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Temporal knowledge graphs (TKGs) inherently reflect the transient nature of real-world knowledge, as opposed to static knowledge graphs. Naturally, automatic TKG completion has drawn much research interests for a more realistic modeling of relational reasoning. However, most of the existing mod-els for TKG completion extend static KG embeddings that donot fully exploit TKG structure, thus lacking in 1) account-ing for temporally relevant events already residing in the lo-cal neighborhood of a query, and 2) path-based inference that facilitates multi-hop reasoning and better interpretability. In this paper, we propose T-GAP, a novel model for TKG completion that maximally utilizes both temporal information and graph structure in its encoder and decoder. T-GAP encodes query-specific substructure of TKG by focusing on the temporal displacement between each event and the query times-tamp, and performs path-based inference by propagating attention through the graph. Our empirical experiments demonstrate that T-GAP not only achieves superior performance against state-of-the-art baselines, but also competently generalizes to queries with unseen timestamps. Through extensive qualitative analyses, we also show that T-GAP enjoys from transparent interpretability, and follows human intuition in its reasoning process.