PRover: Proof Generation for Interpretable Reasoning over Rules

Abstract

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. 1

Explainable Multi-hop Verbal Reasoning Through Internal Monologue

“…The second baseline is PROVER (Saha et al, 2020), which handles the reasoning problem as a graph problem. This approach takes the input C and Q to produce both the final answer {T rue, F alse}, and a graph that indicates the reasoning path.…”

multiPRover: Generating Multiple Proofs for Improved Interpretability in Rule Reasoning

“…PROVER (Saha et al, 2020) builds on top of RoBERTa (Liu et al, 2019) and consists of a question answering (QA) module, a node module and an edge module where the node and edge modules are used to predict a single proof graph. The input to RoBERTa is the concatenation of the facts, rules and the question.…”

“…Following PROVER, we generate valid proofs during inference using an ILP, subject to multiple global constraints (see Saha et al (2020)). For each predicted proof, the predicted nodes and edge probabilities from MULTIPROVER, we obtain the corresponding predicted edges using Eqn.…”

“…Thus, in a recent work, bypass the creation of intermediate logical forms and show that transformers (Vaswani et al, 2017) can act as "soft theorem provers" by answering questions over natural language (English) rule-bases, consisting of facts and rules. In order to reliably interpret these predicted answers, Saha et al (2020) propose PROVER, a transformerbased model that generates the corresponding proof graph, thus emulating formal reasoning closely. Consider the two example rule-bases with two questions and corresponding proofs in Figure 1, where a proof is a directed graph consisting of the relevant facts and rules from the corresponding rule-base.…”

“…We find that PROVER (Saha et al, 2020), when trained on all proofs as independent training examples (Eq. 2) and extended to generate top-p proofs during inference (Eq.…”