A Logic for Reasoning About Aggregate-Combine Graph Neural Networks
This work provides a foundational framework for using logical methods to reason about GNN properties, such as querying and equivalence checking, which is incremental in advancing the theoretical understanding of GNN expressiveness.
The authors tackled the problem of reasoning about graph neural networks (GNNs) by proposing a modal logic with counting modalities in linear inequalities, showing that formulas can be transformed into equivalent GNNs and vice versa, and proving that the satisfiability problem is PSPACE-complete.
We propose a modal logic in which counting modalities appear in linear inequalities. We show that each formula can be transformed into an equivalent graph neural network (GNN). We also show that a broad class of GNNs can be transformed efficiently into a formula, thus significantly improving upon the literature about the logical expressiveness of GNNs. We also show that the satisfiability problem is PSPACE-complete. These results bring together the promise of using standard logical methods for reasoning about GNNs and their properties, particularly in applications such as GNN querying, equivalence checking, etc. We prove that such natural problems can be solved in polynomial space.