applied. At the moment the value of ǫ is set in the validation process, and only communicated informally to planner-engineers, but it might be better to allow a **domain designer**
to define an ǫ **appropriate for use in the particular domain. There remain several issues**
concerning the correct management of the buffers during validation (particularly the usual problem concerning the transitivity of "fuzzy closeness") which are important issues for temporal reasoning as a whole and are not restricted to the planning context. We do not yet have solutions to all of these problems.

## 11. Related Work: Representing And Reasoning About Time

Representation of, and reasoning with, statements about time and the temporal extent of propositions has long been a subject of research in AI including planning research (Allen, 1984; McDermott, 1982; Sandewall, 1994; Kowalski & Sergot, 1986; Laborie & Ghallab, 1995; Muscettola, 1994; Bacchus & Kabanza, 2000). Important issues raised during the extension of pddl **to handle temporal features have, of course, already been examined by**
other researchers, for example in Shanahan's work (1990) on continuous change within the event calculus, in Shoham's work (1985) and Reichgelt's work (1989) on temporal reasoning and work on non-reified temporal systems (Bacchus, Tenenberg, & Koomen, 1991).

Vila (1994) provides an excellent survey of work in temporal reasoning in AI. In this section we briefly review some of the central issues that have been addressed, **and their treatment**
in the literature, and set pddl2.1 **in the context of research in temporal logics.**
Several researchers in temporal logics have considered the problems of reasoning about concurrency, continuous change and temporal extent. These works have focussed on the problem of reasoning about change when the world is described using arbitrary logical formulae, and most have been concerned with making meta-level statements (such as that effect cannot precede cause). The need to handle complex logical formulae makes the frame problem difficult to resolve, and an approach based on circumscription **(McCarthy,**
1980) and default reasoning (Reiter, 1980) is typical. The strips **assumption provides a**
simple solution to the frame problem when states are described using atomic formulae.

The classical planning assumption is that states can be described atomically **but this is** not a general view of the modelling of change. Although simplifying, this assumption is surprisingly expressive. The bench mark domains introduced in the third International Planning Competition suggest that atomic modelling is powerful enough to capture some complex domains which closely approximate real problems. The temporal reasoning issues we confront are not simplified as a consequence of having made a simplifying assumption about how states are updated. We remain concerned with the major issues of temporal reasoning: concurrency, continuous change and temporal extent.

In the development of pddl2.1 **we made a basic decision to consider the end points of**
durative actions as instantaneous state transitions. This allows us to concentrate on the truth of propositions at points instead of over intervals. The decision to consider actions in this way is similar to that made by many temporal reasoning researchers (Shanahan, 1990; McCarthy & Hayes, 1969; McDermott, 1982). In the context of pddl2.1 **the approach has**
the advantage of smoothly integrating with the classical planning view of actions as state transitions. Nevertheless, Allen has shown that a temporal ontology based on intervals can be a basis for planning (Allen, 1984, 1991) and several planning systems have been