Graph

Gas meter prover

Mathematics

Proof complexity

Mathematical proof

Artificial intelligence

Set (abstract data type)

Programming language

Automated theorem proving

Geometry

Interpretability

Computer science

Theoretical computer science

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.

multiPRover: Generating Multiple Proofs for Improved Interpretability in Rule Reasoning