Consider the following simplified Hanoi towers planning problem in PDDL.

Init(On(B,One)∧On(S,Two)∧Clear(B)∧Clear(S)∧Clear(Three)∧Disk(B)∧Disk(S)∧CanPutOn(S,B)∧CanPutOn(B,One)∧CanPutOn(B,Two)∧CanPutOn(B,Three)∧CanPutOn(S,One)∧CanPutOn(S,Two)∧CanPutOn(S,Three))

Goal(On(B,Two),On(S,B))

Action(Move(d,x,y)
PRECOND:On(d,x)∧Disk(d)∧Clear(d)∧Clear(y)∧CanPutOn(d,y)
EFFECT:On(d,y)∧¬Clear(y)∧¬On(d,x)∧Clear(x))

Which of the following action sequences is a solution to the problem?

Question

Consider the following simplified Hanoi towers planning problem in PDDL.

Init(On(B,One)∧On(S,Two)∧Clear(B)∧Clear(S)∧Clear(Three)∧Disk(B)∧Disk(S)∧CanPutOn(S,B)∧CanPutOn(B,One)∧CanPutOn(B,Two)∧CanPutOn(B,Three)∧CanPutOn(S,One)∧CanPutOn(S,Two)∧CanPutOn(S,Three))

Goal(On(B,Two),On(S,B))

Action(Move(d,x,y)
PRECOND:On(d,x)∧Disk(d)∧Clear(d)∧Clear(y)∧CanPutOn(d,y)
EFFECT:On(d,y)∧¬Clear(y)∧¬On(d,x)∧Clear(x))

Which of the following action sequences is a solution to the problem?

BlackTom AI · Accepted Answer

Question restatement: The problem provides an initial Hanoi-like state and an action definition Move(d, x, y) with its preconditions and effects, then asks which of the given action sequences solves the planning problem to reach On(B,Two) ∧ On(S,B).

Option analysis:
- The only listed option sequence is: Move(S,Two,Three),Move(B,One,Two),Move(S,Three,B)Move(S,Two,Three),Move(B,One,Two),Move(S,Three,B).
  This sequence appears to be a concatenation of two parts without a clear separator, but we treat it as a single proposed plan consisting of six moves (ignoring the missing comma): 1) Move(S,Two,Three) 2) Move(B,One,Two) 3) Move(S,Three,B) 4) Move(S,Two,Three) 5) Move(B,One,Two) 6) Move(S,Three,B).

Step-by-step evaluation of each move with preconditions and effects:
- Move(S,Two,Three) as the first move:
  Precondition checks: On(S,Two) is true in the initial state, Disk(S) is true, Clear(S) is true, Clear(Three) is true, and CanPutOn(S,Three) is true (from the initial CanPutOn facts). All preconditions are satisfied, so this move is legally executable. After this move, On(S,Three) holds, Clear(Three) becomes false (since S is now on Three), On(S,Two) becomes false, and Clear(Two) becomes true (assuming nothing is on Two after S leaves).

- Move(B,One,Two) as the second move:
  Precondition checks after the first move: On(B,One) is true in the initial state, Disk(B) is true, Clear(B) is true, Clear(Two) is true (Two is now clear since S moved off it), and CanPutOn(B,Two) is true (listed in initial facts). All preconditions are satisfied, so this move is executable. After this move, On(B,Two) holds, Clear(Two) becomes false, On(B,One) becomes false, and Clear(One) becomes true.

- Move(S,Three,B) as the third move:
  Precondition checks after two moves: We have On(S,Three) from the first move, Disk(S) is true, Clear(S) needs to be true (no disk on top of S). Typically, S being the top disk on Three means Clear(S) is true. However, the destination B must be Clear(B) and CanPutOn(S,B) must hold. From the initial state, CanPutOn(S,B) is not specified and not implied by the given CanPutOn facts (we only have CanPutOn(S,One), CanPutOn(S,Two), CanPutOn(S,Three)); thus CanPutOn(S,B) is not known to be true. Clear(B) would be true since B is on Two and there’s nothing on top of B, but the missing CanPutOn(S,B) precondition makes this move invalid in the actual ruleset.

- The remaining moves (Move(S,Two,Three), Move(B,One,Two), Move(S,Three,B)) repeat patterns from earlier steps:
  If the third move is invalid due to CanPutOn(S,B) being false (as analyzed), the entire sequence fails at that point. Even if one tries to interpret variants or consider whether CanPutOn(S,B) could become true later, the plan would require satisfying the same precondition that is not present in the initial description, and it does not align with the stated preconditions for Move(d,x,y).

Why this option is incorrect in summary:
- The third move Move(S,Three,B) cannot be executed because the precondition CanPutOn(S,B) is not given as true in the initial state; the plan relies on a condition that is not established by the problem statement.
- Since a required move in the sequence is infeasible, the entire sequence cannot reach the goal On(B,Two) ∧ On(S,B).

Additional notes and considerations:
- The initial step Move(S,Two,Three) is valid and moves S off Two onto Three, which would enable the second move Move(B,One,Two). However, the subsequent attempt to move S onto B fails due to the missing CanPutOn(S,B) information, breaking the intended plan.
- If a correct solution exists, it would need to use only moves whose preconditions are satisfied by the evolving state, including explicit CanPutOn relationships for each intended destination.
- The given option appears to conflate two separate sequences or omit a necessary precondition, which is a common pitfall in hand-constructed planning sequences where all preconditions must be verified at each step.

DD2380 HT24 (AIHT24_2) Q9: Planning

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