Active integrity constraints and revision programming

Abstract

We study active integrity constraints and revision programming, two formalisms designed to describe integrity constraints on databases and to specify policies on preferred ways to enforce them. Unlike other more commonly accepted approaches, these two formalisms attempt to provide a declarative solution to the problem. However, the original semantics of founded repairs for active integrity constraints and justified revisions for revision programs differ. Our main goal is to establish a comprehensive framework of semantics for active integrity constraints, to find a parallel framework for revision programs, and to relate the two. By doing so, we demonstrate that the two formalisms proposed independently of each other and based on different intuitions when viewed within a broader semantic framework turn out to be notational variants of each other. That lends support to the adequacy of the semantics we develop for each of the formalisms as the foundation for a declarative approach to the problem of database update and repair. In the paper we also study computational properties of the semantics we consider and establish results concerned with the concept of the minimality of change and the invariance under the shifting transformation.

A Dynamic View of Active Integrity Constraints

“…It is known that deciding the existence of a repair is NP-complete for PMA repairs and for founded weak repairs, while it is Σ 2 P complete for founded repairs [CT11]. We leave to future work the investigation of the complexity of dynamic repairs.…”

“…In our propositional language they are nothing but boolean formulas. Two ways of repairing databases can be found in the literature on active integrity constraints [CT11]. Both consist in first finding an appropriate set of update actions U and then building the update V • U of V by U as defined in Section 2.…”

“…We refer to [CT11] for an overview. Just as for static constraints, all definitions are based on the notion of repair set: an appropriate set of update actions U such that V • U no longer violates the integrity constraints, where V • U is the result of updating V with U as defined in Section 2 and is called the repaired database.…”

“…This opens up two perspectives. First, our definition also covers revision programs [CT11]; we leave it to future work to establish the exact relationship. Second, we could further generalise the action R(r) from a set of update actions to arbitrary DL-PA programs.…”

“…Just as [CT11,CF14] we only consider ground constraints, i.e., we work with a propositional language.…”