  Ontology-based query answering (OBQA) asks whether a Boolean conjunctive
query is satisfied by all models of a logical theory consisting of a relational
database paired with an ontology. The introduction of existential rules (i.e.,
Datalog rules extended with existential quantifiers in rule-heads) as a means
to specify the ontology gave birth to Datalog+/-, a framework that has received
increasing attention in the last decade, with focus also on decidability and
finite controllability to support effective reasoning. Five basic decidable
fragments have been singled out: linear, weakly-acyclic, guarded, sticky, and
shy. Moreover, for all these fragments, except shy, the important property of
finite controllability has been proved, ensuring that a query is satisfied by
all models of the theory iff it is satisfied by all its finite models. In this
paper we complete the picture by demonstrating that finite controllability of
OBQA holds also for shy ontologies, and it therefore applies to all basic
decidable Datalog+/- classes. To make the demonstration, we devise a general
technique to facilitate the process of (dis)proving finite controllability of
an arbitrary ontological fragment. This paper is under consideration for
acceptance in TPLP.
