Symbolic-Neural Soft-Logic Reasoning: Towards Robust and Verifiable Thinking Chains via Cooperative Evolution

Abstract

Large Language Models (LLMs) have demonstrated impressive progress in complex reasoning tasks, largely driven by the Chain-of-Thought (CoT) paradigm, which decomposes difficult problems into intermediate steps. However, CoT reasoning remains fundamentally constrained by the probabilistic nature of neural generation, leading to unfaithful reasoning chains that undermine reliability. Neuro-symbolic approaches attempt to address these issues by combining LLMs with symbolic solvers, yet they face persistent challenges, including hallucinated translations, the mismatch between natural language and formal logic, and the limited enhancement of the LLM's intrinsic reasoning ability. To overcome these limitations, we propose Symbolic-Neural Soft-Logic Reasoning (SSR), a unified framework that integrates LLMs with symbolic reasoning and improves robustness by relaxing strict logical determinism while preserving verifiability. Our approach improves reasoning performance, automatically generates verifiable and human-like logical thinking chains for training and fine-tuning, and facilitates cross-disciplinary applications such as AI for mathematics. Experiments across multiple models and benchmarks demonstrate that SSR consistently outperforms existing reasoning frameworks, highlighting its effectiveness in enhancing both the robustness and interpretability of LLM reasoning.