@article{Niskanen_Neugebauer_Järvisalo_Rothe_2020, title={Deciding Acceptance in Incomplete Argumentation Frameworks}, volume={34}, url={https://ojs.aaai.org/index.php/AAAI/article/view/5686}, DOI={10.1609/aaai.v34i03.5686}, abstractNote={<p>Expressing incomplete knowledge in abstract argumentation frameworks (AFs) through incomplete AFs has recently received noticeable attention. However, algorithmic aspects of deciding acceptance in incomplete AFs are still under-developed. We address this current shortcoming by developing algorithms for NP-hard and coNP-hard variants of acceptance problems over incomplete AFs via harnessing Boolean satisfiability (SAT) solvers. Focusing on nonempty conflict-free or admissible sets and on stable extensions, we also provide new complexity results for a refined variant of skeptical acceptance in incomplete AFs, ranging from polynomial-time computability to hardness for the second level of the polynomial hierarchy. Furthermore, central to the proposed SAT-based counterexample-guided abstraction refinement approach for the second-level problem variants, we establish conditions for redundant atomic changes to incomplete AFs from the perspective of preserving extensions. We show empirically that the resulting SAT-based approach for incomplete AFs scales at least as well as existing SAT-based approaches to deciding acceptance in AFs.</p>}, number={03}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Niskanen, Andreas and Neugebauer, Daniel and Järvisalo, Matti and Rothe, Jörg}, year={2020}, month={Apr.}, pages={2942-2949} }