<p>In recent years, the field of AI &amp; Law has increasingly focused on predicting legal judgments, particularly in civil cases. While traditional neural network methods are highly effective at automatically learning patterns from large datasets, they often suffer from a lack of interpretability. To address this limitation, we propose a neuro-symbolic framework for legal judgment prediction, based on large language models (LLMs). This framework combines legal knowledge (e.g., legal rules), represented through first-order logic rules, with deep neural networks (DNNs), using a discrepancy loss to minimize prediction differences between the two components. By integrating the logic module during end-to-end training, knowledge is effectively transferred to the model parameters. Additionally, we develop a Chain-of-Thought prompt that uses LLMs to extract fact elements from legal cases. These elements act as logical variables within the rules, supporting the reasoning process in the logic module and improving overall interpretability. To validate the effectiveness of this framework, we conduct extensive experiments on a large dataset of private lending cases. The results demonstrate that the framework not only improves predictive performance but also enhances the interpretability of judgment predictions.</p>