Abstract

Artificial intelligence research has historically been shaped by two dominant paradigms: logic-based symbolic reasoning and probability-based uncertainty modeling. While logic-based AI emphasizes formal deduction, structured knowledge, and explainability, probabilistic AI focuses on reasoning under uncertainty and incomplete evidence. More recently, these paradigms have converged in probabilistic logic systems and neuro-symbolic architectures, which integrate symbolic structure with statistical learning. This paper provides a structured review of these four interconnected strands—logic-based AI, probabilistic AI, probabilistic logic, and neuro-symbolic AI—highlighting their theoretical foundations, recent advances, and emerging convergence. The analysis shows that modern AI systems increasingly treat logic as a structure for reasoning, probability as a mechanism for uncertainty, and neural networks as a computational substrate that links both.

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