  Graph Neural Networks share with Logic Programming several key relational
inference mechanisms. The datasets on which they are trained and evaluated can
be seen as database facts containing ground terms. This makes possible modeling
their inference mechanisms with equivalent logic programs, to better understand
not just how they propagate information between the entities involved in the
machine learning process but also to infer limits on what can be learned from a
given dataset and how well that might generalize to unseen test data.
  This leads us to the key idea of this paper: modeling with the help of a
logic program the information flows involved in learning to infer from the link
structure of a graph and the information content of its nodes properties of new
nodes, given their known connections to nodes with possibly similar properties.
The problem is known as graph node property prediction and our approach will
consist in emulating with help of a Prolog program the key information
propagation steps of a Graph Neural Network's training and inference stages.
  We test our a approach on the ogbn-arxiv node property inference benchmark.
To infer class labels for nodes representing papers in a citation network, we
distill the dependency trees of the text associated to each node into directed
acyclic graphs that we encode as ground Prolog terms. Together with the set of
their references to other papers, they become facts in a database on which we
reason with help of a Prolog program that mimics the information propagation in
graph neural networks predicting node properties. In the process, we invent
ground term similarity relations that help infer labels in the test set by
propagating node properties from similar nodes in the training set and we
evaluate their effectiveness in comparison with that of the graph's link
structure. Finally, we implement explanation generators that unveil performance
upper bounds inherent to the dataset.
  As a practical outcome, we obtain a logic program, that, when seen as machine
learning algorithm, performs close to the state of the art on the node property
prediction benchmark.
