We study the problem of schema discovery for knowledge graphs. We propose a solution where an agent engages in multi-turn dialog with an expert for this purpose. Each mini-dialog focuses on a short natural language statement, and looks to elicit the expert’s desired schema-based interpretation of that statement, taking into account possible augmentations to the schema. The overall schema evolves by performing dialog over a collection of such statements. We take into account the probability that the expert does not respond to a query, and model this probability as a function of the complexity of the query. For such mini-dialogs with response uncertainty, we propose a dialog strategy that looks to elicit the schema over as short a dialog as possible. By combining the notion of uncertainty sampling from active learning with generalized binary search, the strategy asks the query with the highest expected reduction of entropy. We show that this significantly reduces dialog complexity while engaging the expert in meaningful dialog.