IFDNS: An Iterative Feedback-Driven Neuro-Symbolic Method for Faithful Logical Reasoning

Large language models (LLMs) have demonstrated impressive capabilities across a wide range of reasoning tasks, including logical and mathematical problem-solving. While prompt-based methods like Chain-of-Thought (CoT) can enhance LLM reasoning abilities to some extent, they often suffer from a lack of faithfulness, where the derived conclusions may not align with the generated reasoning chain. To address this issue, researchers have explored neuro-symbolic approaches to bolster LLM logical reasoning capabilities. However, existing neuro-symbolic methods still face challenges with information loss during the process. To overcome these limitations, we introduce Iterative Feedback-Driven Neuro-Symbolic (IFDNS), a novel prompt-based method that employs a multi-round feedback mechanism to address LLM limitations in handling complex logical relationships. IFDNS utilizes iterative feedback during the logic extraction phase to accurately extract causal relationship statements and translate them into propositional and logical implication expressions, effectively mitigating information loss issues. Furthermore, IFDNS is orthogonal to existing prompt methods, allowing for seamless integration with various prompting approaches. Empirical evaluations across six datasets demonstrate the effectiveness of IFDNS in significantly improving the performance of CoT and Chain-of-Thought with Self-Consistency (CoT-SC). Specifically, IFDNS achieves a +9.40% accuracy boost for CoT on the LogiQA dataset and a +11.70% improvement for CoT-SC on the PrOntoQA dataset.