ontological frameworks for organizing modeling knowledge (processes, components, and field) are summarized, along with research on automatically assembling models for particular tasks from such knowledge. Qualitative simulation and how it carves up time into meaningful units is discussed. We discuss several accounts of causal reasoning about dynamical systems, based on different choices of qualitative mathematics and ontology. Qualitative spatial reasoning is explored, both in terms of relational systems and visual reasoning. Applications of qualitative models of particular interest to cognitive scientists are described, including how they have been used to capture the expertise of scientists and engineers and how they have been used in education. Open questions and frontiers are also discussed, focusing on relationships between ideas developed in the qualitative modeling community and other areas of cognitive science. (C) 2010 John Wiley & Sons, Ltd. WIREs Cogn Sci 2011 2 374-391 DOI: 10.1002/wcs.115