Logical rules constitute a cornerstone of knowledge graph (KG) reasoning, valued for their interpretability and ability to model relational patterns. However, existing rule mining methods predominantly focus on simple chain-like rules and therefore neglect the richer relational information encoded in graph-like structures, such as cycles and branches. This limitation is further exacerbated by computational bottlenecks caused by the combinatorial explosion of the search space, which is especially challenging for graph-like rules. Meanwhile, generative approaches such as diffusion models, despite their success in other domains, cannot be directly applied to rule mining because their training objectives are not aligned with the goal of learning high-quality rules, and non-differentiable KG rule quality metrics cannot directly guide model optimization. To address these limitations, we propose GRiD, a framework that reformulates graph-like rule discovery as a discrete generative process conditioned on the target relation. GRiD employs a two-phase training strategy. First, supervised pre-training enables GRiD to capture structural priors from subgraphs sampled from the KG meta-graph. Subsequently, reinforcement learning is applied to fine-tune GRiD through policy gradient optimization guided directly by non-differentiable rule-quality metrics. Experiments on six benchmark datasets show that GRiD achieves competitive performance on KG completion tasks. Ablation studies confirm the efficiency and robustness of GRiD and further show that graph-like rules complement chain-like rules in KG completion. Our code and datasets are available in https://github.com/Haoxiang-Cheng/GRiD.
Knowledge graphs (KGs) can be enhanced through rule mining; however, the resulting logical rules are often difficult for humans to interpret due to their inherent complexity and the idiosyncratic labeling conventions of individual KGs. This work presents Rule2Text, a comprehensive framework that leverages large language models (LLMs) to generate natural language explanations for mined logical rules, thereby improving KG accessibility and usability. We conduct extensive experiments using multiple datasets, including Freebase variants (FB-CVT-REV, FB+CVT-REV, and FB15k-237) as well as the ogbl-biokg dataset, with rules mined using AMIE 3.5.1. We systematically evaluate several LLMs across a comprehensive range of prompting strategies, including zero-shot, few-shot, variable type incorporation, and Chain-of-Thought reasoning. To systematically assess models' performance, we conduct a human evaluation of generated explanations on correctness and clarity. To address evaluation scalability, we develop and validate an LLM-as-a-judge framework that demonstrates strong agreement with human evaluators. Leveraging the best-performing model (Gemini 2.0 Flash), LLM judge, and human-in-the-loop feedback, we construct high-quality ground truth datasets, which we use to fine-tune the open-source Zephyr model. Our results demonstrate significant improvements in explanation quality after fine-tuning, with particularly strong gains in the domain-specific dataset. Additionally, we integrate a type inference module to support KGs lacking explicit type information. All code and data are publicly available at https://github.com/idirlab/KGRule2NL.
Knowledge Graphs (KGs) are composed of triples, and the goal of Knowledge Graph Completion (KGC) is to infer the missing factual triples. Traditional KGC tasks predict missing elements in a triple given one or two of its elements. As a more realistic task, the Triple Set Prediction (TSP) task aims to infer the set of missing triples conditioned only on the observed knowledge graph, without assuming any partial information about the missing triples. Existing TSP methods predict the set of missing triples in a triple-by-triple manner, falling short in capturing the dependencies among the predicted triples to ensure consistency. To address this issue, we propose a novel discrete diffusion model termed DiffTSP that treats TSP as a generative task. DiffTSP progressively adds noise to the KG through a discrete diffusion process, achieved by masking relational edges. The reverse process then gradually recovers the complete KG conditioned on the incomplete graph. To this end, we design a structure-aware denoising network that integrates a relational context encoder with a relational graph diffusion transformer for knowledge graph generation. DiffTSP can generate the complete set of triples in a one-pass manner while ensuring the dependencies among the predicted triples. Our approach achieves state-of-the-art performance on three public datasets. Code: https://github.com/ADMIS-TONGJI/DiffTSP.
Large language models (LLMs) excel at reasoning but struggle with knowledge-intensive questions due to limited context and parametric knowledge. However, existing methods that rely on finetuned LLMs or GNN retrievers are limited by dataset-specific tuning and scalability on large or unseen graphs. We propose the LLM-KGFR collaborative framework, where an LLM works with a structured retriever, the Knowledge Graph Foundation Retriever (KGFR). KGFR encodes relations using LLM-generated descriptions and initializes entities based on their roles in the question, enabling zero-shot generalization to unseen KGs. To handle large graphs efficiently, it employs Asymmetric Progressive Propagation (APP)- a stepwise expansion that selectively limits high-degree nodes while retaining informative paths. Through node-, edge-, and path-level interfaces, the LLM iteratively requests candidate answers, supporting facts, and reasoning paths, forming a controllable reasoning loop. Experiments demonstrate that LLM-KGFR achieves strong performance while maintaining scalability and generalization, providing a practical solution for KG-augmented reasoning.