Which of the following action schemes in PDDL yield an applicable action in the initial state
𝐼
𝑛
𝑖
𝑡
(
𝑇
𝑖
𝑟
𝑒
(
𝐴
)
∧
𝐹
𝑙
𝑎
𝑡
(
𝐴
)
∧
𝑃
𝑢
𝑛
𝑐
𝑡
𝑢
𝑟
𝑒
(
𝐴
)
∧
𝑇
𝑖
𝑟
𝑒
(
𝐵
)
)
?

Question

Which of the following action schemes in PDDL yield an applicable action in the initial state 
𝐼
𝑛
𝑖
𝑡
(
𝑇
𝑖
𝑟
𝑒
(
𝐴
)
∧
𝐹
𝑙
𝑎
𝑡
(
𝐴
)
∧
𝑃
𝑢
𝑛
𝑐
𝑡
𝑢
𝑟
𝑒
(
𝐴
)
∧
𝑇
𝑖
𝑟
𝑒
(
𝐵
)
)
?

BlackTom AI · Accepted Answer

We start from the given initial state literals to reason about applicability of each action schema. The initial state explicitly contains Tire(A), Tire(B), Flat(A), and Puncture(A). Any other literals not stated are not assumed true unless the problem explicitly provides them, so we treat only what is clearly given as true.

Option 1: Action(Change(x,y)) with PRECOND: Tire(x) ∧ Puncture(y)
- Because Tire(A) and Puncture(A) are both true in the initial state, we can instantiate x := A and y := A. Then the precondition Tire(A) ∧ Puncture(A) is satisfied, so this action is applicable in the initial state. The reasoning here hinges on using the explicitly true literals we have: a tire exists for some x (A) and there is a puncture for some y (A).

Option 2: Action(Change(x,y)) with PRECOND: Flat(x) ∧ ¬Flat(y)
- We do have Flat(A) true, so Flat(x) can be satisfied by x := A. For ¬Flat(y) to hold, y must be a value for which Flat(y) is not true. In the initial state we do not have any Flat(y) assertion beyond Flat(A); for y := B, Flat(B) is not stated as true. In STRIPS-style reasoning, unless Flat(B) is known to be true, ¬Flat(B) can be treated as satisfied. Thus we could instantiate x := A, y := B and satisfy Flat(A) ∧ ¬Flat(B). This would make the action appear applicable, but it relies on default assumptions about the absence of Flat(B). If the convention is closed-world (i.e., anything not stated is false), then ¬Flat(B) would indeed hold and the precondition would be satisfied. If the convention requires explicit negation facts, this would not be guaranteed. Given typical PDDL interpretation, this precondition is not guaranteed solely from the provided initial literals, so this option is uncertain without a clear closed-world assumption.

Option 3: Action(Change(x,y)) with PRECOND: Flat(x) ∧ ¬Flat(y)
- This is the same structural form as Option 2 but presented as a separate alternative. The assessment follows the same logic: Flat(x) can be satisfied by x := A, but ¬Flat(y) requires a y for which Flat(y) is not true. As explained above, depending on whether we adopt a closed-world interpretation (where non-listed facts are false) or an open-world interpretation, this may or may not be guaranteed. Under open-world, this would not be guaranteed; under closed-world, it could be applicable with y := B. Because the problem statement provides only explicit positives, we should flag this as not definitively applicable without a stated assumption.

Option 4: Action(Change(x,y)) with PRECOND: Tire(x) ∧ Tire(y) ∧ Flat(y)
- We have Tire(A) and Tire(B), so we can satisfy Tire(x) and Tire(y) by choosing x := B and y := A. Additionally, Flat(y) requires Flat(A), which is true in the initial state. Therefore, this precondition can be satisfied (Tire(B) ∧ Tire(A) ∧ Flat(A) holds in the initial state). Hence this action is applicable in the initial state.

Option 5: Action(Change(x,y)) with PRECOND: Tire(x) ∧ Tire(y) ∧ ¬Flat(x) ∧ Puncture(y)
- We again can meet Tire(x) and Tire(y) by x := A and y := A (or x := B and y := A, etc.). For ¬Flat(x), we need to ensure x is not flat. Flat(A) is true, so choosing x := A would violate ¬Flat(A). If we instead pick x := B, we have Tire(B) true, and we need ¬Flat(B). Flat(B) is not stated in the initial facts; under a closed-world assumption, ¬Flat(B) would hold, satisfying the precondition. For Puncture(y), we can use y := A since Puncture(A) is true. Therefore, this option could be applicable if we assume ¬Flat(B) is true in the initial state. If the problem does not permit inferring ¬Flat(B) from lack of information, this would be uncertain.

Summary of applicability considerations:
- Option 1 is straightforwardly applicable by selecting x = A, y = A, using explicitly true literals (Tire(A) and Puncture(A)).
- Option 4 is also clearly supportable by choosing x = B, y = A (Tire(B), Tire(A), and Flat(A) are all true). This makes the precondition satisfied.
- Options 2, 3, and 5 depend on how we treat the unknown Fluency of ¬Flat(y) or ¬Flat(x) for entities not explicitly stated as not flat. If we adopt a closed-world view (anything not stated is false), then ¬Flat(B) would hold and these options could also be applicable with appropriate instantiations; if we adopt an open-world view, these preconditions would not be guaranteed to hold based solely on the given facts, making applicability uncertain.

In planning problems, clarity about the default truth values for unspecified literals is crucial. The two options that are unambiguously applicable given the explicit initial facts are Option 1 (Change with precondition Tire(x) ∧ Puncture(y) instantiated to x = A, y = A) and Option 4 (Change with precondition Tire(x) ∧ Tire(y) ∧ Flat(y) instantiated to x = B, y = A). The remaining options hinge on how ¬Flat(...) is treated for entities not explicitly flat in the initial state.

DD2380 HT24 (AIHT24_2) Q9: Planning

Which of the following action schemes in PDDL yield an applicable action in the initial state 𝐼 𝑛 𝑖 𝑡 ( 𝑇 𝑖 𝑟 𝑒 ( 𝐴 ) ∧ 𝐹 𝑙 𝑎 𝑡 ( 𝐴 ) ∧ 𝑃 𝑢 𝑛 𝑐 𝑡 𝑢 𝑟 𝑒 ( 𝐴 ) ∧ 𝑇 𝑖 𝑟 𝑒 ( 𝐵 ) ) ?

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