arXiv:2507.05110v1 Announce Type: new Abstract: Knowledge graph (KG) reasoning remains a critical research area focused on inferring missing knowledge by analyzing relationships among observed facts. Despite its success, a key limitation of existing KG reasoning methods is their dependence on the I.I.D assumption. This assumption can easily be violated due to unknown sample selection bias during training or agnostic distribution shifts during testing, significantly compromising model performance and reliability. To facilitate the deployment of KG reasoning in wild environments, this study investigates learning logical rules from KGs affected by unknown selection bias. Additionally, we address test sets with agnostic distribution shifts, formally defining this challenge as out-of-distribution (OOD) KG reasoning-a previously underexplored problem. To solve the issue, we propose the Stable Rule Learning (StableRule) framework, an end-to-end methodology that integrates feature decorrelation with rule learning network, to enhance OOD generalization performance. By leveraging feature decorrelation, the StableRule framework mitigates the adverse effects of covariate shifts arising in OOD scenarios, thereby improving the robustness of the rule learning component in effectively deriving logical rules. Extensive experiments on seven benchmark KGs demonstrate the framework's superior effectiveness and stability across diverse heterogeneous environments, underscoring its practical significance for real-world applications.