The argumentation scheme for plan proposals presented later in this chapter builds on the argumentation scheme foraction proposals AS1 presented in [11] (see Section 2.3.4). In this chapter, I present an extension toAS1 that considers durative actions.
In [11], actions in the AS1 argumentation scheme are presented as operations from a state or current circumstances that cause new circumstances or effects to become true resulting in a new state. The authors assume a finite set of distinct actions giving no consideration to time (i.e. the duration of the action, the start-time and end-time) and effects and conditions that hold throughout the action duration (start effects, invariant conditions and termination conditions), all of which are important to define temporal multi-agent plans.
This section takes concepts from the Planning Domain Description Language (PDDL) 2.1 temporal action specification presented in [71] used to describe actions used for tem- poral planning (cf. section 2.4.1). In the PDDL 2.1 action specification, instead of considering actions only with preconditions and effects, actions are presented as dura- tive entities with additional conditions and effects that hold and become true at different times.
Action end
Action start
Time
End effects Start Effects Action duration Preconditions Termination Conditions Invariant ConditionsFigure 3.3 presents a durative action diagram as presented in the PDDL 2.1 specifi- cation. A durative action for the purpose of this thesis has the following elements and characteristics:
- A set of preconditions that hold before the action can start. A state is formed by a set of predicates and the preconditions of an action are a subset of these predicates with specific values for the action to be executed.
- The action has aduration or interval of execution.
- The action has arangewhich indicates the the permitted value by which an action duration can increase or decrease without affecting the effects of the action (see explanation below).
- Once the action starts a set of start effects becomes true. The start effects are predicates with specific values that are made true by the action and can be different from the end effects.
- Throughout the complete duration of the action invariant conditions hold. These conditions are not caused by the action.
- A set of termination conditionshold before the action can end.
- A set of end effects which begin to hold when the action is complete i.e. the effects of actions only change the value of predicates. It is assumed that predicates not mentioned in the effects of the action stay with the same value, unless another action changes their value.
The actions have a duration that may change within a range, that is, increasing or decreasing the duration within the range without affecting the effects of the action. From the running example, moving through zones with the actionmove() has duration 4 with range 1, which means the action can take 5 or 3 time units without changing the effects of the action. I assume here agents have control about the duration the action, leaving aside variations in the duration due to conditions unknown to the agents. In [34], for example, the Multi-agent Planning Language MAPL (an extension of PDDL 2.1) introduces actions whose duration is determined in runtime. The intention behind of presenting durative actions with a range is to give agents elements to engage in dialogues using action elements that include temporal elements and so to enable a richer argumentation-based dialogue over cooperative plans.
An example of a durative action for the agentN GO using the example from Appendix A is as follows (see Table A.5):
the durative actionmove(ag, X, Y) with duration 4 and a range of 1 (see Tables ??and haspreconditions:
(ii) the fuel should be full/low, (iii) the route (X,Y) should exist, (iv) ZoneX should be a secure zone. (v) Route (X,Y) should be a secure route. The start effects of the action are:
(i) the fuel starts decreasing, and
(ii) the agent starts moving and is no longer in zoneX. The invariant condition is that the fuel keeps reducing. The action has no termination conditions
The end effects of the action are are: (i) the agent arrives in zoneY and (ii) the fuel is reduced to low/empty.
Another example of a durative action is the action control() in Table A.9. The invariant condition for the action control() is that the GroundForce is deployed. This does not change throughout the action duration and is not part of the end effects. Note that GroundF orce(deployed) is also a start effect of the action. In this scenario it is possible to represent that an effect of the action should remain true throughout the execution of it and the way to do it is specify them as a start effect and a condition.
This model of time still presents some limitations as durative actions should allow effects and/or conditions to be asserted at arbitrary points during the interval of exe- cution, or to be a function of duration (until actions). The planning community is still developing ways to create planners that handle temporally extended actions [71].
The extended argument scheme for action proposal AS2 is as follows 1: 1
In [11], authors make no difference between resolving on a future action and justifying a past action, for the purpose of this thesis I assume the proposal presumptively justifies a future action part of a plan to execute.
- Given current circumstances R - where preconditionsP hold
- agent Agi should perform action Acwith duration dat timets - that generates start effects E
- with invariant conditions I - and termination conditions C
- with end effects EE that hold in stateS - which will realize goal G
- and promote/demote value v.
where R is the initial state, Ac is an arbitrary action of agent Agi, S is the final state, the goalGis a finite set of formulae that holds inS, andvis a value that justifies the transition from state R to state S. It is assumed that values are qualitative social interests of agents and the preference over these values is subjective to the agents.
An example of how the AS2 can be instantiated is: - Given stateR
- where preconditions: (inZone(N GO,1),F uel(f ull)) hold
- agent Agi should perform action Ac = move(N GO,1,2) with duration d=3 at timets =0,
- that generates start effects: F uel(decreasing),moving(N GO) - with invariant condition: F uel(decreasing)
- with end effects EE inZone(N GO,2),F uel(low) that hold in state S - which will realize goal G= inZone(N GO,2)
- and promote the value vmob
I now present a discussion analysis on multi-agent temporal plans, action dependency and concurrent actions and the implications to the plan proposal scheme.