The first part of PoS is maintaining explicit belief states that record the current world and unresolved requirements. It organizes the task-relevant world using entities, states, and relations: the cup, microwave, and cabinet are entities; whether the cup is hot and whether the microwave is closed are states; where the cup is located and who is holding it are expressed through relations. This representation keeps only the information that will affect actions, outcome judgments, and goal completion.
The second part is making "what is still missing" explicit. PoS divides unresolved requirements into two types: an Epistemic Gap refers to things that still need to be figured out, and an Achievement Gap refers to things that still need to be changed through action. When facing multiple unresolved requirements, PoS selects one Active Gap to prioritize at the moment; the agent can still see the complete task state, but its actions have a clear focus.
The third part is Belief Health and Trapping-Aware Recovery. The paper's setup starts detection after accumulating 8 verified transitions, and enters trapping diagnosis when belief health Hₜ ≤ 0.25. Recovery unfolds along two dimensions: behavioral patterns are classified as Static, Cycle, or Drift and judged in that order; for the blocked gap type, it compares the persistence of the epistemic gap and the achievement gap and selects the more stubborn one.
There is a design point here that is easy to overlook: the recovery constraints are handed to the original agent as additional conditions, and it continues to choose actions, with the current Active Gap remaining unchanged. After each new transition is verified, health is recalculated; if it is above the threshold, the temporary constraints are released, and if it is still trapped, the diagnosis and constraints are updated. Trapping detection, constraint generation, and post-recovery re-evaluation form a continuous closed loop.