# A Modal Logic for Explaining some Graph Neural Networks

arXiv: https://arxiv.org/abs/2307.05150 · HTML: https://mlsanity.com/paper/2307.05150/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 25 references that are in the map.
- First posted on arXiv 11 Jul 2023.

## Builds on (most cited first, 7 of 7)

- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Explainability in Graph Neural Networks: A Taxonomic Survey](https://mlsanity.com/paper/2012.15445/) (2020)
- [The Logic of Graph Neural Networks](https://mlsanity.com/paper/2104.14624/) (2021)
- [Global Explainability of GNNs via Logic Combination of Learned Concepts](https://mlsanity.com/paper/2210.07147/) (2022)
- [DT+GNN: A Fully Explainable Graph Neural Network using Decision Trees](https://mlsanity.com/paper/2205.13234/) (2022)
- [Facebook and the Epistemic Logic of Friendship](https://mlsanity.com/paper/1310.6440/) (2013)

## Abstract (arXiv)

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.