Semiotic logical hexagon theory for LLM logical reasoning

2026-07-23

AI Summary

This work addresses the tendency of large language models to err in tasks requiring both semantic understanding and logical reasoning due to incomplete semantic representations. To mitigate this, the authors propose HexLogicAgent, a novel framework that integrates the Semantic Hexagon theory into large language model reasoning for the first time. By explicitly modeling semantic oppositions, the framework structures natural language inputs into coherent semantic configurations and introduces a verification mechanism grounded in complete semantic structures to guide logical inference. Empirical evaluations across multiple challenging logical reasoning benchmarks demonstrate that HexLogicAgent substantially enhances the reasoning reliability of diverse large language models, thereby confirming the critical role of comprehensive semantic oppositional structures in high-order logical tasks.

Abstract

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.

Problem

• logical reasoning
• semantic structure
• large language models
• implicit semantics
• reasoning reliability

Innovation

• logical hexagon
• semantic opposition
• HexLogicAgent
• semantic organization
• LLM reasoning