Contributions to AI: This paper proposes a neuro-symbolic search architecture integrating discrete rule-based logic with lightweight Neural Network Feedback Control (NNFC). Utilizing cascade filtering to isolate neural mispredictions while dynamically compensating for static heuristic biases, the framework theoretically guarantees search stability and efficiency in massive discrete state spaces. Contributions to Engineering Applications: The framework provides a scalable, divide-and-conquer solution coordinating heterogeneous rule-sets in knowledge-intensive industrial systems (e.g., multi-domain relational inference and symbolic derivation), eliminating maintenance bottlenecks and state-space explosion of monolithic reasoning engines. Modern industrial AI requires dynamic orchestration of modular domain logic, yet reliable cross-domain rule management remains lacking. We address this with Chain-Oriented Objective Logic (COOL), a high-performance neuro-symbolic framework introducing: (1) Chain-of-Logic (CoL), a divide-and-conquer paradigm partitioning complex reasoning into expert-guided, hierarchical sub-DSLs via runtime keywords; and (2) Neural Network Feedback Control (NNFC), a self-correcting mechanism using lightweight agents and a cascade filtering architecture to suppress erroneous predictions and ensure industrial-grade reliability. Theoretical analysis establishes complexity bounds and Lyapunov stability. Ablation studies on relational and symbolic tasks show CoL achieves 100% accuracy (70% improvement), reducing tree operations by 91% and accelerating execution by 95%. Under adversarial drift and forgetting, NNFC further improves accuracy and reduces computational cost by 64%.