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

Abstract: Inference-time planning with LLMs 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.

• The paper introduces SQ-BCP, a framework combining explicit precondition tracking, self-querying, and categorical verification to reduce feasibility errors in LLM planning.
• The methodology integrates bidirectional search with deterministic uncertainty resolution, achieving significant reductions in resource-violation rates across WikiHow and RecipeNLG.
• Experimental results confirm that SQ-BCP offers strong theoretical guarantees, robust model transferability, and scalable inference-time efficiency for under-specified reasoning tasks.

Self-Querying Category-Theoretic Planning for Under-Specified LLM Reasoning

Motivation and Context

LLMs enable inference-time multi-step reasoning for real-world tasks such as procedural planning and recipe adaptation. However, in scenarios with partial observability—where user queries lack key applicability facts or hidden environment attributes—LLM-based planners tend to hallucinate missing conditions or produce plans that violate hard constraints. Classical planning approaches address feasibility issues by explicit precondition tracking, but direct application to LLMs is hampered by the open-ended nature of natural language actions and unknown applicability conditions. Existing reasoning and information-seeking methods (e.g., Self-Ask) may reduce uncertainty, but lack principled mechanisms to guarantee hard-constraint satisfaction and compositional plan correctness.

Method: Self-Querying Bidirectional Categorical Planning (SQ-BCP)

SQ-BCP is designed for robust inference-time planning under underspecification. It introduces three key algorithmic advances: explicit precondition status modeling, deterministic uncertainty resolution (via self-querying and bridging), and compositional categorical verification.

Explicit Precondition Tracking

Each candidate hypothesis in SQ-BCP is structured as a tuple comprising a natural language action, labeled preconditions (Sat/Viol/Unk), typed effects, and a normalized score. Precondition labels are first-class: Sat (satisfied), Viol (violated), and Unk (unknown). Hypotheses are expanded only when all preconditions are resolved.

Deterministic Refinement: Self-Querying and Bridging

For hypotheses with Unk preconditions, SQ-BCP applies a deterministic policy:

• Attempt bridging actions that modify the environment to establish the missing condition, tracking signatures to avoid cycles.
• If bridging fails, issue a focused query (self-ask) for the missing fact.
• If resolution is unsuccessful or produces violation, the hypothesis is discarded.

This mechanism leverages both autonomous reasoning and targeted information acquisition, dynamically mixing them to resolve unknowns before action commitment.

Bidirectional Search and Pullback-Based Verification

SQ-BCP integrates hypothesis refinement into a bidirectional AND-OR graph search, expanding forward from initial state $w_0$ and backward from goal $w^*$. At meet points, hypotheses are composed, and a pullback-based categorical verifier checks global plan–goal compatibility. Deterministic hard-constraint checks (e.g., resource sufficiency, logical predicates, temporal feasibility) are applied sequentially; only plans passing both verifiers are accepted. Heuristic distances are used strictly for prioritization and pruning, never for correctness certification.

Figure 1: Bidirectional search from $w_0$ and $w^*$, with SQ-BCP self-querying and bridging hypotheses to resolve missing preconditions before categorical verification at meet points.

Theoretical Properties

SQ-BCP achieves three key guarantees under mild assumptions:

• Termination: Refinement of hypotheses with Unk preconditions is bounded (by the number of unknowns and bridging attempts).
• Correctness: Any accepted planning chain passes all hard-constraint checks and categorical verification, ensuring compatibility with the specified goal requirements.
• Bounded Search Complexity: Given finite branching and bounded precondition refinement, the search algorithm finds an accepting plan—if one exists—within a quantifiable budget.

Distance heuristics do not guarantee correctness; only passing explicit verification admits the plan.

Empirical Evaluation

Experimental Protocol

SQ-BCP is evaluated on WikiHow procedural tasks and RecipeNLG recipe adaptation, both featuring unobserved or withheld preconditions. A $k$-reveal protocol creates controlled variants with varying numbers of hidden conditions. An oracle agent provides truthful answers to targeted queries concerning resources, environmental facts, and constraints. All baselines (direct, CoT, ToT, ToS, ReAct, Self-Ask) use the same backbone LLM and oracle feedback for fairness.

Main Results

SQ-BCP demonstrates strong empirical gains in executability:

• Resource-violation rates: Reduced to 14.9% (WikiHow) and 5.8% (RecipeNLG), substantially lower than Self-Ask (26.0%/15.7%) and far below search-based planners (up to 94.7% violation).
• Reference quality: Maintains competitive ROUGE-2 (WikiHow) and BLEU (RecipeNLG), with only minor trade-offs compared to highest-scoring baselines.

Search or question generation alone misses hard-constraint violations; explicit precondition semantics and verification are necessary for executability.

Figure 2: Query and hypothesis counts versus missing preconditions. As uncertainty increases, SQ-BCP generates more targeted queries and explores more hypotheses to resolve unknowns.

Ablation Analyses

Ablations confirm the necessity of multiple components:

• Self-Ask-style querying yields large reductions in violation rates relative to CoT, but residual failures persist.
• Combining precondition status tracking and categorical verification leads to further reductions—demonstrating that explicit modeling and hard verification are irreplaceable for feasibility under partial observability.

Model Transferability

SQ-BCP produces similarly low violation rates across stronger LLM backbones (Qwen3-14B, Claude 3.5) and higher error rates only with smaller architectures, indicating robustness of the methodology to backbone selection.

Search-Efficiency Scaling

The number of oracle queries and explored hypotheses scales tractably with the number of missing preconditions, supporting inference-time applicability in interactive planning with moderate overhead.

Practical and Theoretical Implications

SQ-BCP enables more robust LLM-based planning systems in settings where user intent and environment facts are incompletely specified. Practically, the methodology formalizes the resolution of epistemic uncertainty, enabling planners to ask targeted questions or propose bridging actions before committing to outputs—directly reducing the frequency and severity of infeasible plans. The explicit separation of heuristic ranking from correctness via verification provides stronger guarantees, critical for downstream deployment in risk-sensitive or resource-constrained domains (e.g., robotic control, procedural instruction execution).

Theoretically, SQ-BCP leverages category-theoretic structure for compositional reasoning in natural language domains, operationalizing principled plan–goal compatibility without requiring symbolic domain models. This approach closes a key gap between neuro-symbolic planning and inference-time LLM reasoning, and motivates further investigation into richer categorical abstractions (e.g., functorial problem transfer, higher-order verification) for open-ended planning tasks.

Future Directions

Directions for extension include modeling noisy user oracle responses, incorporating continuous feasibility predicates (geometry, safety margins, probabilistic effects), optimizing inference-time search and verification for long-horizon or real-time applications, and validating generalization in domains beyond procedural instructions and recipe adaptation.

Conclusion

SQ-BCP introduces a principled framework for LLM-based planning under partial observability, unifying explicit precondition labeling, deterministic resolution (self-querying/bridging), and categorical verification within bidirectional search. Experiments on multiple benchmarks demonstrate substantial reductions in constraint violation rates and competitive plan quality. The methodology strengthens both practical robustness and theoretical compositionality for next-generation LLM reasoning and planning systems.