  In this paper, we investigate the problem of reasoning over natural language
statements. Prior neural based approaches do not explicitly consider the
inter-dependency among answers and their proofs. In this paper, we propose
PRobr, a novel approach for joint answer prediction and proof generation. PRobr
defines a joint probabilistic distribution over all possible proof graphs and
answers via an induced graphical model. We then optimize the model using
variational approximation on top of neural textual representation. Experiments
on multiple datasets under diverse settings (fully supervised, few-shot and
zero-shot evaluation) verify the effectiveness of PRobr, e.g., achieving
10%-30% improvement on QA accuracy in few/zero-shot evaluation. Our codes and
models can be found at https://github.com/changzhisun/PRobr/.
