= Solution
A corrected <STRIPS> model can fix object roles in the action names, leaving only room parameters to instantiate. Use the same $a,w,g,r$ and introduce static $\operatorname{pitfree}(z)$ and $\operatorname{exit}(z)$ facts, plus a <planning fluent> $\operatorname{clear}(z)$ meaning “no live monster occupies $z$”. Unlike the supplied adjacency relation, let $\operatorname{adj}$ describe all geometrically adjacent rooms; safety is then explicit rather than hidden by missing <edges>.
Initially the agent, monster and gold have their specified locations, $\operatorname{have}(a,r)$, $\operatorname{alive}(w)$ and $\operatorname{active}$ hold, $\operatorname{exit}(s_{11})$ holds, $\operatorname{pitfree}$ holds at every room except $s_{12}$, and $\operatorname{clear}$ holds at every room except $s_{23}$. All unlisted facts are false by the <closed-world assumption>. The following positive <preconditions>, add lists and delete lists are a complete action specification:
$$
\begin{array}{c|l|l|l}
\text{action}&\text{preconditions}&\text{add}&\text{delete}\\\hline
\operatorname{Walk}(y,z)&\begin{gathered}\operatorname{active},\operatorname{at}(a,y),\operatorname{adj}(y,z),\\\operatorname{pitfree}(z),\operatorname{clear}(z)\end{gathered}&\operatorname{at}(a,z)&\operatorname{at}(a,y)\\[3pt]
\operatorname{Fire}(y,z)&\begin{gathered}\operatorname{active},\operatorname{at}(a,y),\operatorname{adj}(y,z),\\\operatorname{at}(w,z),\operatorname{alive}(w),\operatorname{have}(a,r)\end{gathered}&\begin{gathered}\operatorname{dead}(w),\\\operatorname{clear}(z)\end{gathered}&\begin{gathered}\operatorname{alive}(w),\\\operatorname{have}(a,r)\end{gathered}\\[3pt]
\operatorname{Collect}(z)&\begin{gathered}\operatorname{active},\operatorname{at}(a,z),\\\operatorname{at}(g,z)\end{gathered}&\operatorname{have}(a,g)&\operatorname{at}(g,z)\\[3pt]
\operatorname{Leave}(z)&\begin{gathered}\operatorname{active},\operatorname{at}(a,z),\\\operatorname{exit}(z),\operatorname{have}(a,g)\end{gathered}&\operatorname{exited}&\operatorname{active}
\end{array}
$$
Require $\operatorname{exited}$ as the goal. If reaching the exit suffices, omit $\operatorname{Leave}$ and use the original two goal facts. Instantiating these schemata over the finite room <set> gives ordinary ground <STRIPS> actions.
Only $a$ moves, only $g$ is collectible and only $r$ can be fired at $w$. No action changes the monster’s location; its corpse can stay there, while $\operatorname{clear}$ records that it is harmless. The gold stays at its original room until collection. The arrow is consumed by its only use. By <mathematical induction> on plan length, every applicable action preserves the <planning state invariant> that the active agent occupies one pit-free room without a live monster. Consequently every solution is a safe execution. The plan in part a, followed by $\operatorname{Leave}(s_{11})$, is one such execution.
Back to article page
