Retrieval-Augmented Generation (RAG) is widely used to ground large language models (LLMs) in external knowledge and improve factual accuracy. Prior work has explored iterative and self-reflective mechanisms to refine reasoning, but these approaches rely on internal model judgment and lack formally grounded, verifiable feedback. As a result, RAG systems may still produce logically inconsistent or contradictory answers in multi-step reasoning. In this paper, we propose LCR-RAG, a framework that integrates neuro-symbolic verification with reinforcement learning to explicitly optimize logical consistency. The core of our approach is a Logic-Consistency-driven Reward (LCR), which converts discrete logical signals—such as contradictions or incomplete inference chains—into a structured reward signal. This reward guides a PPO-based agent to iteratively rewrite queries and correct reasoning errors. Experiments on HotpotQA, ASQA, and TriviaQA show that LCR-RAG consistently outperforms strong RAG baselines, with ablation results indicating that the LCR mechanism is the primary source of improvement, even under noisy or conflicting retrieval conditions.

Reinforcement Learning from Human Feedback (RLHF) is crucial for aligning large language models (LLMs) with human values. However, it has been noted that reward models in RLHF often exhibit unintended biases, such as an overemphasis on response length based on the erroneous assumption that longer responses are universally preferred. This “length bias” can lead to excessively verbose responses that compromise the quality of LLMs alignment. Previous efforts to mitigate length bias in reward models have inadvertently decreased their accuracy by neglecting the legitimate influence of response length on human preferences. In this work, we argue that response length is a context-specific factor in human evaluations, with different queries naturally eliciting varying preferences for response length. We propose an adaptive approach to modeling length preference that dynamically adjusts the influence of response length in reward evaluations according to the context of the query. Experimental results demonstrate that our adaptive approach effectively balances the mitigation of undesired length hacking and alignment accuracy, reducing unnecessary verbosity while improving overall response quality.