Complexity of Consistent Query Answering in Databases under Cardinality-Based and Incremental Repair Semantics

TL;DR

This paper explores the computational complexity of consistent query answering in databases, focusing on minimal repairs based on cardinality and incremental updates, providing tight bounds and fixed parameter tractability results.

Contribution

It establishes the first tight complexity bounds for CQA under cardinality-based repairs and analyzes incremental complexity with fixed parameter tractability.

Findings

Tight complexity bounds for CQA under cardinality-based repairs.

Analysis of incremental CQA complexity after database updates.

Investigation of fixed parameter tractability in dynamic CQA scenarios.

Abstract

Consistent Query Answering (CQA) is the problem of computing from a database the answers to a query that are consistent with respect to certain integrity constraints that the database, as a whole, may fail to satisfy. Consistent answers have been characterized as those that are invariant under certain minimal forms of restoration of the database consistency. We investigate algorithmic and complexity theoretic issues of CQA under database repairs that minimally depart -wrt the cardinality of the symmetric difference- from the original database. We obtain first tight complexity bounds. We also address the problem of incremental complexity of CQA, that naturally occurs when an originally consistent database becomes inconsistent after the execution of a sequence of update operations. Tight bounds on incremental complexity are provided for various semantics under denial constraints. Fixed parameter tractability is also investigated in this dynamic context, where the size of the update sequence becomes the relevant parameter.