Improving Graph Neural Network Representations of Logical Formulae with Subgraph Pooling

Maxwell Crouse, Ibrahim Abdelaziz, Cristina Cornelio, Veronika Thost, Lingfei Wu, Kenneth Forbus, Achille Fokoue

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