Graph neural networks (GNNs) can effectively model structural information of graphs, making them widely used in knowledge graph (KG) reasoning. However, existing studies on the expressive power of GNNs mainly focuses on simple single-relation graphs, and there is still insufficient discussion on the power of GNN to express logical rules in KGs. How to enhance the logical expressive power of GNNs is still a key issue. Motivated by this, we propose Path-Neighbor enhanced GNN (PN-GNN), a method to enhance the logical expressive power of GNN by aggregating node-neighbor embeddings on the reasoning path. First, we analyze the logical expressive power of existing GNN-based methods and point out the shortcomings of the expressive power of these methods. Then, we theoretically investigate the logical expressive power of PN-GNN, showing that it not only has strictly stronger expressive power than C-GNN but also that its (k+1)-hop logical expressiveness is strictly superior to that of k-hop. Finally, we evaluate the logical expressive power of PN-GNN on six synthetic datasets and two real-world datasets. Both theoretical analysis and extensive experiments confirm that PN-GNN enhances the expressive power of logical rules without compromising generalization, as evidenced by its competitive performance in KG reasoning tasks.

Among various temporal knowledge graph (TKG) extrapolation methods, rule-based approaches stand out for their explicit rules and transparent reasoning paths. However, the vast search space for rule extraction poses a challenge in identifying high-quality logic rules. To navigate this challenge, we explore the use of generation models to generate new rules, thereby enriching our rule base and enhancing our reasoning capabilities. In this paper, we introduce LLM-DR, an innovative rule-based method for TKG extrapolation, which harnesses diffusion models to generate rules that are consistent with the distribution of the source data, while also amalgamating the rich semantic insights of Large Language Models (LLMs). Specifically, our LLM-DR generates semantically relevant and high-quality rules, employing conditional diffusion models in a classifier-free guidance fashion and refining them with LLM-based constraints. To assess rule efficacy, we meticulously design a coarse-to-fine evaluation strategy that initiates with coarse-grained filtering to eliminate less plausible rules and proceeds with fine-grained scoring to quantify the reliability of the retained. Extensive experiments demonstrate the promising capacity of our LLM-DR.

Knowledge Graphs represent facts with triples containing head entity$h$, tail entity$t$and relation$r$which facilitate applications of many scenarios, for example intelligent web search, community detection and question answering. Knowledge Graph Embedding (KGE) represents elements of triples in a low-dimensional continuous vector space. Though it has been widely studied by both academic and industry communities, most researches focus on learning embeddings of entities and relations separately rather than considering the interactive semantic information between them. However, neither relations nor entities exist lonely out of context. In this paper, we define an interactive semantic space to model the context of triples and propose a novel Bi-linear Semantic Matching Method using Convolutional networks (BiSC). Specifically, we use 1D convolutional neural networks to extract features of the interactive semantics and then compute the similarity scores in the bi-linear space. Compared to existing complex graph network methods, BiSC needs lower computational cost to reach competitive results on link prediction task. The consistent state-of-the-art performance through extensive experiments over two benchmarks demonstrates the advantages of the proposed BiSC model. Further analysis on convergence study and case study of interactive semantic space show the efficiency of our model.