When Verification Hurts: Asymmetric Effects of Multi-Agent Feedback in Logic Proof Tutoring

Effective LLM tutoring depends on correctly identifying the specific error in a student's reasoning before generating feedback. We study this problem in propositional-logic proof tutoring, where student actions can be checked against formal inference rules. We introduce a verifier-grounded architecture that separates diagnosis from language generation. Using 600 balanced student actions, we compare a zero-shot LLM detector, a fine-tuned detector, and a symbolic verifier. Each diagnosis is processed by shared rationale and feedback agents, isolating the effect of the initial diagnosis. The zero-shot detector achieves a macro-F1 of 0.191; fine-tuning raises this to 0.709 but retains systematic errors between structurally related classes. Rationales generally preserve the diagnosis supplied to them, showing that an incorrect diagnosis can be faithfully propagated through the pipeline. Feedback can likewise remain faithful to its rationale, non-revealing, and pedagogically appropriate while addressing the wrong error. Verifier-grounded feedback achieves the highest diagnostic correctness, and expert ratings largely uneven with the automatic feedback evaluations. These findings show that apparent feedback quality can conceal upstream diagnostic errors and that faithfulness must be evaluated separately from correctness. Our code is publicly available

Effective tutoring requires distinguishing optimal, valid but suboptimal, and incorrect student solutions, a distinction central to intelligent tutoring systems (ITS) but untested for LLM-based tutors. As LLMs are increasingly explored as conversational complements to ITS, evaluating their diagnostic precision is essential. We present a benchmark of seven LLM feedback agents in propositional logic using knowledge-graph-derived ground truth across 10,836 solution--feedback pairs and three feedback conditions. Models achieved near-ceiling performance on optimal steps but systematically over-rejected valid but suboptimal reasoning and over-validated incorrect solutions, precisely where adaptive tutoring matters most. These failures persisted across models regardless of solution context, suggesting architectural rather than informational limits. Moreover, accurate diagnosis did not reliably produce pedagogically actionable feedback, revealing a gap between diagnostic judgment and instructional effectiveness. Our findings suggest that LLMs are better suited for hybrid architectures where KG-grounded models handle diagnosis while LLMs support open-ended scaffolding and dialogue.

Large Language Models (LLMs) struggle to rigorously verify complex mathematical proofs. Standard global evaluation approaches suffer from "context poisoning," in which superficially plausible statements mask subtle logical flaws, leading to hallucination or over-skepticism. To address this, we shift from global evaluation to strict step-level verification: our framework maintains detailed context for each deduction step and strictly constrains the sources of applied theorems. We evaluate on a carefully curated adversarial diagnostic suite of research-level proofs drawn from the FirstProof challenge. A systematic ablation study demonstrates that these deductive constraints are indispensable, as unconstrained global prompting consistently fails to localize subtle logical errors. Beyond outperforming global evaluation, our approach fundamentally alters the failure taxonomy. Error analysis reveals that, rather than exhibiting severe logical hallucinations, remaining rejections are primarily instances of "pedantic hyper-rigor" stemming from unstated domain conventions, effectively exposing implicit ambiguities within the expert benchmark itself. Our findings suggest that prompting agents to organize their verification notes in a cautious, human-mathematician-like manner can substantially improve their ability to distinguish rigorous proofs from flawed ones, with the potential to strengthen agentic reasoning on frontier mathematical concepts that the base model does not already know well, and to lay a theoretical foundation for future automated proof-review systems. Code and prompts are available at GitHub.