  Query answering under existential rules -- implications with existential
quantifiers in the head -- is known to be decidable when imposing restrictions
on the rule bodies such as frontier-guardedness [BLM10, BLMS11]. Query
answering is also decidable for description logics [Baa03], which further allow
disjunction and functionality constraints (assert that certain relations are
functions), however, they are focused on ER-type schemas, where relations have
arity two.
  This work investigates how to get the best of both worlds: having decidable
existential rules on arbitrary arity relations, while allowing rich description
logics, including functionality constraints, on arity-two relations. We first
show negative results on combining such decidable languages. Second, we
introduce an expressive set of existential rules (frontier-one rules with a
certain restriction) which can be combined with powerful constraints on
arity-two relations (e.g. GC 2, ALCQIb) while retaining decidable query
answering. Further, we provide conditions to add functionality constraints on
the higher-arity relations.
