| Summary: | We study the interaction of views, queries, and background
knowledge in the form of existential rules. The motivating
questions concern monotonic determinacy of a query using
views w.r.t. rules, which refers to the ability to recover the
query answer from the views via a monotone function. We
study the decidability of monotonic determinacy, and compare with variations that require the “recovery function” to
be in a well-known monotone query language, such as conjunctive queries or Datalog. Surprisingly, we find that even
in the presence of basic existential rules, the borderline between well-behaved and badly-behaved answerability differs
radically from the unconstrained case. In order to understand
this boundary, we require new results concerning entailment
problems involving views and rules.
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