Explainability is essential for autonomous vehicles and other robotics systems interacting with humans and other objects during operation. Humans need to understand and anticipate the actions taken by the machines for trustful and safe cooperation. In this work, we aim to develop an explainable model that generates explanations consistent with both human domain knowledge and the model's inherent causal relation. In particular, we focus on an essential building block of autonomous driving, multi-agent interaction modeling. We propose Grounded Relational Inference (GRI). It models an interactive system's underlying dynamics by inferring an interaction graph representing the agents' relations. We ensure a semantically meaningful interaction graph by grounding the relational latent space into semantic interactive behaviors defined with expert domain knowledge. We demonstrate that it can model interactive traffic scenarios under both simulation and real-world settings, and generate semantic graphs explaining the vehicle's behavior by their interactions.