Logical Expressivity and Explanations for Monotonic GNNs with Scoring Functions

TL;DR

This paper explores the logical expressivity of monotonic GNNs with scoring functions for link prediction, providing methods to extract sound explanations and characterizing their expressive power.

Contribution

It introduces a framework for explaining monotonic GNNs with scoring functions using Datalog rules, extending previous work to more general link prediction models.

Findings

Monotonic GNNs with scoring functions perform well on benchmarks.

Sound rules can be extracted for explaining predictions.

The approach characterizes the expressive power of these models.

Abstract

Graph neural networks (GNNs) are often used for the task of link prediction: predicting missing binary facts in knowledge graphs (KGs). To address the lack of explainability of GNNs on KGs, recent works extract Datalog rules from GNNs with provable correspondence guarantees. The extracted rules can be used to explain the GNN's predictions; furthermore, they can help characterise the expressive power of various GNN models. However, these works address only a form of link prediction based on a restricted, low-expressivity graph encoding/decoding method. In this paper, we consider a more general and popular approach for link prediction where a scoring function is used to decode the GNN output into fact predictions. We show how GNNs and scoring functions can be adapted to be monotonic, use the monotonicity to extract sound rules for explaining predictions, and leverage existing results about the kind of rules that scoring functions can capture. We also define procedures for obtaining equivalent Datalog programs for certain classes of monotonic GNNs with scoring functions. Our experiments show that, on link prediction benchmarks, monotonic GNNs and scoring functions perform well in practice and yield many sound rules.