Sum aggregation plus readout in ACR-GNNs captures FO properties outside C2 on directed and undirected graphs, while bounded local aggregation or bounded degree restores exact match to graded modal logic with global counting.
Proof.LetG ⋆ be the graph obtained fromGby applying Lemma 32
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Towards Understanding the Expressive Power of GNNs with Global Readout
Sum aggregation plus readout in ACR-GNNs captures FO properties outside C2 on directed and undirected graphs, while bounded local aggregation or bounded degree restores exact match to graded modal logic with global counting.