{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/graph-representations-for-higher-order-logic","title":"Graph Representations for Higher-Order Logic and Theorem Proving","arxiv_id":"1905.10006","date":"2019-05-24","proceeding":null,"authors":["Aditya Paliwal","Sarah Loos","Markus Rabe","Kshitij Bansal","Christian Szegedy"],"abstract":"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.","url_abs":"https://arxiv.org/abs/1905.10006v2","url_pdf":"https://arxiv.org/pdf/1905.10006v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[],"tasks":[{"task_slug":"automated-theorem-proving","task_name":"Automated Theorem Proving"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/automated-theorem-proving-on-holist-benchmark","task":"Automated Theorem Proving","dataset":"HOList benchmark","model":"4-hop GNN, sub-expression sharing","rank_in_archive_order":1,"of":4,"metrics":{"Percentage correct":"49.95"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1905.10006","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}