Introduction

Time is an important aspect of any intelligent knowledge representation. This has led to a rising need for reasoning about time in various applications of artificial intelligence such as process control or decision making. Different schemes for temporal information representation have been proposed so far. A natural way to refer to a temporal event consists in making references to a clock providing a quantitative or numerical representation of time, as well as several concepts such as duration and calendar. However, a clock reference is not always available or relevant. In such cases, a qualitative (symbolic) representation of time can be used to describe the situations in question.

In spite of the different representations of temporal information proposed, most are not completely satisfactory. Looking at existing work, Allen's representation [Allen 83] is a very powerful representation in describing the relativity between intervals. Vilain and kautz proposed a subinterval algebra [Vilain & Kautz 86], Ghallab and Mounir [Ghallab & Mounir 89] based on the notion of subinterval algebara, have also proposed a model with symbolic relations but within the framework of subinterval algebra. However, these models don't address numerical aspect of time. On the other hand, the time map of Dean and McDermott [Dean & McDermott 87], Rit geometrical model [Rit 86] and the temporal constraint networks [Dechter, Meiri & Pearl 91] are designed for handling metric information and can't handle in a good way symbolic ones.