TY  - GEN
A1  - Fichte, Johannes Klaus
A1  - Hecher, Markus
A1  - Meier, Arne
T1  - Counting Complexity for Reasoning in Abstract Argumentation
T2  - The Thirty-Third AAAI Conference on Artificial Intelligence, the Thirty-First Innovative Applications of Artificial Intelligence Conference, the Ninth AAAI Symposium on Educational Advances in Artificial Intelligence
N2  - In this paper, we consider counting and projected model counting of extensions in abstract argumentation for various semantics. When asking for projected counts we are interested in counting the number of extensions of a given argumentation framework while multiple extensions that are identical when restricted to the projected arguments count as only one projected extension. We establish classical complexity results and parameterized complexity results when the problems are parameterized by treewidth of the undirected argumentation graph. To obtain upper bounds for counting projected extensions, we introduce novel algorithms that exploit small treewidth of the undirected argumentation graph of the input instance by dynamic programming (DP). Our algorithms run in time double or triple exponential in the treewidth depending on the considered semantics. Finally, we take the exponential time hypothesis (ETH) into account and establish lower bounds of bounded treewidth algorithms for counting extensions and projected extension.
Y1  - 2019
SN  - 978-1-57735-809-1
SP  - 2827
EP  - 2834
PB  - AAAI Press
CY  - Palo Alto
ER  -