Neuro-symbolic AI systems integrate neural perception with symbolic reasoning to enable data-efficient, interpretable, and robust intelligence beyond purely neural models. Although this compositional paradigm has shown superior performance in domains such as reasoning, planning, and verification, its deployment remains challenging due to severe inefficiencies in symbolic and probabilistic inference. Through systematic analysis of representative neuro-symbolic workloads, we identify probabilistic logical reasoning as the inefficiency bottleneck, characterized by irregular control flow, low arithmetic intensity, uncoalesced memory accesses, and poor hardware utilization on CPUs and GPUs. This paper presents REASON, an integrated acceleration framework for probabilistic logical reasoning in neuro-symbolic AI. REASON introduces a unified directed acyclic graph representation that captures common structure across symbolic and probabilistic models, coupled with adaptive pruning and regularization. At the architecture level, REASON features a reconfigurable, tree-based processing fabric optimized for irregular traversal, symbolic deduction, and probabilistic aggregation. At the system level, REASON is tightly integrated with GPU streaming multiprocessors through a programmable interface and multi-level pipeline that efficiently orchestrates compositional execution. Evaluated across six neuro-symbolic workloads, REASON achieves 12-50x speedup and 310-681x energy efficiency over desktop and edge GPUs under TSMC 28 nm node. REASON enables real-time probabilistic logical reasoning, completing end-to-end tasks in 0.8 s with 6 mm2 area and 2.12 W power, demonstrating that targeted acceleration of probabilistic logical reasoning is critical for practical and scalable neuro-symbolic AI and positioning REASON as a foundational system architecture for next-generation cognitive intelligence.