@inproceedings{WallnerNJ:AAAI2016, author = {Johannes Peter Wallner and Andreas Niskanen and Matti J\"arvisalo}, title = {Complexity Results and Algorithms for Extension Enforcement in Abstract Argumentation}, booktitle = {Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI 2016)}, editor = {Dale Schuurmans and Michael Wellman}, pages = {1088--1094}, publisher = {AAAI Press}, year = {2016}, } Abstract: Understanding the dynamics of argumentation frameworks (AFs) is important in the study of argumentation in AI. In this work, we focus on the so-called extension enforcement problem in abstract argumentation. We provide a nearly complete computational complexity map of fixed-argument extension enforcement under various major AF semantics, with results ranging from polynomial-time algorithms to completeness for the second-level of the polynomial hierarchy. Complementing the complexity results, we propose algorithms for NP-hard extension enforcement based on constrained optimization. Going beyond NP, we propose novel counterexample-guided abstraction refinement procedures for the second-level complete problems and present empirical results on a prototype system constituting the first approach to extension enforcement in its generality.