Chain-Oriented Objective Logic with Neural Network Feedback Control and Cascade Filtering for Dynamic Multi-DSL Regulation

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%.

💡 Research Summary

**
The paper introduces COOL (Chain‑Oriented Objective Logic), a neuro‑symbolic framework designed to regulate multiple domain‑specific languages (DSLs) in industrial AI systems. The authors identify a “multi‑DSL regulation paradox”: while modular DSLs are needed for scalability, their interleaved rule application can cause state‑space explosion, nondeterminism, and maintenance overhead. COOL resolves this paradox through two complementary components.

1. Chain‑of‑Logic (CoL) – a divide‑and‑conquer paradigm that partitions a complex reasoning task into expert‑guided sub‑DSLs (G1…G4). Each rule is annotated with a heuristic vector that defines its applicability to a particular sub‑DSL. Runtime control primitives—return, logicjump(n), and abort—act as discrete transition operators, governing deterministic progression, recursion, and early termination of the reasoning chain. By constraining rule application to the appropriate sub‑DSL, CoL reduces the effective branching factor, yielding a theoretical complexity reduction from quadratic to near‑linear (O(N log N)) and an empirical 91 % decrease in tree operations together with a 95 % latency improvement.

2. Neural Network Feedback Control (NNFC) – a set of lightweight neural agents, one per sub‑DSL, that continuously monitor the execution of CoL and provide adaptive compensation for heuristic biases. NNFC employs a cascade‑filtering architecture: predictions flow through multiple sequential filters that amplify discrepancies, allowing erroneous outputs to be blocked before they affect downstream reasoning. The authors formalize NNFC as a feedback control system and prove Lyapunov stability, showing that the Lyapunov function V(x) satisfies dV/dt ≤ ‑αV (α > 0), guaranteeing global convergence even under non‑stationary conditions.

Theoretical contributions include formal proofs of CoL’s expressiveness and complexity bounds, and a stability analysis of NNFC. Empirically, the authors evaluate COOL on two benchmark domains—relational reasoning and symbolic derivation. In static settings, CoL alone raises accuracy by 70 % to reach 100 %, cuts tree operations by 91 %, and speeds execution by 95 % relative to an unregulated baseline. In dynamic settings with drift and forgetting, adding NNFC further improves accuracy by ~6 % and reduces computational cost by 64 %. Figures illustrate static performance (deterministic accuracy, reduced search space) and dynamic performance (robustness of NNFC under changing conditions).

Despite these promising results, several limitations are evident. The experimental evaluation is confined to two synthetic benchmarks; broader validation on real‑world industrial workloads is missing. Comparisons against strong baselines such as monolithic large language models or existing neural‑guided search methods are absent, making it difficult to assess relative advantage. Implementation details of the “lightweight” neural agents (architecture depth, parameter count) and cascade filter thresholds are not disclosed, hindering reproducibility. Moreover, the paper does not provide public code or datasets, limiting external verification.

In summary, COOL offers an innovative combination of hierarchical symbolic control and adaptive neural feedback, addressing a critical gap in modular industrial AI. Its theoretical analysis and initial empirical gains suggest high potential, but further work—especially extensive real‑world testing, detailed ablation of neural components, and open‑source release—is required before the approach can be considered mature for deployment in safety‑critical industrial environments.