Temporalizing Spatial Calculi: On Generalized Neighborhood Graphs

To reason about geographical objects, it is not only necessary to have more or less complete information about where these objects are located in space, but also how they can change their position, shape, and size over time. In this paper we investigate how calculi discussed in the field of qualitative spatial reasoning (QSR) can be temporalized in order to gain reasoning formalisms that can be used to express spatial configurations and their dynamics. In a first step, we briefly discuss temporalized spatial constraint languages. In particular, we investigate how the notion of continuous change can be expressed in such languages and how continuous change is represented in the so-called conceptual neighborhood graph of the spatial calculus at hand. In a second step, we focus on a special reasoning problem, which occurs quite naturally in the context of temporalized spatial calculi: Given an initial spatial scenario of some physical objects, which scenarios are accessible if the set of all possible paths of these objects is constrained by some further conditions? We show that for many spatial calculi this general problem cannot be dealt with by using the information encoded in the classical neighborhood graphs, as usually discussed in the literature. Rather, we introduce a generalized concept of neighborhood graph, which allows for reasoning about objects in such dynamic settings.