Abstract
The restricted chase is a sound and complete algorithm for conjunctive query answering over ontologies of disjunctive existential rules. We develop
acyclicity conditions to ensure its termination. Our
criteria cannot always detect termination (the problem is undecidable), and we develop the first cyclicity criteria to show non-termination of the restricted
chase. Experiments on real-world ontologies show
that our acyclicity notions improve significantly
over known criteria