  We focus on a type of linguistic formal reasoning where the goal is to reason
over explicit knowledge in the form of natural language facts and rules (Clark
et al., 2020). A recent work, named PRover (Saha et al., 2020), performs such
reasoning by answering a question and also generating a proof graph that
explains the answer. However, compositional reasoning is not always unique and
there may be multiple ways of reaching the correct answer. Thus, in our work,
we address a new and challenging problem of generating multiple proof graphs
for reasoning over natural language rule-bases. Each proof provides a different
rationale for the answer, thereby improving the interpretability of such
reasoning systems. In order to jointly learn from all proof graphs and exploit
the correlations between multiple proofs for a question, we pose this task as a
set generation problem over structured output spaces where each proof is
represented as a directed graph. We propose two variants of a proof-set
generation model, multiPRover. Our first model, Multilabel-multiPRover,
generates a set of proofs via multi-label classification and implicit
conditioning between the proofs; while the second model, Iterative-multiPRover,
generates proofs iteratively by explicitly conditioning on the previously
generated proofs. Experiments on multiple synthetic, zero-shot, and
human-paraphrased datasets reveal that both multiPRover models significantly
outperform PRover on datasets containing multiple gold proofs.
Iterative-multiPRover obtains state-of-the-art proof F1 in zero-shot scenarios
where all examples have single correct proofs. It also generalizes better to
questions requiring higher depths of reasoning where multiple proofs are more
frequent. Our code and models are publicly available at
https://github.com/swarnaHub/multiPRover
