Gas meter prover

Calculus (dental)

Mathematics

Algorithm

Proof complexity

Mathematical proof

Political science

Dentistry

Programming language

Automated theorem proving

Proof theory

Geometry

Burden of proof

Computer science

Medicine

Recent work by Clark et al. (2020) shows that transformers can act as "soft theorem provers" by answering questions over explicitly provided knowledge in natural language. In our work, we take a step closer to emulating formal theorem provers, by proposing PRover, an interpretable transformer-based model that jointly answers binary questions over rule-bases and generates the corresponding proofs. Our model learns to predict nodes and edges corresponding to proof graphs in an efficient constrained training paradigm. During inference, a valid proof, satisfying a set of global constraints is generated. We conduct experiments on synthetic, hand-authored, and human-paraphrased rule-bases to show promising results for QA and proof generation, with strong generalization performance. First, PRover generates proofs with an accuracy of 87%, while retaining or improving performance on the QA task, compared to RuleTakers (up to 6% improvement on zero-shot evaluation). Second, when trained on questions requiring lower depths of reasoning, it generalizes significantly better to higher depths (up to 15% improvement). Third, PRover obtains near perfect QA accuracy of 98% using only 40% of the training data. However, generating proofs for questions requiring higher depths of reasoning becomes challenging, and the accuracy drops to 65% for "depth 5", indicating significant scope for future work.

PRover: Proof Generation for Interpretable Reasoning over Rules