Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
On linear time minor tests with depth-first search
Journal of Algorithms
Handle-rewriting hypergraph grammars
Journal of Computer and System Sciences
Graph theoretical structures in logic programs and default theories
Theoretical Computer Science
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
Coherence in finite argument systems
Artificial Intelligence
Context-free Handle-rewriting Hypergraph Grammars
Proceedings of the 4th International Workshop on Graph-Grammars and Their Application to Computer Science
On the Relationship Between Clique-Width and Treewidth
SIAM Journal on Computing
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
Argumentation in artificial intelligence
Artificial Intelligence
Computational properties of argument systems satisfying graph-theoretic constraints
Artificial Intelligence
SIAM Journal on Discrete Mathematics
Symmetric argumentation frameworks
ECSQARU'05 Proceedings of the 8th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Augmenting tractable fragments of abstract argumentation
Artificial Intelligence
Towards fixed-parameter tractable algorithms for abstract argumentation
Artificial Intelligence
Augmenting tractable fragments of abstract argumentation
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Abstract argumentation via monadic second order logic
SUM'12 Proceedings of the 6th international conference on Scalable Uncertainty Management
Toward incremental computation of argumentation semantics: A decomposition-based approach
Annals of Mathematics and Artificial Intelligence
Cliquewidth and knowledge compilation
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
Complexity-sensitive decision procedures for abstract argumentation
Artificial Intelligence
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Most computational problems in the area of abstract argumentation are intractable, thus identifying tractable fragments and developing efficient algorithms for such fragments are important objectives towards practically efficient argumentation systems. One approach to tractability is to view abstract argumentation frameworks (AFs) as directed graphs and bound certain graph parameters. In particular, Dunne showed that many problems can be solved in linear time for AFs of bounded treewidth. In this paper we consider the graph-parameter clique-width, which is more general than treewidth. An additional advantage of clique-width over treewidth is that it applies well to directed graphs and takes the orientation of edges into account. We first give theoretical tractability results for AFs of bounded clique-width and then introduce dynamic-programming algorithms for credulous and skeptical reasoning.