# The promise and limits of LLMs in constructing proofs and hints for logic problems in intelligent tutoring systems

arXiv: https://arxiv.org/abs/2505.04736 · HTML: https://mlsanity.com/paper/2505.04736/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 66 references that are in the map.
- First posted on arXiv 7 May 2025.

## Builds on (most cited first, 23 of 23)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought](https://mlsanity.com/paper/2210.01240/) (2022)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [FOLIO: Natural Language Reasoning with First-Order Logic](https://mlsanity.com/paper/2209.00840/) (2022)
- [Large Language Models for Education: A Survey and Outlook](https://mlsanity.com/paper/2403.18105/) (2024)
- [MathDial: A Dialogue Tutoring Dataset with Rich Pedagogical Properties Grounded in Math Reasoning Problems](https://mlsanity.com/paper/2305.14536/) (2023)
- [Solving Math Word Problems by Combining Language Models With Symbolic Solvers](https://mlsanity.com/paper/2304.09102/) (2023)
- [Testing the General Deductive Reasoning Capacity of Large Language Models Using OOD Examples](https://mlsanity.com/paper/2305.15269/) (2023)
- [The AI Teacher Test: Measuring the Pedagogical Ability of Blender and GPT-3 in Educational Dialogues](https://mlsanity.com/paper/2205.07540/) (2022)
- [LogicBench: Towards Systematic Evaluation of Logical Reasoning Ability of Large Language Models](https://mlsanity.com/paper/2404.15522/) (2024)
- [Unifying AI Tutor Evaluation: An Evaluation Taxonomy for Pedagogical Ability Assessment of LLM-Powered AI Tutors](https://mlsanity.com/paper/2412.09416/) (2024)
- [Stepwise Verification and Remediation of Student Reasoning Errors with Large Language Model Tutors](https://mlsanity.com/paper/2407.09136/) (2024)
- [Enhancing LLM-Based Feedback: Insights from Intelligent Tutoring Systems and the Learning Sciences](https://mlsanity.com/paper/2405.04645/) (2024)
- [Generating High-Precision Feedback for Programming Syntax Errors using Large Language Models](https://mlsanity.com/paper/2302.04662/) (2023)
- [How to Teach Programming in the AI Era? Using LLMs as a Teachable Agent for Debugging](https://mlsanity.com/paper/2310.05292/) (2023)
- [Automating Human Tutor-Style Programming Feedback: Leveraging GPT-4 Tutor Model for Hint Generation and GPT-3.5 Student Model for Hint Validation](https://mlsanity.com/paper/2310.03780/) (2023)
- [Jill Watson: A Virtual Teaching Assistant powered by ChatGPT](https://mlsanity.com/paper/2405.11070/) (2024)
- [Logic-of-Thought: Injecting Logic into Contexts for Full Reasoning in Large Language Models](https://mlsanity.com/paper/2409.17539/) (2024)
- [Next-Step Hint Generation for Introductory Programming Using Large Language Models](https://mlsanity.com/paper/2312.10055/) (2023)
- [Combining Large Language Models with Tutoring System Intelligence: A Case Study in Caregiver Homework Support](https://mlsanity.com/paper/2412.11995/) (2024)
- [Hints-In-Browser: Benchmarking Language Models for Programming Feedback Generation](https://mlsanity.com/paper/2406.05053/) (2024)

## Built on by (most cited first, 1 of 1)

- [PAPPL: Personalized AI-Powered Progressive Learning Platform](https://mlsanity.com/paper/2508.14109/) (2025)

## Abstract (arXiv)

Intelligent tutoring systems have demonstrated effectiveness in teaching formal propositional logic proofs, but their reliance on template-based explanations limits their ability to provide personalized student feedback. While large language models (LLMs) offer promising capabilities for dynamic feedback generation, they risk producing hallucinations or pedagogically unsound explanations. We evaluated the stepwise accuracy of LLMs in constructing multi-step symbolic logic proofs, comparing six prompting techniques across four state-of-the-art LLMs on 358 propositional logic problems. Results show that DeepSeek-V3 achieved superior performance up to 86.7% accuracy on stepwise proof construction and excelled particularly in simpler rules. We further used the best-performing LLM to generate explanatory hints for 1,050 unique student problem-solving states from a logic ITS and evaluated them on 4 criteria with both an LLM grader and human expert ratings on a 20% sample. Our analysis finds that LLM-generated hints were 75% accurate and rated highly by human evaluators on consistency and clarity, but did not perform as well explaining why the hint was provided or its larger context. Our results demonstrate that LLMs may be used to augment tutoring systems with logic tutoring hints, but require additional modifications to ensure accuracy and pedagogical appropriateness.