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Graph Neural Networks share with Logic Programming several key relationalinference mechanisms. The datasets on which they are trained and evaluated canbe seen as database facts containing ground terms. This makes possible modelingtheir inference mechanisms with equivalent logic programs, to better understandnot just how they propagate information between the entities involved in themachine learning process but also to infer limits on what can be learned from agiven 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 alogic program the information flows involved in learning to infer from the linkstructure of a graph and the information content of its nodes properties of newnodes, given their known connections to nodes with possibly similar properties.The problem is known as graph node property prediction and our approach willconsist in emulating with help of a Prolog program the key informationpropagation 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, wedistill the dependency trees of the text associated to each node into directedacyclic graphs that we encode as ground Prolog terms. Together with the set oftheir references to other papers, they become facts in a database on which wereason with help of a Prolog program that mimics the information propagation ingraph neural networks predicting node properties. In the process, we inventground term similarity relations that help infer labels in the test set bypropagating node properties from similar nodes in the training set and weevaluate their effectiveness in comparison with that of the graph's linkstructure. Finally, we implement explanation generators that unveil performanceupper bounds inherent to the dataset.  As a practical outcome, we obtain a logic program, that, when seen as machinelearning algorithm, performs close to the state of the art on the node propertyprediction benchmark.

A Gaze into the Internal Logic of Graph Neural Networks, with Logic