Constructing conceptual neighborhood for reasoning about motion

The notion of conceptual neighborhood has been used in the areas of qualitative temporal reasoning and qualitative spatial reasoning. In this paper, first, we discuss the adjacent relations between generators in Voronoi diagrams and their changes, and then present a method of representing relative positions with adjacent relations qualitatively. Next, we define the conceptual neighborhood for reasoning about motion based on relative positions, and construct it with a line sweep algorithm. The algorithm gradually moves a horizontal sweep-line, finds to record the adjacent relative positions, and then constructs the conceptual neighborhood. Finally, we give the examples for illustrating the use and the potential of the conceptual neighborhood for representing and reasoning about motion.