Querying Visible and Invisible Information

We provide a wide-ranging study of the scenario where a subset of the relations in the schema are visible - that is, their complete contents are known - while the remaining relations are invisible. We also have integrity constraints (invariants given by logical sentences) which may relate the visible relations to the invisible ones. We want to determine which information about a query (a positive existential sentence) can be inferred from the visible instance and the constraints. We consider both positive and negative query information, that is, whether the query or its negation holds. We consider the instance-level version of the problem, where both the query and the visible instance are given, as well as the schema-level version, where we want to know whether truth or falsity of the query can be inferred in some instance of the schema.