temporal Reasoning

Temporal reasoning problems arise in many areas of AI, including planning , reasoning about physical systems, discourse analysis, and analysis of time-dependent data. Work in temporal reasoning can be classiied in three general categories: algebraic systems; temporal logics; and logics of action. Although useful for many practical tasks, there is little evidence that any of these approaches accurately model human cognition about time. Less formal but more psychologically grounded approaches are discussed in some of the work in AI on plan recognition (Schmidt et al. 1978), work in linguistics on SEMANTICS and TENSE (Jackendoo 1983), and the vast psychological literature on MEMORY. Algebraic systems concentrate on the relationships between time points and/or time intervals, which are represented by named variables. A set of either quantitative or qualitative equations constrain the values that could be assigned to the temporal variables. These equations could take the form a constraint satisfaction problem (CSP), a set of linear equations, or even a set of assertions in a restricted subset of rst-order logic. The goal of the reasoning problem may be to determine consistency, to nd a minimal labeling of the CSP, or to nd consistent bindings for all the variables over some set of mathematical objects. In all of the algebraic systems described below, time itself is modeled as a continuous linear structure, although there has also been some investigation of discrete linear-time models (Dechter et al. 1991) and branching-time models (Ladkin et al. 1990). The qualitative temporal algebra, originally devised by Allen (1983) and formalized as an algebra by Ladkin and Maddux (1994), takes time intervals to be primitive. There are 13 primitive possible relationships between a pair of intervals: for example, before (<), meets (m) (the end of the rst corresponds to the beginning of the second), overlaps (o), etc. These primitive relationships can be combined to form 2 13 complex relationships. For example, the constraint I 1 (< m >)I 2 means that I 1 is either before, meets, or is after I 2. Allen showed how a set of such constraints could be represented by a CSP, and how path-consistency could be used as a incomplete algorithm for computing a minimal set of constraints. The general problem of determining consistency is NP-complete (Vilain et al. 1989). Quantitative algebras allow one to reason about durations of intervals and other metric information. The simple temporal constraint problems (STCSP) of Dechter et al. …