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Dialogue meaning representation formulates natural language utterance semantics in their conversational context in an explicit and machine-readable form. Previous work typically follows the intent-slot framework, which is easy for annotation yet limited in scalability for complex linguistic expressions. A line of works alleviates the representation issue by introducing hierarchical structures but challenging to express complex compositional semantics, such as negation and coreference. We propose Dialogue Meaning Representation (DMR), a pliable and easily extendable representation for task-oriented dialogue. Our representation contains a set of nodes and edges to represent rich compositional semantics. Moreover, we propose an inheritance hierarchy mechanism focusing on domain extensibility. Additionally, we annotated DMR-FastFood, a multi-turn dialogue dataset with more than 70k utterances, with DMR. We propose two evaluation tasks to evaluate different dialogue models and a novel coreference resolution model GNNCoref for the graph-based coreference resolution task. Experiments show that DMR can be parsed well with pre-trained Seq2Seq models, and GNNCoref outperforms the baseline models by a large margin. The dataset and code are available at https://github.com/amazon-research/dialogue-meaning-representation