Social media has greatly accelerated the speed of information dissemination, but it has also inevitably led to a proliferation of rumors. Due to the deceptive nature of rumors, people often find it difficult to distinguish truth from falsehood, resulting in economic losses and social panic. Existing pre-trained models often focus on keywords while neglecting logic, making them prone to semantic traps. To address this, we propose the Logic-Reasoning Augmented DeBERTa (LoRAD) model. LoRAD utilizes an LLM to generate logical evidence and leverages DeBERTa’s disentangled attention mechanism to effectively integrate this evidence with the source text. We evaluate our method on three public datasets and a newly constructed dataset, Twitter26-Mini. Results show that LoRAD achieves state-of-the-art performance on all datasets. Furthermore, experiments demonstrate that LoRAD offers better performance and robustness than large language models (LLMs) while maintaining high inference speed, making it suitable for real-time rumor detection.