Computing Repairs from Active Integrity Constraints

Abstract

Abstract-Repairing an inconsistent knowledge base is a wellknown problem for which several solutions have been proposed and implemented in the past. In this paper, we start by looking at databases with active integrity constraints -consistency requirements that also indicate how the database should be updated when they are not met -as introduced by Caroprese et al. We show that the different kinds of repairs considered by those authors can be effectively computed by searching for leaves of specific kinds of trees. Although these computations are in general not very efficient (deciding the existence of a repair for a given database with active integrity constraints is N P -complete), on average the algorithms we present make significant reductions on the number of nodes in the search tree. Finally, these algorithms also give an operational characterization of different kinds of repairs that can be used when we extend the concept of active integrity constraints to the more general setting of knowledge bases.

Semantics for Active Integrity Constraints Using Approximation Fixpoint Theory

“…This is the case for most semantics of AICs (the notorious exception being the semantics of justified repairs [Caroprese and Truszczyński, 2011], which poses several other problems [Cruz-Filipe et al, 2013]). In the current paper, we assume all AICs are normal.…”

“…Definition 2.4 ( [Cruz-Filipe et al, 2013]). A (weak) repair U for DB, η is well-founded if there exists a sequence of actions α 1 , .…”

“…If the AFT-well-founded repair is twovalued, it is also well-founded (as defined by Cruz-Filipe et al [2013]). Example 3.13.…”

“…They come with a set of declarative semantics [Caroprese and Truszczyński, 2011] that identifies several progressively more restricted classes of repairs, which can be used as criteria to select a preferred repair. These repairs can be computed by means of tree algorithms [Cruz-Filipe et al, 2013;Cruz-Filipe et al, 2015].…”

“…Still, it has been hard to find satisfying semantics for AICs. As shown by Cruz-Filipe et al [2013], the semantics of founded repairs [Caroprese et al, 2006] unexpectedly fails to respect the common-sense law of inertia, while the more restricted semantics of justified repairs [Caroprese and Truszczyński, 2011] forbids natural repairs. That work proposed the operational semantics of wellfounded repairs, which however is not modular [Cruz-Filipe, 2014] and therefore restricted in its practical applicability.…”