KR2023Proceedings of the 20th International Conference on Principles of Knowledge Representation and ReasoningProceedings of the 20th International Conference on Principles of Knowledge Representation and Reasoning

Rhodes, Greece. September 2-8, 2023.

Edited by

ISSN: 2334-1033
ISBN: 978-1-956792-02-7

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Copyright © 2023 International Joint Conferences on Artificial Intelligence Organization

On the Correspondence Between Monotonic Max-Sum GNNs and Datalog

  1. David Tena Cucala(University of Oxford)
  2. Bernardo Cuenca Grau(University of Oxford)
  3. Boris Motik(University of Oxford)
  4. Egor V. Kostylev(University of Oslo)


  1. Interplay between logic & neural and other learning paradigms
  2. Expressive power of learning representations
  3. Explainable AI
  4. KR and machine learning, inductive logic programming, knowledge acquisition


Although there has been significant interest in applying machine learning techniques to structured data, the expressivity (i.e., a description of what can be learned) of such techniques is still poorly understood. In this paper, we study data transformations based on graph neural networks (GNNs). First, we note that the choice of how a dataset is encoded into a numeric form processable by a GNN can obscure the characterisation of a model's expressivity, and we argue that a canonical encoding provides an appropriate basis. Second, we study the expressivity of monotonic max-sum GNNs, which cover a subclass of GNNs with max and sum aggregation functions. We show that, for each such GNN, one can compute a Datalog program such that applying the GNN to any dataset produces the same facts as a single round of application of the program's rules to the dataset. Monotonic max-sum GNNs can sum an unbounded number of feature vectors which can result in arbitrarily large feature values, whereas rule application requires only a bounded number of constants. Hence, our result shows that the unbounded summation of monotonic max-sum GNNs does not increase their expressive power. Third, we sharpen our result to the subclass of monotonic max GNNs, which use only the max aggregation function, and identify a corresponding class of Datalog programs.