Graph Representations for Higher-Order Logic and Theorem Proving
This addresses the challenge of formalizing mathematical theories for theorem proving, though it appears incremental as it builds on existing methods for a specific domain.
The paper tackles the problem of applying graph neural networks to higher-order proof search, demonstrating that GNNs can improve state-of-the-art results on the HOList benchmark.
This paper presents the first use of graph neural networks (GNNs) for higher-order proof search and demonstrates that GNNs can improve upon state-of-the-art results in this domain. Interactive, higher-order theorem provers allow for the formalization of most mathematical theories and have been shown to pose a significant challenge for deep learning. Higher-order logic is highly expressive and, even though it is well-structured with a clearly defined grammar and semantics, there still remains no well-established method to convert formulas into graph-based representations. In this paper, we consider several graphical representations of higher-order logic and evaluate them against the HOList benchmark for higher-order theorem proving.