Knowledge graphs (KGs) are vital for enabling knowledge reasoning across various domains. Recent KG reasoning methods that integrate both global and local information have achieved promising results. However, existing methods often suffer from score over-smoothing, which blurs the distinction between correct and incorrect answers and hinders reasoning effectiveness. To address this, we propose DuetGraph, a coarse-to-fine KG reasoning mechanism with dual-pathway global-local fusion. DuetGraph tackles over-smoothing by segregating -- rather than stacking -- the processing of local (via message passing) and global (via attention) information into two distinct pathways, preventing mutual interference and preserving representational discrimination. In addition, DuetGraph introduces a coarse-to-fine optimization, which partitions entities into high- and low-score subsets. This strategy narrows the candidate space and sharpens the score gap between the two subsets, which alleviates over-smoothing and enhances inference quality. Extensive experiments on various datasets demonstrate that DuetGraph achieves state-of-the-art (SOTA) performance, with up to an 8.7% improvement in reasoning quality and a 1.8$\times$ acceleration in training efficiency. Our code is available at https://github.com/USTC-DataDarknessLab/DuetGraph.git.

Logical rule learning, a prominent category of knowledge graph (KG) reasoning methods, constitutes a critical research area aimed at learning explicit rules from observed facts to infer missing knowledge. However, like all KG reasoning methods, rule learning suffers from a critical weakness-its dependence on the I.I.D. assumption. This assumption can easily be violated due to selection bias during training or agnostic distribution shifts during testing (e.g., as in query shift scenarios), ultimately undermining model performance and reliability. To enable robust KG reasoning in wild environments, this study investigates logical rule learning in the presence of agnostic test-time distribution shifts. We formally define this challenge as out-of-distribution (OOD) KG reasoning-a previously underexplored problem, and propose the Stable Rule Learning (StableRule) framework as a solution. StableRule is an end-to-end framework that combines feature decorrelation with rule learning network, to enhance OOD generalization in KG reasoning. By leveraging feature decorrelation, StableRule mitigates the adverse effects of covariate shifts arising in OOD scenarios, improving the robustness of the rule learning network. Extensive experiments on seven benchmark KGs demonstrate the framework's superior effectiveness and stability across diverse heterogeneous environments, highlighting its practical significance for real-world applications.

Graph Neural Networks (GNNs) have been recently introduced to learn from knowledge graph (KG) and achieved state-of-the-art performance in KG reasoning. However, a theoretical certification for their good empirical performance is still absent. Besides, while logic in KG is important for inductive and interpretable inference, existing GNN-based methods are just designed to fit data distributions with limited knowledge of their logical expressiveness. We propose to fill the above gap in this paper. Specifically, we theoretically analyze GNN from logical expressiveness and find out what kind of logical rules can be captured from KG. Our results first show that GNN can capture logical rules from graded modal logic, providing a new theoretical tool for analyzing the expressiveness of GNN for KG reasoning; and a query labeling trick makes it easier for GNN to capture logical rules, explaining why SOTA methods are mainly based on labeling trick. Finally, insights from our theory motivate the development of an entity labeling method for capturing difficult logical rules. Experimental results are consistent with our theoretical results and verify the effectiveness of our proposed method.

Knowledge graph (KG) reasoning is becoming increasingly popular in both academia and industry. Conventional KG reasoning based on symbolic logic is deterministic, with reasoning results being explainable, while modern embedding-based reasoning can deal with uncertainty and predict plausible knowledge, often with high efficiency via vector computation. A promising direction is to integrate both logic-based and embedding-based methods, with the vision to have advantages of both. It has attracted wide research attention with more and more works published in recent years. In this paper, we comprehensively survey these works, focusing on how logics and embeddings are integrated. We first briefly introduce preliminaries, then systematically categorize and discuss works of logic and embedding-aware KG reasoning from different perspectives, and finally conclude and discuss the challenges and further directions.

Walk-based models have shown their unique advantages in knowledge graph (KG) reasoning by achieving state-of-the-art performance while allowing for explicit visualization of the decision sequence. However, the sparse reward signals offered by the KG during a traversal are often insufficient to guide a sophisticated reinforcement learning (RL) model. An alternate approach to KG reasoning is using traditional symbolic methods (e.g., rule induction), which achieve high precision without learning but are hard to generalize due to the limitation of symbolic representation. In this paper, we propose to fuse these two paradigms to get the best of both worlds. Our method leverages high-quality rules generated by symbolic-based methods to provide reward supervision for walk-based agents. Due to the structure of symbolic rules with their entity variables, we can separate our walk-based agent into two sub-agents thus allowing for additional efficiency. Experiments on public datasets demonstrate that walk-based models can benefit from rule guidance significantly.