Current knowledge editing methods for large language models (LLMs) struggle to maintain logical consistency when propagating ripple effects to associated facts. We propose ChainEdit, a framework that synergizes knowledge graph-derived logical rules with LLM logical reasoning capabilities to enable systematic chain updates. By automatically extracting logical patterns from structured knowledge bases and aligning them with LLMs' internal logics, ChainEdit dynamically generates and edits logically connected knowledge clusters. Experiments demonstrate an improvement of more than 30% in logical generalization over baselines while preserving editing reliability and specificity. We further address evaluation biases in existing benchmarks through knowledge-aware protocols that disentangle external dependencies. This work establishes new state-of-the-art performance on ripple effect while ensuring internal logical consistency after knowledge editing.