This background is given in order to provide the foundations for the numeric and durative extensions made in developing pddl2.1**. The paper then focusses on the specific extensions**
introduced: numeric expressions and durative actions. In Section 3 we **start by explaining**
the syntax of numeric expressions and their use in action descriptions. **We then explain,** in Section 4, how metrics **can be provided as part of the problem description so that the**
quality of a plan involving numeric change can be evaluated in terms appropriate to the problem domain. We present the syntax in which metrics are expressed **and give examples.**
In Section 5 the paper introduces the notion of durative **action as a way of modelling the**
temporal properties of a planning domain. Both discretised and continuous durative actions are considered. The syntax is described and examples of modelling power and limitations are presented in both cases. Having given examples of the syntactic representation of durative actions we present a formal semantics for both discretised and continuous actions and for plans. Sections 6, 7, 8 and 9 provide the details. The semantics gives us a way of tackling the problem of confirming plan validity - something that becomes an important issue in the face of concurrent activity. In Section 10 we describe the process by which plans were validated in the competition and discuss the complexity of the validation question for pddl2.1**. Finally, Section 11 describes some related work in the temporal reasoning** community, in order to put the contributions made by pddl2.1 **into a wider context. A full** bnf description of pddl2.1 **can be found in the appendix.**
pddl2.1 **was developed for use in the third International Planning Competition in which**
competing planners demonstrated that many discretized temporal and metric models can now be efficiently handled by both domain-independent planners and those using handtailored control rules. For ease of reference in the competition we identified **the features of**
pddl2.1 with a series of levels of increasing expressive power. Thus, the strips **fragment of** pddl2.1 **was referred to as level 1, the numeric extensions comprised level 2, the addition**
of discretised durative actions resulted in level 3, continuous durative actions resulted in level 4 and a final level, level 5, comprised all of the extensions of pddl2.1 **and additional**
components to support the modelling of spontaneous events and physical processes. Level 5 is not discussed in this paper but details can be found in earlier work by **Fox and Long (2002).** The competition focussed on the use of levels 1, 2 and 3 and did not use levels 4 or 5 because the planning technology was not at that stage sufficiently advanced to handle the additional complexities. Despite the fact that level 4 was not used in the competition we **devote some** discussion to it in this paper. We feel that level 4 presents some important immediate challenges for the planning community that affect the extent to which planning can be applied to real problems.

The purpose of this paper is to provide an overview of the new features introduced in pddl2.1, discuss the rationale for our language choices and explain some of the issues that have arisen in trying to extend pddl. Although we have provided the bnf for pddl2.1 **as an appendix, this paper is not intended to be either a language manual or a tutorial on the use of the language. For examples of the use of the language**
and other relevant materials, readers should consult archived resources **currently held at** http://www.dur.ac.uk/d.p.long/competition.html.