A state is {At(Robot, Hall), Holding(Box)}. The action Go(Robot, Hall, Lab) has precondition At(Robot, Hall), delete list {At(Robot, Hall)} and add list {At(Robot, Lab)}. What state results from applying the action?
A{At(Robot, Lab)}
B{At(Robot, Hall), At(Robot, Lab), Holding(Box)}
C{At(Robot, Lab), Holding(Box)}
DThe action cannot be applied
The precondition holds, so the action applies. The new state is the old state minus the delete list plus the add list: Holding(Box) is untouched, At(Robot, Hall) is removed and At(Robot, Lab) is added.
Question 2 Multiple Choice
Many planning heuristics are computed by solving a relaxed version of the problem in which every action's delete list is ignored. Why does this help?
AIt makes the planner return the exact optimal plan in linear time
BFacts can only be added, never removed, so the relaxed problem is much easier to solve approximately, and its solution length estimates the true distance to the goal
CIt removes all preconditions, so any action can be applied anywhere
DIt converts the planning problem into a single-step problem
Without deletions, progress toward the goal can never be undone, so a relaxed plan can be found quickly. Its length gives an informative estimate of the remaining cost for guiding search. Finding an optimal relaxed plan is still hard in general, so practical planners such as FF use a fast approximation.
Question 3 True / False
Under the closed-world assumption used in classical planning, a fact that is not listed in the current state is treated as false.
TTrue
FFalse
Answer: True
A state lists only the facts that are true. Any other ground fact is assumed false. This keeps states compact and makes the result of an action easy to compute.
Question 4 Short Answer
In the Sussman anomaly, block C starts on A, and A and B are on the table. The goal is On(A, B) and On(B, C). Explain why achieving one subgoal completely and then the other fails.
Think about your answer, then reveal below.
Model answer: If you first achieve On(A, B), you must move C off A and stack A on B, but then B is covered and cannot be moved onto C without undoing On(A, B). If you first achieve On(B, C), you stack B on C, which buries A under C and B, so achieving On(A, B) requires undoing On(B, C). The correct plan interleaves the subgoals: move C to the table, put B on C, then put A on B.
The anomaly shows that subgoals can interact, so planners must be able to interleave actions that serve different subgoals rather than solving them strictly in sequence.