Research on Qualitative Representation and Its Reasoning for Spatial Data

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In this research, we have proposed a new model for qualitative treatment of the spatial data such as figures and images which have been treated quantitatively. The goal of the research is the development of software with high performance and reliability based on the model.In the previous research, we have proposed PLCA, a framework for qualitative reasoning which provides a symbolic representation for spatial data based on simple objects of points, lines, circuits and areas, with several constraints.The research results are as follows :1.We have defined the operations of division and addition of the objects on PLCA. We have related these operations on a PLCAexpression to those on a figure, and proved the correctness of these operations. As the result, computational complexity can be reduced since information on size or shape is not required for the data.2.We have found the conditions for two-dimensional realizability for a PLCA expression and proved it Moreover, we have given an algorithm for drawing a figure on a two-dimensional plane from the PLCA expression that satisfies the condition, and proved its correctness. As the result, the relationship between a PLCAexpression and a two-dimensional plane has been clarified.3.We have developed the reasoning system on the extended PLCA by adding attributes of size, shape or semantic information such as the properties which hold on the regions. As the result, the application areas of PLCA is extended to such as GIS and design support.4.We have investigated the relationship between PLCA and the other theories : mereology(whole-and-part-relationship), topology, graph theory and other qualitative spatial frameworks. The correspondence with graph theory has made theoretical analysis of PLCA possible.5.We have implemented PLCA using Java for the core part and Prolog for semantic reasoning part. This system can be regarded as the one that connects qualitative representation and quantitative representation.