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

• URL: http://arxiv.org/abs/2601.20014v1
• Date: Tue, 27 Jan 2026 19:41:10 GMT
• Title: Teaching LLMs to Ask: Self-Querying Category-Theoretic Planning for Under-Specified Reasoning
• Authors: Shuhui Qu,
• Abstract summary: Inference-time planning with large language models frequently breaks under partial observability.<n>We introduce textbfSelf-Querying Bidirectional Categorical Planning (SQ-BCP), which explicitly represents precondition status.<n>We prove that when the verifier succeeds and hard constraints pass deterministic checks, accepted plans are compatible with goal requirements.
• Score: 1.8055130471307603
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: 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.

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