Qualitative Reasoning and Spatio-Temporal Continuity
Ernest Davis · Advances in geospatial technologies book series · 2012
This chapter discusses the use of transition graphs for reasoning about continuous spatial change over time. The chapter first presents a general definition of a transition graph for a partition of a topological space. Then it defines the path-connected and the homogeneous refinements of such a partition. The qualitative behavior of paths through the space corresponds to the structure of paths through the associated transition graphs, and of associated interval label sequences, and the authors prove a number of metalogical theorems that characterize these correspondences in terms of the expressivity of associated first-order languages. They then turn to specific real-world problems and show how this theory can be applied to domains such as rigid objects, strings, and liquids.