Figures for Thought: Temporal Reasoning with Pictures

Gérard Ligozat

This paper describes the application of pictorial representations for reasoning about Allen’s algebra. We examine four questions: Characterizing useful subclasses of relations, such as convex, pointizable, and ORD-Horn relations. Elucidating the basic properties of ORD-Horn relations which make them tractable. Understanding the nature of relations which are not ORD-IIorn. Proving the fact that any relation which is not ORD-Horn generates one of four specific relations (corner relations). We show how using pictorial representations for Allen’s relations solves -- or helps in solving -- those questions. Similar pictorial techniques can be of value in related fields. The study of concrete cases where diagrams are effectively used in reasoning should result in a deeper understanding of the general domain in Artificial Intelligence concerned with reasoning using pictures and diagrams.

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