Inconsistent Databases and Argumentation Frameworks with Collective Attacks

TL;DR

This paper explores the relationship between repairs of inconsistent databases with certain integrity constraints and argumentation frameworks with collective attacks, establishing new correspondences and computational methods.

Contribution

It introduces a novel connection between database repairs under denial constraints and tuple-generating dependencies and SETAFs, extending the understanding of argumentation frameworks in this context.

Findings

Repairs under denial constraints correspond to naive, preferred, and stable extensions in SETAFs.

Preprocessing can compute a unique stable and naive extension for certain dependencies.

Inclusion dependencies can be translated into plain argumentation frameworks with simple attacks.

Abstract

The connection between subset-maximal repairs for inconsistent databases involving various integrity constraints and acceptable sets of arguments within argumentation frameworks has recently drawn growing interest. In this paper, we contribute to this domain by establishing a new connection when integrity constraints (ICs) include denial constraints and local-as-view tuple-generating dependencies. It turns out that SET-based Argumentation Frameworks (SETAFs), an extension of Dung's argumentation frameworks (AFs) allowing collective attacks, are needed. It is known that subset-maximal repairs under denial constraints correspond to the naive extensions, which also coincide with the preferred and stable extensions in the resulting SETAFs. Our main findings establish that repairs under the considered fragment of tuple-generating dependencies correspond to the preferred extensions. Moreover, for these dependencies, additional preprocessing allows computing a unique extension that is stable and naive. Allowing both types of constraints breaks this relationship, and even the pre-processing does not help as only preferred semantics captures these repairs. Finally, while it is known that functional dependencies do not require set-based attacks, we prove the same regarding inclusion dependencies. Thus, one can translate inconsistent databases under these restricted classes of ICs to plain AFs with attacks only between arguments.