Bacchus baccComm proposes an alternative to the continuous durative actions of PDDL2.1 which has similarities with the start-process-stop model of PDDL+. Both approaches recognise that durative activity is sometimes best modelled using an underlying, interruptible process. Whilst Bacchus proposes that the initiation and running of the processes be wrapped up into durative actions with conditional effects, PDDL+ achieves the same effect with cleanly separated continuous autonomous processes and events. PDDL+ can express behaviours that are dependent on continuous variables other than time, while Bacchus' proposal is limited to purely time-dependent processes (he does not allow interacting processes so does not consider other forms of continuous change).
McDermott and Boddy have consistently supported the use of autonomous processes in the representation of continuous change. In his commentary McDermott drewComm identifies the weaknesses of the durative action-based representation of change and argues that the continuous durative actions of PDDL2.1, which allow the modelling of duration inequalities and time-dependent effects, are ``headed for extinction in favour of straightforward autonomous processes''. The start-process-stop model of PDDL+ replaces the continuous durative actions of PDDL2.1 with constructs that fully exploit autonomous processes to support richer and more natural models of continuous domains. As we have shown in this paper, the modelling of events adds expressive power as Boddy anticipates [BoddyBoddy2003].
In his commentary Smith daveComm raises some philosophical objections to the durative action model of PDDL2.1 which he argues is too restrictive to support convenient models of interesting durative behaviours. In PDDL2.1 actions specify effects only at their start and end points, although conditions can be required to remain invariant over the whole durative interval. Smith proposes a durative action model that is richer than that proposed in PDDL2.1, in which effects can occur at arbitrary points within the durative interval and conditions might also be required to hold at identified timepoints other than at the start or end of an action. Although, in principle, it is possible to decompose PDDL2.1 durative actions into sequences of actions that achieve these effects, Smith correctly observes that this would generally result in inconvenient and impractical models. He argues that action representations should encapsulate the many consequences of their application in a way that frees a planner from the burden of reasoning about them in their minutiae. He observes that the computational effort involved, in stringing together the sub-actions that are required to realise a complex activity, would normally be prohibitive.
We agree that the PDDL2.1 durative action model is restrictive in forcing effects to occur only at the end points of the actions. Smith's rich durative model can be seen as encapsulating the effects of starting and ending one or more processes, together with the effects of these processes, into an action-based representation. By committing the activity to a certain amount of time these actions abstract out the time-dependent details and avoid the need for the planner to reason about them or their interactions. This is a simplification that is no doubt sufficient in many practical contexts (and indeed, is sufficient for the satellite domain that he discusses in his commentary). It might indeed be of interest to provide such representations as abstractions of the start-process-stop model.
This point goes to the heart of the contribution of this paper: we have provided a set of primitives for building modelling constructs. In providing a formal semantics for these primitives we have provided a way of interpreting abstract constructs built from these primitives. We argue that, in combination with natural modelling concepts like fixed-length durative actions, the start-process-stop primitives provide a usable planning domain description language. However, we are concerned here with the formal underpinnings of the language rather than with the modelling convenience it provides. We agree with Smith that abstract modelling constructs, built from the primitives, might enhance the modelling experience in the same way that abstract programming constructs enhance the programming experience over programming at the machine code level.
Derek Long 2006-10-09