Self-organized logic inference through 2-satisfiability dynamics in neural energy systems

The integration of symbolic reasoning and neural dynamics provides a promising nonlinear-systems perspective for understanding how logic constraints emerge within distributed computational media. Existing neuro-symbolic architectures often suffer from instability and overfitting when reasoning over complex logical manifolds such as 3-Satisfiability, revealing unresolved issues of dynamic equilibrium and self-organization in high-dimensional information spaces. To address these challenges, this study introduces a Forward 2-Satisfiability Reverse Analysis (F2SATRA) framework based on the Discrete Hopfield Neural Network (DHNN), in which mean-field interactions and energy-minimization principles govern the fusion of multiple information sources. From the standpoint of nonlinear dynamics, the proposed system performs decision-level fusion through the co-evolution of symbolic rules and neural states, producing emergent attractors that correspond to stable logical solutions. Analytical formulations demonstrate that F2SATRA reduces redundant attributes while preserving the energetic consistency of the decision landscape. Numerical experiments further reveal the framework's capacity to maintain global stability and robustness under imbalanced conditions, indicating potential applications to complex, self-organizing decision systems. The results provide new insights into nonlinear information fusion, collective reasoning, and energy-based logic computation within the broader context of nonlinear science and complex adaptive networks.