A revised theory of action and time based on intervals and points

This paper examines J. F. Allen's interval-based theory of action and time and correspondin revisions suggested by A. P. Galton which have been proposed to accommodate the representation of facts concerning continuous change. Agreeing with Galton's argument that Allen's system needs revisions by means of diversifying the temporal ontology to include points, we show that Galton's determination to define time points in terms of the «meeting places» of time intervals does not, as it stands, axiomatize points on the same footing as intervals, and hence that some problems still remain in these revisions. It is shown that it is necessary to revise the fundamental axioms about time itself so as to extend the abstract concept of time elements to include both intervals and points, and to extend the temporal relations between intervals to address points'as well. We provide here a further revised theory which overcomes the problems in Allen's and Galton's systems. The revised system utilizes a new axiomatization of time, given preriously by the authors, as the underlying temporal basis. A diversification of the range of properties/ occurrences over intervals and points is also proposed which may replace both Allen's and Galton's results