SymBa: Symbolic Backward Chaining for Multi-step Natural Language Reasoning

Large Language Models (LLMs) have recently demonstrated remarkable reasoning ability as in Chain-of-thought prompting, but faithful multi-step reasoning remains a challenge. We specifically focus on backward chaining, where the query is recursively decomposed using logical rules until proven. To address the limitations of current backward chaining implementations, we propose SymBa (Symbolic Backward Chaining). In SymBa, the symbolic top-down solver controls the entire proof process and the LLM is called to generate a single reasoning step only when the solver encounters a dead end. By this novel solver-LLM integration, while being able to produce an interpretable, structured proof, SymBa achieves significant improvement in performance, proof faithfulness, and efficiency in diverse multi-step reasoning benchmarks (ProofWriter, Birds-Electricity, GSM8k, CLUTRR-TF, ECtHR Article 6) compared to backward chaining baselines.