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Existing studies on semantic parsing focus primarily on mapping a natural-language utterance to a corresponding logical form in one turn. However, because natural language can contain a great deal of ambiguity and variability, this is a difficult challenge. In this work, we investigate an interactive semantic parsing framework that explains the predicted logical form step by step in natural language and enables the user to make corrections through natural-language feedback for individual steps. We focus on question answering over knowledge bases (KBQA) as an instantiation of our framework, aiming to increase the transparency of the parsing process and help the user appropriately trust the final answer. To do so, we construct INSPIRED, a crowdsourced dialogue dataset derived from the ComplexWebQuestions dataset. Our experiments show that the interactive framework with human feedback has the potential to greatly improve overall parse accuracy. Furthermore, we develop a pipeline for dialogue simulation to evaluate our framework w.r.t. a variety of state-of-the-art KBQA models without involving further crowdsourcing effort. The results demonstrate that our interactive semantic parsing framework promises to be effective across such models.