LogicSAGE: Neuro-Symbolic Reasoning with Socratic-Guided Enhancement

Large Language Models (LLMs) often struggle with complex logical reasoning. Existing approaches typically rely on either purely neural reasoning in natural language or offloading to formal solvers via symbolic representations. However, both paradigms face significant limitations: while LLMs exhibit strong semantic intuition they are prone to hallucinations, whereas symbolic solvers offer rigorous derivation but remain highly sensitive to minor syntactic errors. To combine the strengths of these two paradigms while mitigating their respective limitations, we introduce LogicSAGE (Logic-informed Socratic Agent for Guided Enhancement), a dual-process framework that integrates a robust neural reasoner (System 1) with a rigorous symbolic validator (System 2). Specifically, our framework employs a Socratic Error Correction mechanism that treats solver feedback not as terminal failures but as pedagogical signals, engaging in a dialectic loop to iteratively refine logic programs and resolve semantic ambiguities. Extensive experiments on five benchmarks show that LogicSAGE (8B) achieves a state-of-the-art 92.36% average accuracy, significantly outperforming GPT-4 baselines, which establishes that architectural innovation can supersede model scale in faithful reasoning.

Large language models (LLMs) are powerful at understanding language but often struggle with complex logical puzzles, frequently making confident yet incorrect guesses. Conversely, traditional computer programs can solve logic perfectly but fail when instructions are even slightly ambiguous. Our paper introduces "LogicSAGE," a new AI framework that combines the best of both worlds: it uses an LLM to interpret natural language and a rigorous logic checker to verify the reasoning. Uniquely, our system acts like a thoughtful tutor, engaging in a back-and-forth dialogue to catch and correct subtle errors that other systems miss. This approach allows smaller, more efficient AI models to outperform much larger ones in logical reasoning, paving the way for more reliable and trustworthy AI assistants in fields like law, medicine, and science.