The correspondence between bounded graph neural networks and fragments of first-order logic

Conference item

Graph Neural Networks (GNNs) address two key challenges in applying deep learning to graph-structured data: they handle varying size input graphs and ensure invariance under graph isomorphism. While GNNs have demonstrated broad applicability, understanding their expressive power remains an important question. In this paper, we propose GNN architectures that correspond precisely to prominent fragments of first-order logic (FO), including various modal logics as well as more expressive twovariable fragments. To establish these results, we apply methods from finite model theory of first-order and modal logics to the domain of graph representation learning. Our results provide a unifying framework for understanding the logical expressiveness of GNNs within FO.

Authors: Cuenca Grau, B; Walega, P; Feng, E

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: AAAI Press
• Host title: Proceedings of the AAAI Conference on Artificial Intelligence
• Volume: 40
• Issue: 23
• Pages: 19135-19142
• Place of publication: Washington, DC, USA
• Publication date: 2026-03-17
• Acceptance date: 2025-11-07
• Event title: 40th Annual AAAI Conference on Artificial Intelligence
• Event location: Singapore
• Event website: https://aaai.org/conference/aaai/aaai-26/
• Event start date: 2026-01-20
• Event end date: 2026-01-27
• DOI: 10.1609/aaai.v40i23.38987
• EISSN: 2374-3468
• ISSN: 2159-5399
• ISBN-10: 1577359062
• ISBN-13: 9781577359067
• Language: English