In this paper, 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 each GNN can be transformed into a formula. We show that the satisfiability problem is decidable. We also discuss some variants that are in PSPACE.
@article{arxiv.2307.05150,
title = {A Modal Logic for Explaining some Graph Neural Networks},
author = {Pierre Nunn and François Schwarzentruber},
journal= {arXiv preprint arXiv:2307.05150},
year = {2023}
}