The chase revisited.

We revisit the standard chase procedure, studying its properties and applicability to classical database problems. We settle (in the negative) the open problem of decidability of termination of the standard chase, and we provide sufficient termination conditions which are strictly less over-conservative than the best previously known. We investigate the adequacy of the standard chase for checking query containment under constraints, constraint implication and computing certain answers in data exchange, gaining a deeper understanding by separating the algorithm from its result. We identify the properties of the chase result that are essential to the above applications, and we introduce the more general notion of F-universal model set , which supports query and constraint languages that are closed under a class F of mappings. By choosing F appropriately, we extend prior results to existential first-order queries and ∀∃-firstorder constraints. We show that the standard chase is incomplete for finding universal model sets, and we introduce the extended core chase which is complete, i.e. finds an F -universal model set when it exists. A key advantage of the new chase is that the same algorithm can be applied for all mapping classes F of interest, simply by modifying the set of constraints given as input. Even when restricted to the typical input in prior work, the new chase supports certain answer computation and containment/implication tests in strictly more cases than the incomplete standard chase.