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.
A Logic for Reasoning about Aggregate-Combine Graph Neural Networks
Troquard, Nicolas
2024-01-01
Abstract
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.File | Dimensione | Formato | |
---|---|---|---|
2024_33rdIJCAI2024_3532_Nunn.pdf
accesso aperto
Tipologia:
Versione Editoriale (PDF)
Licenza:
Creative commons
Dimensione
198.99 kB
Formato
Adobe PDF
|
198.99 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.