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Efficient Abductive Planning: A Comparative Study in Event Calculus

Explore the isomorphism between partial order planning & abductive reasoning in Event Calculus, showcasing abductive planners' method efficiency. The study provides formal systematic and redundant planning specs, evaluating the performance based on domain characteristics and planning methods. Implementation constraints aim to unify data structures and computational resources. Three planning methods—POP, SNLP, and TWEAK—are compared with respective abduction counterparts, showcasing protection policies and plan refinement strategies. Two experiments discuss isomorphism between partial order and abductive planning, and comparative performance across different planning algorithms in diverse test domains. 8

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Efficient Abductive Planning: A Comparative Study in Event Calculus

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  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 Shanahan’s 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 (initiallynandinitiallyp)  : 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 A B

  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. 16 14 10 12 8 6 4 10 30 50 20 40 Same problem solving methods: search space sizes are equal 12 18 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 60 25 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))], [42<40, ...], [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. 0.09 0.01 0.02 3.0 2.0 4.5 4.0 2.5 1.5 0.5 1.0 0.14 0.12 3.5 0.08 0.06 0.02 0.04 0.10 0.10 0.08 0.07 0.06 0.05 0.04 0.03 Planning efficiency 0.09 0.08 POP D1S1 D0S1 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

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