A computing device displays a data visualization interface and receives user selection of a data source and a natural language command directed to the data source. The device forms a first intermediate expression according to a context-free grammar and a semantic model of data fields in the data source. In accordance with a determination that the first intermediate expression omits sufficient information for generating a data visualization, the device infers the omitted information associated with the data source using one or more inferencing rules based on syntactic and semantic constraints imposed by the context-free grammar. The device forms an updated intermediate expression, and translates the updated intermediate expression into database queries. It executes the database queries to retrieve data sets from the data source, then generates and displays a data visualization of the retrieved data sets.