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Temporal grounding in videos aims to localize one target video segment that semantically corresponds to a given query sentence. Thanks to the semantic diversity of natural language descriptions, temporal grounding allows activity grounding beyond pre-defined classes and has received increasing attention in recent years. The semantic diversity is rooted in the principle of compositionality in linguistics, where novel semantics can be systematically described by combining known words in novel ways (compositional generalization). However, current temporal grounding datasets do not specifically test for the compositional generalizability. To systematically measure the compositional generalizability of temporal grounding models, we introduce a new Compositional Temporal Grounding task and construct two new dataset splits, i.e., Charades-CG and ActivityNet-CG. Evaluating the state-of-the-art methods on our new dataset splits, we empirically find that they fail to generalize to queries with novel combinations of seen words. To tackle this challenge, we propose a variational cross-graph reasoning framework that explicitly decomposes video and language into multiple structured hierarchies and learns fine-grained semantic correspondence among them. Experiments illustrate the superior compositional generalizability of our approach. The repository of this work is at https://github.com/YYJMJC/ Compositional-Temporal-Grounding.