Markov Logic Networks (MLNs), which elegantly combine logic rules and
probabilistic graphical models, can be used to address many knowledge graph
problems. However, inference in MLN is computationally intensive, making the
industrial-scale application of MLN very difficult. In recent years, graph
neural networks (GNNs) have emerged as efficient and effective tools for
large-scale graph problems. Nevertheless, GNNs do not explicitly incorporate
prior logic rules into the models, and may require many labeled examples for a
target task. In this paper, we explore the combination of MLNs and GNNs, and
use graph neural networks for variational inference in MLN. We propose a GNN
variant, named ExpressGNN, which strikes a nice balance between the
representation power and the simplicity of the model. Our extensive experiments
on several benchmark datasets demonstrate that ExpressGNN leads to effective
and efficient probabilistic logic reasoning.

本研究探讨了 Markov 逻辑网络和图神经网络的组合，并使用图神经网络进行 MLN 中的变分推理。研究提出了一种名为 ExpressGNN 的 GNN 变体，并通过多个基准数据集的广泛实验表明，ExpressGNN 在有效和高效的概率逻辑推理方面具有领先优势。