# Towards Logically Sound Natural Language Reasoning with Logic-Enhanced Language Model Agents

arXiv: https://arxiv.org/abs/2408.16081 · HTML: https://mlsanity.com/paper/2408.16081/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 21 of its 37 references that are in the map.
- First posted on arXiv 28 Aug 2024.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 21 of 21)

- [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)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Generative Agents: Interactive Simulacra of Human Behavior](https://mlsanity.com/paper/2304.03442/) (2023)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofs](https://mlsanity.com/paper/2210.12283/) (2022)
- [Autoformalization with Large Language Models](https://mlsanity.com/paper/2205.12615/) (2022)
- [MathPrompter: Mathematical Reasoning using Large Language Models](https://mlsanity.com/paper/2303.05398/) (2023)
- [Playing repeated games with Large Language Models](https://mlsanity.com/paper/2305.16867/) (2023)
- [Foundational Challenges in Assuring Alignment and Safety of Large Language Models](https://mlsanity.com/paper/2404.09932/) (2024)
- [LLMs Can't Plan, But Can Help Planning in LLM-Modulo Frameworks](https://mlsanity.com/paper/2402.01817/) (2024)
- [Agent AI: Surveying the Horizons of Multimodal Interaction](https://mlsanity.com/paper/2401.03568/) (2024)
- [Solving Math Word Problems by Combining Language Models With Symbolic Solvers](https://mlsanity.com/paper/2304.09102/) (2023)
- [GTBench: Uncovering the Strategic Reasoning Limitations of LLMs via Game-Theoretic Evaluations](https://mlsanity.com/paper/2402.12348/) (2024)
- [Can Large Language Models Serve as Rational Players in Game Theory? A Systematic Analysis](https://mlsanity.com/paper/2312.05488/) (2023)
- [LLM-based NLG Evaluation: Current Status and Challenges](https://mlsanity.com/paper/2402.01383/) (2024)
- [nl2spec: Interactively Translating Unstructured Natural Language to Temporal Logics with Large Language Models](https://mlsanity.com/paper/2303.04864/) (2023)
- [NL2TL: Transforming Natural Languages to Temporal Logics using Large Language Models](https://mlsanity.com/paper/2305.07766/) (2023)
- [Coupling Large Language Models with Logic Programming for Robust and General Reasoning from Text](https://mlsanity.com/paper/2307.07696/) (2023)
- [Language Models can be Logical Solvers](https://mlsanity.com/paper/2311.06158/) (2023)
- [Fifty Years of Prolog and Beyond](https://mlsanity.com/paper/2201.10816/) (2022)

## Built on by (most cited first, 5 of 5)

- [A Survey of Context Engineering for Large Language Models](https://mlsanity.com/paper/2507.13334/) (2025)
- [Approximating Human Strategic Reasoning with LLM-Enhanced Recursive Reasoners Leveraging Multi-agent Hypergames](https://mlsanity.com/paper/2502.07443/) (2025)
- [Autoformalization of Game Descriptions using Large Language Models](https://mlsanity.com/paper/2409.12300/) (2024)
- [The Influence of Human-inspired Agentic Sophistication in LLM-driven Strategic Reasoners](https://mlsanity.com/paper/2505.09396/) (2025)
- [VeryTrace: Verifying Reasoning Traces through Compilable Formalism and Structured Verification](https://mlsanity.com/paper/2606.24124/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are increasingly explored as general-purpose reasoners, particularly in agentic contexts. However, their outputs remain prone to mathematical and logical errors. This is especially challenging in open-ended tasks, where unstructured outputs lack explicit ground truth and may contain subtle inconsistencies. To address this issue, we propose Logic-Enhanced Language Model Agents (LELMA), a framework that integrates LLMs with formal logic to enable validation and refinement of natural language reasoning. LELMA comprises three components: an LLM-Reasoner, an LLM-Translator, and a Solver, and employs autoformalization to translate reasoning into logic representations, which are then used to assess logical validity. Using game-theoretic scenarios such as the Prisoner's Dilemma as testbeds, we highlight the limitations of both less capable (Gemini 1.0 Pro) and advanced (GPT-4o) models in generating logically sound reasoning. LELMA achieves high accuracy in error detection and improves reasoning correctness via self-refinement, particularly in GPT-4o. The study also highlights challenges in autoformalization accuracy and in evaluation of inherently ambiguous open-ended reasoning tasks.