Reasoning over natural language is a challenging problem in NLP. In this work, we focus on proof generation: Given a hypothesis and a set of supporting facts, the model generates a proof tree indicating how to derive the hypothesis from supporting facts. Compared to generating the entire proof in one shot, stepwise generation can better exploit the compositionality and generalize to longer proofs but has achieved limited success on real-world data. Existing stepwise methods struggle to generate proof steps that are both logically valid and relevant to the hypothesis. Instead, they tend to hallucinate invalid steps given the hypothesis. In this paper, we present a novel stepwise method, NLProofS (Natural Language Proof Search), which learns to generate relevant steps conditioning on the hypothesis. At the core of our approach, we train an independent verifier to check the validity of the proof steps to prevent hallucination. Instead of generating steps greedily, we search for proofs maximizing a global proof score judged by the verifier. NLProofS achieves state-of-the-art performance on EntailmentBank and RuleTaker. Specifically, it improves the correctness of predicted proofs from 27.7% to 33.3% in the distractor setting of EntailmentBank, demonstrating the effectiveness of NLProofS in generating challenging human-authored proofs.
- Pub Date:
- May 2022
- Computer Science - Computation and Language;
- Computer Science - Machine Learning;
- Computer Science - Logic in Computer Science
- EMNLP 2022. Code and models are available at https://github.com/princeton-nlp/NLProofS. v3 added evaluation of GPT-3 and Codex