the management of processes by making it necessary to solve differential **equations. The**
complication has not deterred other authors from taking this approach: McDermott (2003) takes this approach in his process planner.

The introduction of continuous processes into the planning problem represents a considerable complication, even over a model that includes temporal features and supports concurrency. It is an area of active research and the community has not yet agreed on matters of representation, let alone semantics. There remain many open problems for the planning community to address, both in the development of languages and planning algorithms and also in in the development of plan verification tools that can embody **a widely**
accepted semantics.

## 12. Conclusions

Recent developments in AI planning research have been leading the community closer to the application of planning technology to realistic problems. This has necessitated the development of a representation language capable of modelling domains with temporal and metric features. The approach we have taken towards the development of such **a language**
is to extend McDermott's pddl **domain representation standard to support temporal and**
metric models.

The development of the pddl **sequence towards greater expressive power is important**
to the planning community because pddl **has provided a common foundation for a great**
deal of recent research effort. The problems involved in modelling the **behaviour of domains** with both discrete and continuous behaviours have been well explored **in the temporal logic**
and model checking communities but there have been no widely adopted models within the planning community. Our work on pddl2.1 **provides a way of making the relevant** developments in these communities accessible to planning. Furthermore, pddl2.1 **begins**
to bridge the gap between basic research and applications-oriented planning by providing the expressive power necessary to capture real problems.

pddl2.1 **has the expressive power to represent a class of deterministic mixed discretecontinuous domains as planning domains. The language introduces a form of durative action**
based on three connected parts: the initiation of an interval in which numeric **change**
might occur and its explicit termination by means of an action that produces the state corresponding to the end of the durative interval. This form of action allows the modelling of both discrete and continuous behaviours - discretized change can be represented by means of step functions, whilst continuous change can be modelled using the \#t **variable.** The language provides solutions to the critical issues of concurrency, continuous change and temporal extent. The semantics of the language is derived from the familiar state transition semantics of strips**, extended to interpret invariants holding over intervals in**
which continuous functions might also be active. Our semantics allows us to **interpret more**
plans than we can efficiently validate. We describe the criteria that a plan must satisfy in order to be practically verifiable.

This paper has focussed primarily on a discussion of the numeric and discretised temporal features of pddl2.1**. However, the modelling capability of discretized durative actions**
is in some respects limited and it is important for the planning community **to address the** challenges presented by continuous change. Indeed, even using the continuous actions of