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