The Complexity of Repairing, Adjusting, and Aggregating of Extensions in Abstract Argumentation

TL;DR

This paper investigates the computational complexity of modifying and aggregating extensions in abstract argumentation frameworks, focusing on problems like repair, adjustment, and finding central extensions within a parameterized complexity setting.

Contribution

It provides a comprehensive analysis of the complexity of repair, adjustment, and aggregation problems across various semantics in abstract argumentation, using parameterized complexity with distance k.

Findings

Complexity results vary across different semantics.

Many problems are fixed-parameter tractable for certain semantics.

The study offers a unified complexity framework for dynamic argumentation tasks.

Abstract

We study the computational complexity of problems that arise in abstract argumentation in the context of dynamic argumentation, minimal change, and aggregation. In particular, we consider the following problems where always an argumentation framework F and a small positive integer k are given. - The Repair problem asks whether a given set of arguments can be modified into an extension by at most k elementary changes (i.e., the extension is of distance k from the given set). - The Adjust problem asks whether a given extension can be modified by at most k elementary changes into an extension that contains a specified argument. - The Center problem asks whether, given two extensions of distance k, whether there is a "center" extension that is a distance at most (k-1) from both given extensions. We study these problems in the framework of parameterized complexity, and take the distance k as the parameter. Our results covers several different semantics, including admissible, complete, preferred, semi-stable and stable semantics.