Integrating Metric And Qualitative Temporal Reasoning

Abstract

Research in Artificial Intelligence on constraint-based representations for temporal reasoning has largely concentrated on two kinds of formalisms: systems of simple linear inequalities to encode metric relations between time points, and systems of binary constraints in Allen’s temporal calculus to encode qualitative relations between time intervals. Each formalism has certain advantages. Linear inequalities can represent dates, durations, and other quantitive information; Allen’s qualitative calculus can express relations between time intervals, such as disjointedness, that are useful for constraint-based approaches to planning. In this paper we demonstrate how metric and Allen-style constraint networks can be integrated in a constraint-based reasoning system. The highlights of the work include a simple but powerful logical language for expressing both quantitative and qualitative information; translation algorithms between the metric and Allen sublanguages that entail minimal loss of information; and a constraint-propagation procedure for problems expressed in a combination of metric and Allen constraints.