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Most existing knowledge graphs suffer from incompleteness. Embedding knowledge graphs into continuous vector spaces has recently attracted increasing interest in knowledge base completion. However, in most existing embedding methods, only fact triplets are utilized, and logical rules have not been thoroughly studied for the knowledge base completion task. To overcome the problem, we propose an association rules enhanced knowledge graph attention network (AR-KGAT). The AR-KGAT captures both entity and relation features for high-order neighborhoods of any given entity in an end-to-end manner under the graph attention network framework. The major component of AR-KGAT is an encoder of an effective neighborhood aggregator, which addresses the problems by aggregating neighbors with both association-rules-based and graph-based attention weights. Additionally, the proposed model also encapsulates the representations from multi-hop neighbors of nodes to refine their embeddings. The decoder enables AR-KGAT to be translational between entities and relations while keeping the superior link prediction performance. A logic-like inference pattern is utilized as constraints for knowledge graph embedding. Then, the global loss is minimized over both atomic and complex formulas to achieve the embedding task. In this manner, we learn embeddings compatible with triplets and rules, which are certainly more predictive for knowledge acquisition and inference. We conduct extensive experiments on two benchmark datasets: WN18RR and FB15k-237, for two knowledge graph completion tasks: the link prediction and triplet classification to evaluate the proposed AR-KGAT model. The results show that the proposed AR-KGAT model achieves significant and consistent improvements over state-of-the-art methods.