Preserving Constraints with the Stable Chase

Conjunctive query answering over databases with constraints – also known as (tuple-generating) dependencies – is considered a central database task. To this end, several versions of a construction called chase have been described. Given a set Σ of dependencies, it is interesting to ask which constraints not contained in Σ that are initially satisfied in a given database instance are preserved when computing a chase over Σ. Such constraints are an example for the more general class of incidental constraints which when added to Σ as new dependencies do not affect the certain answers and might even speed up query answering. After formally introducing incidental constraints, we show that deciding incidentality is undecidable for tuple-generating dependencies, even when restricting to classes for which query entailment is decidable. We find that for dependency sets admitting a finite universal model, the core chase can be used to decide incidentality. For the infinite case, we propose the stable chase, which is a generalisation of the core chase, and study its relation to incidental constraints. 1998 ACM Subject Classification F.4.1 Mathematical Logic, H.2.3 Languages, I.2.3 Deduction and Theorem Proving, I.2.4 Knowledge Representation Formalisms and Methods