Graph Representations for Higher-Order Logic and Theorem Proving

2020-06-02

Proceedings of the AAAI Conference on Artificial Intelligence, 34

Volume

Vol. 34 No. 03: AAAI-20 Technical Tracks 3

AAAI Technical Track: Knowledge Representation and Reasoning

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.

10.1609/aaai.v34i03.5689