Studies on Qualitative Analysis of Dynamical Systems and its Application to Engineering Problem Solving

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Qualitative reasoning plays an important role in human problem solving process. Given a complex problem, human experts first try to grasp qualitative nature of the problem by rough analysis. This kind of mental process has received much less attention than quantitative computation.The purpose of this research is to model and implement qualitative reasoning by human experts and to establish a well founded ground for engineering problem solving.The result of this research can be summarized as follows: 1. Studies on qualitative representation and reasoning about commonsense Knowledge about space. We have developed a method of reasoning about three-dimensional spatial configuration using a technique called potential model. We developed a potential minimization algorithm applicable to high dimensional parameter space concerning space such as position, size, shape, orientation, or neighborhood. 2. Studies on maintenance and utilization of incomplete information about quantity. We have developed a system which can answer questions by maximally making use of available information. We employed various kind of heuristic knowledge for this system. 3. Automated modeling by heuristic knowledge. We have developed a program which can automatically produce a model appropriate for a given problem by applying various model modification operators to basic model components. We make use of heuristic knowledge concerning causal analysis of underlying differential equations.