On Bounded Positive Existential Rules.

We consider the existential rule framework, which generalizes Horn description logics. We study and compare several boundedness notions in this framework. Our main result states that (strongly-) bounded rules are exactly those at the intersection of two well-known abstract classes of existential rules, namely fes (finite expansion sets, which ensure the finiteness of the core chase) and fus (finite unification sets, which correspond to UCQ-rewritable rules).