Inconsistent Databases and Argumentation Frameworks with Collective Attacks

Problem
This paper addresses the gap in understanding the relationship between subset-maximal repairs for inconsistent databases and argumentation frameworks, particularly when integrity constraints (ICs) include denial constraints and local-as-view tuple-generating dependencies. The authors highlight that while previous work has explored these connections, the specific case of SET-based Argumentation Frameworks (SETAFs) accommodating collective attacks has not been thoroughly investigated. This work is presented as a preprint and has not yet undergone peer review.

Method
The authors introduce a novel framework that connects subset-maximal repairs under denial constraints to naive extensions in SETAFs. They leverage the properties of SETAFs, which extend Dung’s argumentation frameworks by allowing collective attacks among arguments. The core technical contributions include the establishment that repairs under the specified fragment of tuple-generating dependencies correspond to preferred extensions in SETAFs. The authors also propose a preprocessing step that enables the computation of a unique extension that is both stable and naive. They demonstrate that when both denial constraints and tuple-generating dependencies are present, the relationship between repairs and extensions is disrupted, with preferred semantics being the only applicable framework. The paper also proves that inclusion dependencies, like functional dependencies, do not necessitate set-based attacks, allowing for a translation of inconsistent databases into standard argumentation frameworks.

Results
The authors provide theoretical results rather than empirical benchmarks, focusing on the logical relationships between repairs and argumentation semantics. They establish that subset-maximal repairs under denial constraints align with naive extensions, while repairs under tuple-generating dependencies correspond to preferred extensions. The preprocessing step is shown to yield a unique stable and naive extension, although this is contingent on the specific types of constraints applied. The implications of these findings suggest that the complexity of argumentation frameworks can be reduced under certain conditions, allowing for more efficient reasoning about inconsistent databases.

Limitations
The authors acknowledge that their findings are limited to specific classes of integrity constraints and do not generalize to all types of ICs. They note that the introduction of both denial constraints and tuple-generating dependencies complicates the relationship between repairs and argumentation semantics, which may limit the applicability of their results. Additionally, the paper does not provide empirical validation or performance metrics, which could strengthen the practical implications of their theoretical contributions.

Why it matters
This work has significant implications for the fields of database theory and argumentation, particularly in scenarios involving inconsistent data. By clarifying the connections between database repairs and argumentation frameworks, the findings can inform the design of more robust systems for automated reasoning in databases. The ability to translate inconsistent databases into simpler argumentation frameworks could enhance the efficiency of reasoning processes, making it easier to derive conclusions from incomplete or contradictory information. This research opens avenues for further exploration of argumentation semantics in the context of database integrity and inconsistency management.

Authors: Yasir Mahmood, Jonni Virtema, Timon Barlag, Axel-Cyrille Ngonga Ngomo
Source: arXiv:2605.03954
URL: https://arxiv.org/abs/2605.03954v1