In Pascal Amsili, Mario Borillo, and Laure Vieu (editors), Time, Space and Movement: Meaning and Knowledge in the Sensible World, Workshop notes of the 5th International Workshop TSM'95, Château de Bonas, 23-27 June 1995. Group "Langue, Raisonnement, Calcul", IRIT/ERSS.
Abstract
The standard mathematical treatment of continuity for real-valued functions presupposes a model in which arbitrarily fine distinctions can be drawn between neighbouring states. In a qualitative model these distinctions are obliterated by treating whole ranges of states as qualitatively indistinguishable. In this paper we show how topological considerations can be used, in the form of a relation called `dominance', to handle continuity in discrete qualitative state-spaces derived from an underlying continuous space. A general theorem concerning the composition of such state-spaces is proved, and its potential usefulness illustrated by application to three different areas of spatio-temporal reasoning.
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