Teaching LLMs to Ask: Self-Querying Category-Theoretic Planning for Under-Specified Reasoning

Inference-time planning with large language models frequently breaks under partial observability: when task-critical preconditions are not specified at query time, models tend to hallucinate missing facts or produce plans that violate hard constraints. We introduce \textbf{Self-Querying Bidirectional Categorical Planning (SQ-BCP)}, which explicitly represents precondition status (\texttt{Sat}/\texttt{Viol}/\texttt{Unk}) and resolves unknowns via (i) targeted self-queries to an oracle/user or (ii) \emph{bridging} hypotheses that establish the missing condition through an additional action. SQ-BCP performs bidirectional search and invokes a pullback-based verifier as a categorical certificate of goal compatibility, while using distance-based scores only for ranking and pruning. We prove that when the verifier succeeds and hard constraints pass deterministic checks, accepted plans are compatible with goal requirements; under bounded branching and finite resolution depth, SQ-BCP finds an accepting plan when one exists. Across WikiHow and RecipeNLG tasks with withheld preconditions, SQ-BCP reduces resource-violation rates to \textbf{14.9\%} and \textbf{5.8\%} (vs.\ \textbf{26.0\%} and \textbf{15.7\%} for the best baseline), while maintaining competitive reference quality.