Decidability of Graph Neural Networks via Logical Characterizations

Authors Michael Benedikt , Chia-Hsuan Lu , Boris Motik , Tony Tan

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Author Details

Michael Benedikt
  • University of Oxford, UK
Chia-Hsuan Lu
  • University of Oxford, UK
Boris Motik
  • University of Oxford, UK
Tony Tan
  • University of Liverpool, UK

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Michael Benedikt, Chia-Hsuan Lu, Boris Motik, and Tony Tan. Decidability of Graph Neural Networks via Logical Characterizations. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 127:1-127:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


We present results concerning the expressiveness and decidability of a popular graph learning formalism, graph neural networks (GNNs), exploiting connections with logic. We use a family of recently-discovered decidable logics involving "Presburger quantifiers". We show how to use these logics to measure the expressiveness of classes of GNNs, in some cases getting exact correspondences between the expressiveness of logics and GNNs. We also employ the logics, and the techniques used to analyze them, to obtain decision procedures for verification problems over GNNs. We complement this with undecidability results for static analysis problems involving the logics, as well as for GNN verification problems.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Logic
  • Graph Neural Networks


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