Neuro-symbolic reasoning aims to combine the pattern-recognition power of deep learning with the structure and guarantees of symbolic logic, but progress is fragmented and largely architecture-driven. This paper takes a question-first perspective. We first review subsymbolic and symbolic approaches and propose a unifying taxonomy of neuro-symbolic paradigms: logic-guided learning, differentiable logic, program synthesis and neural program induction, and constraint-based training. Building on this taxonomy, we identify four cross-cutting challenge axes—optimization and stability under symbolic constraints, expressivity and compositional generalization, semantics and explainability, and data and symbol grounding. Along these axes, we formulate eight concrete open problems that cut across existing models and benchmarks. We conclude with a roadmap highlighting short-, medium-, and long-term directions. The result is a structured agenda for turning neuro-symbolic reasoning from a collection of techniques into a principled, scalable paradigm.
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