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

TL;DR

This paper investigates the internal computational strategies of large language models during propositional logical reasoning, revealing a structured architecture with four key mechanisms that generalize across models and reasoning types.

Contribution

It provides the first detailed mechanistic analysis of how LLMs organize computation for propositional reasoning, identifying four core mechanisms involved.

Findings

Models use staged computation and information flow strategies.

Persistent fact re-access supports reasoning accuracy.

Mechanisms are consistent across model sizes and reasoning depths.

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.