  We present a logic based interpretable model for learning on graphs and an
algorithm to distill this model from a Graph Neural Network (GNN). Recent
results have shown connections between the expressivity of GNNs and the
two-variable fragment of first-order logic with counting quantifiers (C2). We
introduce a decision-tree based model which leverages an extension of C2 to
distill interpretable logical classifiers from GNNs. We test our approach on
multiple GNN architectures. The distilled models are interpretable, succinct,
and attain similar accuracy to the underlying GNN. Furthermore, when the ground
truth is expressible in C2, our approach outperforms the GNN.
