Graph Representations for Higher-Order Logic and Theorem Proving

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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.