Spatio-Temporal Reasoning and Linear Inequalities

Abstract

Time and space are sufficiently similar to warrant in certain cases a common representation in AI problem-solving systems. What is represented is often the constraints that hold between objects, and a concern is the overall consistency of a set of constraints. This paper scrutinizes two current approaches to spatio-temporal reasoning. The suitableness of Allen's temporal algebra for constraint networks is influenced directly by the mathematical properties of the algebra. These properties are extracted by a formulation as a network of set-theoretic relations, such that some previous theorems due to Montanari apply. Some new theorems concerning consistency of these temporal constraint networks are also presented.