Research on Qualitative Representation and Its Reasoning for Spatial Data

在本研究中，我们提出了一种新的模型，用于对经过量化处理的图形和图像等空间数据进行定性处理。在前人的研究中，我们提出了一种定性推理框架PLCA，它以点、线、线、面等简单对象为基础，在多个约束条件下对空间数据进行符号表示。研究结果如下：1.在PLCA上定义了对象的除法和加法运算。我们将PLCA表达式上的这些运算与图形上的运算联系起来，并证明了这些运算的正确性。给出了PLCA表达式的二维可实现性条件并进行了证明，给出了由满足条件的PLCA表达式在二维平面上绘制图形的算法，并证明了该算法的正确性。3.在扩展后的PLCA上增加了尺寸、形状或语义等属性，如区域上的属性等，从而开发了PLCA的推理系统。研究了PLCA与其他理论的关系，包括整体与部分关系理论、拓扑学、图论等定性空间框架。与图论的契合使得PLCA的理论分析成为可能。5.实现了以Java为核心部分，以Prolog为语义推理部分的PLCA。这一体系可以说是一个连接定性表征和定量表征的体系。

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.