Leveraging LLMs for Hypothetical Deduction in Logical Inference: A Neuro-Symbolic Approach

Large Language Models (LLMs) have exhibited remarkable potential across a wide array of reasoning tasks, including logical reasoning. Although massive efforts have been made to empower the logical reasoning ability of LLMs via external logical symbolic solvers, crucial challenges of the poor generalization ability to questions with different features and inevitable question information loss of symbolic solver-driven approaches remain unresolved. To mitigate these issues, we introduce LINA, a LLM-driven neuro-symbolic approach for faithful logical reasoning. By enabling an LLM to autonomously perform the transition from propositional logic extraction to sophisticated logical reasoning, LINA not only bolsters the resilience of the reasoning process but also eliminates the dependency on external solvers. Additionally, through its adoption of a hypothetical-deductive reasoning paradigm, LINA effectively circumvents the expansive search space challenge that plagues traditional forward reasoning methods. Empirical evaluations demonstrate that LINA substantially outperforms both established propositional logic frameworks and conventional prompting techniques across a spectrum of five logical reasoning tasks. Specifically, LINA achieves an improvement of 24.34% over LINC on the FOLIO dataset, while also surpassing prompting strategies like CoT and CoT-SC by up to 24.02%. Our code is available at https://github.com/wufeiwuwoshihua/nshy.

GroupDebate: Enhancing the Efficiency of Multi-Agent Debate Using Group Discussion

In recent years, Large Language Models (LLMs) have demonstrated remarkable capabilities across diverse NLP tasks. Extensive research has explored how to enhance the logical reasoning abilities such as Chain-of-Thought, Chain-of-Thought with Self-Consistency, Tree-Of-Thoughts, and multi-agent debates. In the context of multi-agent debates, significant performance improvements can be achieved with an increasing number of agents and debate rounds. However, the escalation in the number of agents and debate rounds can drastically raise the tokens cost of debates, thereby limiting the scalability of the multi-agent debate technique. To better harness the advantages of multi-agent debates in logical reasoning tasks, this paper proposes a method to significantly reduce token cost in multi-agent debates. This approach involves dividing all agents into multiple debate groups, with agents engaging in debates within their respective groups and sharing interim debate results between groups. Comparative experiments across multiple datasets have demonstrated that this method can reduce the total tokens by up to 51.7% during debates and while potentially enhancing accuracy by as much as 25%. Our method significantly enhances the performance and efficiency of interactions in the multi-agent debate.