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Transformers have been shown to emulate logical deduction over naturallanguage theories (logical rules expressed in natural language), reliablyassigning true/false labels to candidate implications. However, their abilityto generate implications of a theory has not yet been demonstrated, and methodsfor reconstructing proofs of answers are imperfect. In this work we show that agenerative model, called ProofWriter, can reliably generate both implicationsof a theory and the natural language proof(s) that support them. In particular,iterating a 1-step implication generator results in proofs that are highlyreliable, and represent actual model decisions (rather than post-hocrationalizations). On the RuleTaker dataset, the accuracy of ProofWriter'sproofs exceed previous methods by +9% absolute, and in a way that generalizesto proof depths unseen in training and on out-of-domain problems. We also showthat generative techniques can perform a type of abduction with high precision:Given a theory and an unprovable conclusion, identify a missing fact thatallows the conclusion to be proved, along with a proof. These resultssignificantly improve the viability of neural methods for systematicallyreasoning over natural language.

ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language