Large Language Models (LLMs) have achieved impressive results across numerous domains, yet they experience notable deficiencies in legal question-answering tasks. LLMs often generate generalized responses that lack the logical specificity required for expert legal advice and are prone to hallucination, providing answers that appear correct but are unreliable. Retrieval-Augmented Generation (RAG) techniques offer partial solutions to address this challenge, but existing approaches typically focus only on semantic similarity, neglecting the logical structure essential to legal reasoning. In this paper, we propose the Logical-Semantic Integration Model (LSIM), a novel supervised framework that bridges semantic and logical coherence. LSIM comprises three components: reinforcement learning predicts a structured fact-rule chain for each question, a trainable Deep Structured Semantic Model (DSSM) retrieves the most relevant candidate questions by integrating semantic and logical features, and in-context learning generates the final answer using the retrieved content. Our experiments on a real-world legal QA dataset-validated through both automated metrics and human evaluation-demonstrate that LSIM significantly enhances accuracy and reliability compared to existing methods.