The goals are :

1
The goals are

• to show there is an isomorphism between partial
  order planning and abductive reasoning in the
  event calculus (as an extention to Shanahans
  work)
• to show how an abductive planner can implement
  sistematic and redundant planning methods
• to provide a formal specification of
  sistematicity and redundancy in planning
• to show the efficiency of abductive planning in
  terms of domain characteristics and the
  implemented planning method (as in tradicional AI
  planning)

2
Abductive planning

• ? domain specification (initiates,
  terminates and releases)
• ? initial state (initiallyn and
  initiallyp)
• ? goal state (holdsAt)
• EC conjunction of Event Calculus axioms
  
• abductive planning has to find a set of facts
  ? (happens and before) such that
• (a) CIRC? initiates, terminates, releases
  ?
• CIRC? ? ? happens ? EC is
  consistent
• (b) CIRC? initiates, terminates, releases
  ?
• CIRC? ? ? happens ? EC ? ?

3
Abductive EC planner

• abp(holds_at(F1,T3)Gs1,R1,R5,N1,N4) -
• abresolve(initiates(A,F1,T1),R1,Gs2,R1),
• abresolve(happens(A,T1,T2),R1,,R2),
• abresolve(before(T2,T3),R2,,R3),
• add_neg(clipped(T1,F1,T3),N1,N2),
• nafs(N2,R3,R4,N2,N3),
• append(Gs2,Gs1,Gs3),
• abp(Gs3,R4,R5,N3,N4).

EC axiom
holdsAt(F,T) ? happens(A,T1,T2) ?
initiates(A,F,T1) ? (T2?T ) ? ?clipped(T1,F,T)
4
Domain specification
S0

• initiallyp( clear(c) )
• initiallyp( on(c,a) ) ...
• initiates(move(X,Y,Z), clear(Y), T) ?
• holdsAt( clear(X), T) ?
• holdsAt( clear(Z), T) ?
• holdsAt( on(X,Y), T) ?
• X?Z ...
• terminates(move(X,Y,Z), clear(Z), T) ?
• holdsAt( clear(X), T) ?
• holdsAt( clear(Z), T) ?
• holdsAt( on(X,Y), T) ?
• X?Z ...

C
B
A
5
Implemented systems

• Classical planners POP, SNLP e TWEAK
• Abductive planners ABP, SABP e RABP
• Implementation constraints (as much as
  possible)
• same data structures and computacional resources
• same access time to the action representation
  (domain model)
• simplified version of the EC only the classical
  planning assumptions are specified

6
Goal protection policies in 3 planning methods

• POP/ABP
• protects already established goals only from
  negative threats
• refines only consistent plans
• SNLP/ SABP (systematic planning)
• protects established goals from negative or
  positive threats
• refines only consistent plans
• never visits the same plan more than once
• TWEAK/RABP (redundant planning)
• protects established goals form only part of
  negative threats
• refines consistent and inconsistent plans
• can visit the same plan several times

7
Experiment I POP ? ABP

• Goal
• to show the isomorphism between partial order
  planning and abductive reasoning in the event
  calculus
• Test domains (Barret Weld)
• independent goals D0S1
• serializable goals D1S1 e DmS1
• non-serializable goals DmS2
• Statistics
• search space size
• average CPU-time

8
Same problem solving methods search space sizes
are equal
18
12
POP
POP
D1S1
D0S1
ABP
10
ABP
8
nodes/plans processed
nodes/plans processed
6
4
2
2
1
2
3
4
5
6
1
2
3
4
5
6
25
60
POP
DmS2
DmS1
20
POP
ABP
ABP
15
nodes/plans processed
nodes/plans processed
10
5
0
0
1
2
3
4
5
6
1
2
3
4
5
6
number of subgoals
number of subgoals
9
Same problem solving methods the planners visit
the same partial plans

• plan(step(42, unstack(c,a)),
• step(40, stack(b,c)),
• step(18, stack(a,b)),
• 42lt40, ..., link(i,on(c,a),42), ...)
• residue(happens(unstack(c,a), 42),
• happens(stack(b,c), 40),
• happens(stack(a,b), 18),
• before(42,40), ..., clipped(0,on(c,a),42
  ), ...)

10
Planning efficiency
0.09
0.08
POP
D0S1
D1S1
POP
0.07
ABP
0.06
ABP
0.05
CPU-time (sec)
CPU-time (sec)
0.04
0.03
0.02
0.01
2
2
1
2
3
4
5
6
1
2
3
4
5
6
POP
DmS1
DmS2
POP
ABP
ABP
CPU-time (sec)
CPU-time (sec)
0
0
1
2
3
4
5
6
1
2
3
4
5
6
number of subgoals
number of subgoals
11
Experiment II

• Goal
• to show that different implementations of
  abductive planning can have the same behavior as
  the tradicional AI planning algorithms have
• Sistems to compare
• POP ? ABP
• SNLP ? SABP
• TWEAK ? RABP
• Test domains (based on Knoblock Yang)
• variable difficulty AxDyS2
• Statistics
• search space size
• CPU-time

12
Systematicity vs. Redundancy
Abductive planners presented the same behavior
as the respective planning algorithms