@article{Baumeister_Neugebauer_Rothe_Schadrack_2018, title={Complexity of Verification in Incomplete Argumentation Frameworks}, volume={32}, url={https://ojs.aaai.org/index.php/AAAI/article/view/11562}, DOI={10.1609/aaai.v32i1.11562}, abstractNote={ <p> Abstract argumentation frameworks are a well-established formalism to model nonmonotonic reasoning processes. However, the standard model cannot express incomplete or conflicting knowledge about the state of a given argumentation. Previously, argumentation frameworks were extended to allow uncertainty regarding the set of attacks or the set of arguments. We combine both models into a model of general incompleteness, complement previous results on the complexity of the verification problem in incomplete argumentation frameworks, and provide a full complexity map covering all three models and all classical semantics. Our main result shows that the complexity of verifying the preferred semantics rises from coNP- to Sigma^p_2-completeness when allowing uncertainty about either attacks or arguments, or both. </p> }, number={1}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Baumeister, Dorothea and Neugebauer, Daniel and Rothe, Jörg and Schadrack, Hilmar}, year={2018}, month={Apr.} }