用于大语言模型逻辑推理的符号逻辑六边形理论

中文摘要 AI 辅助

大语言模型已成为语言理解和逻辑推理的强大工具，但在需要理解语义和遵循逻辑的问题上仍会出错。关键原因是自然语言陈述在正式推理前常带有隐含语义关系，若这些隐藏含义未妥善组织，即便后续推理过程逻辑有效，模型也可能得出错误结论。现有方法通过分解、符号翻译、外部求解器或自我验证来改进推理，但较少关注推理所依赖的语义结构。本文进一步研究语义组织如何影响大语言模型的逻辑推理，提出HexLogicAgent框架，先组织自然语言陈述的含义，再通过结构化验证指导逻辑推理。研究发现不完整的语义表示而非演绎推理本身是大语言模型逻辑推理失败的主要来源，明确建模语义对立的完整结构可大幅延迟推理性能随逻辑复杂度增加而下降。在具有挑战性的逻辑推理基准测试上的实验表明，HexLogicAgent能持续提高多个大语言模型的推理可靠性，其核心思想得到逻辑六边形理论支持，该理论解释了为何对立含义的完整结构对可靠推理是必要的。

英文摘要

Large language models (LLMs) have become powerful tools for language understanding and logical reasoning. However, they still make mistakes when a problem requires both understanding meaning and following logic. A key reason is that natural-language statements often carry implicit semantic relations before any formal reasoning begins. If these hidden meanings are not properly organized, the model may reach incorrect conclusions even when the subsequent reasoning process appears logically valid. Existing methods improve reasoning through decomposition, symbolic translation, external solvers, or self-verification, but pay comparatively less attention to the semantic structure on which reasoning depends. In this paper, we further investigate how semantic organization influences logical reasoning in LLMs. To this end, we propose HexLogicAgent, a framework that first organizes the meaning of natural-language statements and then guides logical reasoning through structured verification. In our investigation, we also make two observations. First, incomplete semantic representations, rather than deductive inference itself, are a major source of logical reasoning failures in LLMs. Second, explicitly modeling the complete structure of semantic opposition substantially delays the degradation of reasoning performance as logical complexity increases. Experiments on challenging logical reasoning benchmarks demonstrate that HexLogicAgent consistently improves reasoning reliability across multiple LLMs. The core idea is supported by a logical hexagon theory, which explains why a complete structure of opposing meanings is necessary for reliable reasoning.

发表机构

• Huazhong University of Science and Technology（华中科技大学）

机构由 AI 辅助整理，请以论文原文为准。