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We present a novel abstractive summarization framework that draws on the recent development of a treebank for the Abstract Meaning Representation (AMR). In this framework, the source text is parsed to a set of AMR graphs, the graphs are transformed into a summary graph, and then text is generated from the summary graph. We focus on the graph-to-graph transformation that reduces the source semantic graph into a summary graph, making use of an existing AMR parser and assuming the eventual availability of an AMR-to-text generator. The framework is data-driven, trainable, and not specifically designed for a particular domain. Experiments on gold-standard AMR annotations and system parses show promising results. Code is available at: https://github.com/summarization
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