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The paper presents a declarative semantics for the maintenance of integrity constraints expressed by means of production rules. A production rule is a special form of active rule, called active integrity constraint, whose body contains an integrity constraint (conjunction of literals which must be false) and whose head contains a disjunction of update atoms, i.e. actions to be performed if the corresponding constraints are not satisfied (i.e. are true). The paper introduces i) a formal declarative semantics allowing the computation of founded repairs, that is repairs whose actions are specified and supported by active integrity constraint, ii) an equivalent semantics obtained by rewriting production rules into disjunctive logic rules, so that repairs can be derived from the answer sets of the logic program, iii) a characterization of production rules allowing a methodology for integrity maintenance.

In this paper we deal with inconsistent databases and propose a logic framework that allows specifying sets of actions which should be performed to make databases consistent (repairs). The motivation of this work stems from the observation that in repairing a database it is natural to express among a set of update operations, the (preferred) actions which should be performed to repair the database. We introduce (conditioned) active integrity constraints, a simple and powerful form of active rules with declarative semantics, well suited for computing database repairs and consistent answers. We first consider a "prescriptive" semantics where the allowed actions are those specified by the constraints. Under such a semantics the existence of repairs and consistent answers is not guaranteed. Thus, we also investigate the class of universally quantified constraints under a different semantics where actions are interpreted as preference conditions on the set of possible repairs ("preferable" semantics). Under such a semantics every database with integrity constraints admits repairs and consistent answers. We show that (conditioned) active integrity constraints can be rewritten into disjunctive Datalog programs with classical negation and that (preferred) repairs can be derived through the computation of (preferred) disjunctive stable models. We study the complexity of computing repairs and consistent answers and show that active integrity constraints can also be used to express hard problems. * The author is also supported by ICAR-CNR and Exeura S.r.l.