LAMBADA: Backward Chaining for Automated Reasoning in Natural Language

Remarkable progress has been made on automated reasoning with knowledge specified as unstructured, natural text, by using the power of large language models (LMs) coupled with methods such as Chain-of-Thought prompting and Selection-Inference. These techniques search for proofs in the forward direction from axioms to the conclusion, which suffers from a combinatorial explosion of the search space, and thus high failure rates for problems requiring longer chains of reasoning. The classical automated reasoning literature has shown that reasoning in the backward direction (i.e. from the intended conclusion to the set of axioms that support it) is significantly more efficient at proof-finding problems. We import this intuition into the LM setting and develop a Backward Chaining algorithm, which we call LAMBADA, that decomposes reasoning into four sub-modules, each of which can be simply implemented by few-shot prompted LM inference. We show that LAMBADA achieves massive accuracy boosts over state-of-the-art forward reasoning methods on two challenging logical reasoning datasets, particularly when deep and accurate proof chains are required.