Declarative Semantics for Active Integrity Constraints

We study active integrity constraints, a formalism designed to describe integrity constraints on databases and to specify preferred ways to enforce them. The original semantics proposed for active integrity constraints is based on the concept of a founded repair. We point out that groundedness underlying founded repairs does not prevent cyclic justifications and so, may be inappropriate in some applications. Thus, using a different notion of grounding, with roots in logic programming and revision programming, we introduce two new semantics: of justified weak repairs, and of justified repairs. We study properties of these semantics, relate them to earlier semantics of active integrity constraints, and establish the complexity of basic decision problems.