  We provide a wide-ranging study of the scenario where a subset of the
relations in a relational vocabulary are visible to a user --- that is, their
complete contents are known --- while the remaining relations are invisible. We
also have a background theory --- invariants given by logical sentences ---
which may relate the visible relations to invisible ones, and also may
constrain both the visible and invisible relations in isolation. We want to
determine whether some other information, given as a positive existential
formula, can be inferred using only the visible information and the background
theory. This formula whose inference we are concered with is denoted as the
\emph{query}. We consider whether positive information about the query can be
inferred, and also whether negative information -- the sentence does not hold
-- can be inferred. We further consider both the instance-level version of the
problem, where both the query and the visible instance are given, and 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.
