Towards a Mechanistic Understanding of Propositional Logical Reasoning in Large Language Models

2026-01-07

arXiv.org

AI Summary

This study investigates the internal computational mechanisms underlying propositional logic reasoning in large language models. Leveraging the PropLogic-MI dataset, the authors conduct an interpretability analysis of Qwen3 (8B/14B) and propose a unified four-component architecture comprising staged computation, information propagation, fact retrieval, and specialized attention heads. Through functional classification of attention heads, cross-layer information flow tracing, and boundary token aggregation, the work systematically reveals how the model orchestrates multi-layer computations to perform both one-hop and two-hop logical inference. The proposed architecture demonstrates robust generalization across model scales, rule types, and reasoning depths, offering mechanistic evidence for the structured logical reasoning capabilities of large language models.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Natural Language Processing: (Large) Language Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Large language models for search

Abstract

Understanding how Large Language Models (LLMs) perform logical reasoning internally remains a fundamental challenge. While prior mechanistic studies focus on identifying taskspecific circuits, they leave open the question of what computational strategies LLMs employ for propositional reasoning. We address this gap through comprehensive analysis of Qwen3 (8B and 14B) on PropLogic-MI, a controlled dataset spanning 11 propositional logic rule categories across one-hop and two-hop reasoning. Rather than asking''which components are necessary,''we ask''how does the model organize computation?''Our analysis reveals a coherent computational architecture comprising four interlocking mechanisms: Staged Computation (layer-wise processing phases), Information Transmission (information flow aggregation at boundary tokens), Fact Retrospection (persistent re-access of source facts), and Specialized Attention Heads (functionally distinct head types). These mechanisms generalize across model scales, rule types, and reasoning depths, providing mechanistic evidence that LLMs employ structured computational strategies for logical reasoning.

Problem

• propositional logic
• logical reasoning
• large language models
• mechanistic understanding
• computational strategies

Innovation

• mechanistic interpretability
• propositional logic reasoning
• computational architecture
• staged computation
• specialized attention heads