Abstract
Abstract argumentation and Dung’s framework are popular for modeling and evaluating arguments in artificial intelligence. We consider various counting problems in abstract argumentation under practical aspects. We revisit algorithms and establish a framework that employs dynamic programming on tree decompositions for counting extensions of abstract argumentation frameworks under admissible, stable, and complete semantics. We provide an empirical evaluation and investigate conditions under which our approach is useful.
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Notes
- 1.
System and supplement are available on github:gorczyca/dp_on_dbs and Zenodo.
- 2.
\(\mu \)-toksia does not have encodings readily accessible as it is tightly coupled to a SAT solver. This would require extraction from source code or implementing it ourselves.
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Acknowledgements
Research was funded by the DFG through the Collaborative Research Center, Grant TRR 248 project ID 389792660, the BMBF, Grant 01IS20056_NAVAS, the Vienna Science and Technology Fund (WWTF) grant ICT19-065, and the Austrian Science Fund (FWF) grants P32830 and Y698.
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Dewoprabowo, R., Fichte, J.K., Gorczyca, P.J., Hecher, M. (2022). A Practical Account into Counting Dung’s Extensions by Dynamic Programming. In: Gottlob, G., Inclezan, D., Maratea, M. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2022. Lecture Notes in Computer Science(), vol 13416. Springer, Cham. https://doi.org/10.1007/978-3-031-15707-3_30
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