On using belief maintenance systems to assist mathematical modeling

Mathematical modeling systems are an important component in the toolkit of decision support system (DSS) generators. These systems provide a language in which mathematical models can be stated, and enable access to algorithms which may be used to manipulate (e.g., optimize, what-if analysis) the model. While these features are useful, we believe that these systems should also support other important aspects of the DSS model development process. We focus on two such aspects in this paper. These include support for the iterative refinement of models, and for the management of multiple model versions which are created when alternative problem scenarios are investigated. Building on empirical studies of the model development process, we argue that support for these aspects of model development requires knowledge of the rationale for modeling decisions, the dependencies that relate them, and of methods that maintain their consistency. We then demonstrate how belief maintenance concepts developed in the artificial intelligence literature can be used to implement our proposals. While the issues we discuss are relevant to all kinds of mathematical modeling, we examine them in the context of mathematical programming model development and present an implemented system called MODFORM