A growing body of work studies how to answer a question or verify a claim by generating a natural language "proof": a chain of deductive inferences yielding the answer based on a set of premises. However, these methods can only make sound deductions when they follow from evidence that is given. We propose a new system that can handle the underspecified setting where not all premises are stated at the outset; that is, additional assumptions need to be materialized to prove a claim. By using a natural language generation model to abductively infer a premise given another premise and a conclusion, we can impute missing pieces of evidence needed for the conclusion to be true. Our system searches over two fringes in a bidirectional fashion, interleaving deductive (forward-chaining) and abductive (backward-chaining) generation steps. We sample multiple possible outputs for each step to achieve coverage of the search space, at the same time ensuring correctness by filtering low-quality generations with a round-trip validation procedure. Results on a modified version of the EntailmentBank dataset and a new dataset called Everyday Norms: Why Not? show that abductive generation with validation can recover premises across in- and out-of-domain settings

翻译：越来越多的研究致力于通过生成自然语言“证明”来回答问题或验证主张：即基于一组前提，通过一系列演绎推理得出答案的链条。然而，这些方法仅在推理源自给定证据时才能作出合理的推断。我们提出了一种新系统，能够处理未明确指定的场景，即并非所有前提在初始阶段都已陈述；换言之，需要具体化额外的假设来证明某个主张。通过使用自然语言生成模型，基于一个前提和结论进行溯因推理来推断缺失的前提，我们可以填补使结论成立所需的缺失证据片段。我们的系统以双向方式搜索两个边界，交织演绎（前向链）和溯因（后向链）生成步骤。我们对每一步的多个可能输出进行采样，以覆盖搜索空间，同时通过往返验证程序过滤低质量生成来确保正确性。在修改版EntailmentBank数据集和名为《日常规范：为何不？》的新数据集上的实验结果表明，结合验证的溯因生成能够恢复域内和域外场景中的前提。