Go to AAAI 2026 Bridge LMReasoning homepageLogical-SAGE: A Logical Socratic Architecture for Guided Evolution in Neuro-Symbolic Reasoning
Keywords: Neuro-Symbolic Reasoning, LLM
Abstract: While Large Language Models (LLMs) excel at semantic understanding, they fundamentally lack the rigorous deductive reliability required for complex reasoning, often succumbing to hallucinations. Neuro-Symbolic (NeSy) approaches attempt to bridge this gap by offloading reasoning to formal solvers, yet they suffer from a critical \textit{``Translation Fragility''} bottleneck: a single syntactic error in the generated logic program causes catastrophic execution failure. Existing paradigms typically adopt a \textit{Generate-and-Hope} strategy, treating the solver as a binary judge and discarding imperfect code. In this paper, we introduce \textbf{Logical-SAGE} (\textbf{L}ogic-informed \textbf{S}ocratic \textbf{A}gent for \textbf{G}uided \textbf{E}volution), a novel Dual-Process architecture that shifts the paradigm to \textit{Guided Evolution.} Synergizing a \textit{System 1} neural reasoner with a \textit{System 2} symbolic validator, our framework features a \textit{Socratic Error Correction} mechanism. Instead of rejecting failed programs, Logical-SAGE treats solver error messages as pedagogical feedback, engaging in a dialectic loop to iteratively repair and evolve logic programs towards executability. We further introduce an Adaptive Fusion mechanism to balance rigorous proofs with robust neural intuition. Extensive experiments on five benchmarks (FOLIO, ProofWriter, ProntoQA, LogicalDeduction, AR-LSAT) demonstrate a breakthrough result: Logical-SAGE, powered by a parameter-efficient 8B model (Qwen-3-8B), achieves a new state-of-the-art average accuracy of 90.42\%, significantly outperforming baselines relying on the massive GPT-4. This establishes that architectural innovation can supersede model scale in achieving faithful and grounded reasoning.
Submission Number: 78
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