Construction of a Planar PLCA Expression: A Qualitative Treatment of Spatial Data

Qualitative spatial reasoning (QSR) is a method of representing spatial data by extracting necessary information depending on a user’s purpose, and allowing reasoning on this representation. Although many studies have examined QSR, little work has been carried out from the viewpoint of computational models, which are necessary for practical use in an implemented system. This paper presents a computational model of a qualitative spatial representation and shows the correspondence of an image and its symbolic expression. Specifically, we take PLCA as a framework of QSR, which represents a figure using the objects used to construct it, i.e., points, lines, circuits, and areas, as well as the relationships among them, without using numerical data. We describe a method of constructing a PLCA expression inductively, and prove that the defined class coincides with a subclass of PLCA that can be realized on a two-dimensional plane. Part of the proof is implemented using the proof assistant Coq.