Consistent Query Answering for Existential Rules with Closed Predicates
Lorenzo Marconi, Riccardo Rosati
TL;DR
This paper addresses consistent query answering under a closed-world assumption for existential rules expressed as $DED^{\ne}$, focusing on data complexity of repair checking and AR/IAR entailment for boolean unions of conjunctive queries with inequalities across key rule classes. It introduces a framework for repairs, semantics, and recoverability, and establishes tractable data-complexity and FO-rewritability results for several combinations of acyclic, linear, full, guarded, and sticky dependencies. The work also contrasts closed-world results with prior open-world analyses, providing algorithmic insights such as a linearly-implemented repair algorithm and FO-based rewritings. Overall, it advances practical methods for CQA in expressive rule-based knowledge bases, with implications for scalable implementations under closed predicates.
Abstract
Consistent Query Answering (CQA) is an inconsistency-tolerant approach to data access in knowledge bases and databases. The goal of CQA is to provide meaningful (consistent) answers to queries even in the presence of inconsistent information, e.g. a database whose data conflict with meta-data (typically the database integrity constraints). The semantics of CQA is based on the notion of repair, that is, a consistent version of the initial, inconsistent database that is obtained through minimal modifications. We study CQA in databases with data dependencies expressed by existential rules. More specifically, we focus on the broad class of disjunctive embedded dependencies with inequalities (DEDs), which extend both tuple-generating dependencies and equality-generated dependencies. We first focus on the case when the database predicates are closed, i.e. the database is assumed to have complete knowledge about such predicates, thus no tuple addition is possible to repair the database. In such a scenario, we provide a detailed analysis of the data complexity of CQA and associated tasks (repair checking) under different semantics (AR and IAR) and for different classes of existential rules. In particular, we consider the classes of acyclic, linear, full, sticky and guarded DEDs, and their combinations.