  Formulating selective information needs results in queries that implicitly
specify set operations, such as intersection, union, and difference. For
instance, one might search for "shorebirds that are not sandpipers" or
"science-fiction films shot in England". To study the ability of retrieval
systems to meet such information needs, we construct QUEST, a dataset of 3357
natural language queries with implicit set operations, that map to a set of
entities corresponding to Wikipedia documents. The dataset challenges models to
match multiple constraints mentioned in queries with corresponding evidence in
documents and correctly perform various set operations. The dataset is
constructed semi-automatically using Wikipedia category names. Queries are
automatically composed from individual categories, then paraphrased and further
validated for naturalness and fluency by crowdworkers. Crowdworkers also assess
the relevance of entities based on their documents and highlight attribution of
query constraints to spans of document text. We analyze several modern
retrieval systems, finding that they often struggle on such queries. Queries
involving negation and conjunction are particularly challenging and systems are
further challenged with combinations of these operations.
