| Summary: | 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 concerned
with is denoted as the 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.
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