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

arXiv: https://arxiv.org/abs/2601.04260 · HTML: https://mlsanity.com/paper/2601.04260/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 3 of its 34 references that are in the map.
- First posted on arXiv 7 Jan 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 3 of 3)

- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [Causal Mediation Analysis for Interpreting Neural NLP: The Case of Gender Bias](https://mlsanity.com/paper/2004.12265/) (2020)
- [Language Models Use Trigonometry to Do Addition](https://mlsanity.com/paper/2502.00873/) (2025)

## Built on by (most cited first, 1 of 1)

- [Complementary Roles of Activation and Parametric Memory in Few-Shot Learning](https://mlsanity.com/paper/2609.28250/) (2026)

## Abstract (arXiv)

Understanding how Large Language Models (LLMs) perform logical reasoning internally remains a fundamental challenge. While prior mechanistic studies focus on identifying task specific circuits, they leave open the question of what computational strategies LLMs employ for propositional reasoning. We address this gap with a causal mechanistic analysis on PropLogic-MI, a controlled benchmark of 11 propositional rules across one- and two-hop tasks, applied to three model families (Qwen3, Llama-3.1, Mistral). Rather than asking which components are necessary, we ask how the reasoning process is organized, and identify four interlocking mechanisms: Staged Computation, where early, middle, and late layers take on distinct functional roles; Information Transmission, where semantic content aggregates at boundary tokens; Fact Retrospection, where fact tokens stay causally active as binding lookup in middle layers and as sustained access in late layers under hard reasoning loads; and Specialized Attention Heads that structurally implement these patterns. A prompt-order control that places the query before the facts confirms that this organization is model-internal rather than input-layout-induced. These findings show that pretrained LLMs solve propositional reasoning through a structured, layer-organized process that recurs across models, rule categories, and reasoning hops.