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In this work, we focus on semantic parsing of natural language conversations. Most existing methods for semantic parsing are based on understanding the semantics of a single sentence at a time. However, understanding conversations also requires an understanding of conversational context and discourse structure across sentences. We formulate semantic parsing of conversations as a structured prediction task, incorporating structural features that model the `flow of discourse' across sequences of utterances. We create a dataset for semantic parsing of conversations, consisting of 113 real-life sequences of interactions of human users with an automated email assistant. The data contains 4759 natural language statements paired with annotated logical forms. Our approach yields significant gains in performance over traditional semantic parsing.