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

Abstract: 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 LLM 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.