Continuous Motion in Discrete Space

Antony Galton

In A. G. Cohn, F. Giunchiglia, and B. Selman (eds.) Principles of Knowledge Representation and Reasoning: Proceedings of the Seventh International Conference (KR2000), pages 26-37. Morgan Kaufmann Publishers, San Francisco, CA, 2000.
ISBN 1-55860-690-4

Abstract

A number of situations arise in the context of knowledge representation where some notion of continuity is desired within a framework that is itself discrete. We survey some varieties of discrete space that have been proposed, and show that they can all be described as instances of a general notion of closure space, of which topological spaces are a specialised sub-class. We extend the usual topological definition of continuity in the obvious way to general closure spaces, and investigate the possible types of continuous motion that arise when both time and space are represented as closure spaces. In so doing we draw some important connections with existing work on spatio-temporal representations.

Full paper (Compressed postscript file, 92K, 12 pages)