Declarative Semantics of Production Rules for Integrity Maintenance

Abstract

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.

Computing Repairs from Active Integrity Constraints

“…At this stage, we have presented direct algorithms to compute repairs and justified repairs for inconsistent databases with (active) integrity constraints. Since the general problem of finding these repairs is at least N P -complete, in the worst case our algorithms are asymptotically equivalent to the techniques presented in [4] (namely, translating the context to production rules and computing a stable model of these).…”

“…In [4] the authors study AICs and define a declarative semantics for them, defining the class of founded repairs. That work is extended in [5], and, as a result of the effort to clarify the relation between the semantics of AICs and revision programming [8], the more restricted class of justified repairs is defined.…”

Declarative Semantics for Active Integrity Constraints

“…If several repairs are possible, guidance on how to select a repair to execute could be useful. The formalism of active integrity constraints (aic's, for short) [2] was designed to address this problem. We will now review it and offer a first extension by introducing the semantics of founded weak repairs.…”

“…The problem can be addressed by formalisms that allow the database designer to formulate integrity constraints and, in addition, to state preferred ways for enforcing them. In this paper, we study a recent formalism of that type: active integrity constraints (aic's, for short) [2].…”

“…To specify the meaning of sets of aic's, [2] proposed the concept of foundedness, and combined it with the requirement of the minimality of change to get the semantics of founded repairs. Foundedness reflects a certain groundedness condition.…”