In Oliviero Stock (editor), Spatial and Temporal Reasoning, Kluwer Academic Publishers, 1997, pages 321-352. ISBN 0-7923-4644-0.
The phenomenon of movement consists of the same object occupying different positions in space at different times. A theory of movement must therefore incorporate a theory of time, a theory of space, a theory of objects, and a theory of position. The central thesis of this paper is that movement events should be specified in terms of their occurrence conditions, necessary and sufficient conditions for the occurrence of a given species of movement at a given time. We consider movement both in dense time and in discrete time, and include both durative and instantaneous movement events in our analyses. Our aim throughout is to approach the task in a systematic way, with a view to generality. Considerations of continuity play an important role in our treatment, and we look in some detail at the implications of continuity for qualitative descriptions of motion. The outcome of this investigation is the introduction of the notion of a dominance space: with this notion, the properties of complex qualitative state-spaces can be derived systematically from those of smaller components, by means of a simple but powerful composition theorem.