MATHEMATICAL LOGIC AS THE ENGINE OF AUTONOMOUS DECISION INTELLIGENCE IN DIGITAL SYSTEMS

Artificial intelligence has accelerated global transformation, yet the lack of logical reasoning within machine learning systems limits their reliability, ethical consistency, and adaptability. This research explored how mathematical logic enhances autonomous decision intelligence by integrating symbolic reasoning, probabilistic inference, and algorithmic optimization into reinforcement learning frameworks. Using secondary data from the S&P Global 1200 firms across 31 countries between 2020 and 2024, the study applied multilevel structural equation modeling and machine learning validation to examine logic-driven adaptability in AI systems. The results revealed strong positive relationships between logic-based reasoning and decision accuracy (β = 0.41), probabilistic inference and ethical consistency (β = 0.29), and algorithmic optimization and learning efficiency (β = 0.22), with computational adaptability moderating these effects (R² = 0.71; F = 18.4; p < 0.01). These findings demonstrate that logic-embedded models significantly improve interpretability, transparency, and ethical accountability across autonomous decision frameworks. This research contributes to theory by extending Reinforcement Learning Theory through the addition of mathematical logic as a structural determinant of rational adaptability, thereby broadening its explanatory scope and offering a refined framework for understanding decision intelligence in global digital systems. The study holds practical value for AI governance, corporate automation, and international policy on ethical artificial intelligence. It also highlights how logic-integrated reinforcement systems can align machine decisions with human reasoning, bridging a critical gap in global AI ethics and governance.