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.

Large language models (LLMs) have shown impressive reasoning capabilities through Chain-of-Thought (CoT). However, the reasoning processes remain inexplicable and uncontrollable. In this paper, we tackle the task hosted by (CITATION) by introducing a Step-Wise Reasoning and Verification (SWRV) framework, a two-stage Parser–Verifier one, that decomposes generated reasoning process into discrete inference steps and rigorously validates each one. First, our Parser extracts problem constraints and the sequence of reasoning steps from the LLM’s reasoning process. Then, our Verifier prompts itself or leverages a deterministic symbolic solver to formally check the logical correctness of every step. To ensure robust parsing, we also fine‐tune a compact LM on a small, high‐quality annotation set produced by a more powerful LLM. Experiments on the dataset (CITATION) demonstrate significant gains over baseline approaches, illustrating the effectiveness of our method for step‐wise analysis of LLM chain-of-thought reasoning. The code is publicly available at https://github.com/Teganone/XLLM_LLMSRhttps://github.com/Teganone/XLLM_LLMSR.