Improving Graph Neural Network Representations of Logical Formulae with Subgraph Pooling

TL;DR

This paper introduces a novel graph neural network architecture with subgraph pooling that enhances the representation of logical formulae, improving performance in theorem proving tasks across different logic systems.

Contribution

The paper presents a new subgraph pooling method for GNNs that better captures logical structure, applicable to various logic expressivities, and achieves state-of-the-art results.

Findings

State-of-the-art performance on premise selection

State-of-the-art performance on proof step classification

Effective across different logic expressivities

Abstract

Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting structure-aware neural methods to work with the underlying graph representations of logical expressions. While more effective than character and token-level approaches, graph-based methods have often made representational trade-offs that limited their ability to capture key structural properties of their inputs. In this work we propose a novel approach for embedding logical formulae that is designed to overcome the representational limitations of prior approaches. Our architecture works for logics of different expressivity; e.g., first-order and higher-order logic. We evaluate our approach on two standard datasets and show that the proposed architecture achieves state-of-the-art performance on both premise selection and proof step classification.