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The spread of COVID-19 has brought a huge disaster to the world, and the automatic segmentation of infection regions can help doctors to make diagnosis quickly and reduce workload. However, there are several challenges for the accurate and complete segmentation, such as the scattered infection area distribution, complex background noises, and blurred segmentation boundaries. To this end, in this paper, we propose a novel network for automatic COVID-19 lung infection segmentation from CT images, named BCS-Net, which considers the boundary, context, and semantic attributes. The BCS-Net follows an encoder-decoder architecture, and more designs focus on the decoder stage that includes three progressively Boundary-Context-Semantic Reconstruction (BCSR) blocks. In each BCSR block, the attention-guided global context (AGGC) module is designed to learn the most valuable encoder features for decoder by highlighting the important spatial and boundary locations and modeling the global context dependence. Besides, a semantic guidance (SG) unit generates the semantic guidance map to refine the decoder features by aggregating multi-scale high-level features at the intermediate resolution. Extensive experiments demonstrate that our proposed framework outperforms the existing competitors both qualitatively and quantitatively.