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.
References
Alviano, M.: The PYGLAF argumentation reasoner. In: ICLP 2017 (Technical Communications). OASICS, vol. 58, pp. 2:1–2:3, Dagstuhl (2017)
Alviano, M., Dodaro, C., Fichte, J.K., Hecher, M., Philipp, T., Rath, J.: Inconsistency proofs for ASP: the ASP - DRUPE format. TPLP 19(5–6), 891–907 (2019)
Amgoud, L., Prade, H.: Using arguments for making and explaining decisions. AIJ 173(3–4), 413–436 (2009)
Besin, V., Hecher, M., Woltran, S.: Utilizing treewidth for quantitative reasoning on epistemic logic programs. TPLP 21(5), 575–592 (2021)
Charwat, G.: Tree-decomposition based algorithms for abstract argumentation framework. Master’s thesis, TU Wien, Vienna, Austria (2012)
Codd, E.F.: A relational model of data for large shared data banks. Commun. ACM 13(6), 377–387 (1970)
Dietz, E., Fichte, J.K., Hamiti, F.: A quantitative symbolic approach to individual human reasoning. In: Proceedings of CogSci 2022 (2022, to appear)
Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. AIJ 77(2), 321–357 (1995)
Dvořák, W., Rapberger, A., Wallner, J.P., Woltran, S.: ASPARTIX-V19 - an answer-set programming based system for abstract argumentation. In: Herzig, A., Kontinen, J. (eds.) FoIKS 2020. LNCS, vol. 12012, pp. 79–89. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-39951-1_5
Dvořák, W., Pichler, R., Woltran, S.: Towards fixed-parameter tractable algorithms for abstract argumentation. AIJ 186, 1–37 (2012)
Fandinno, J., Hecher, M.: Treewidth-aware complexity in ASP: not all positive cycles are equally hard. In: AAAI 2021, pp. 6312–6320. AAAI Press (2021)
Fichte, J.K., Hecher, M., Kieler, M.F.I.: Treewidth-aware quantifier elimination and expansion for QCSP. In: Simonis, H. (ed.) CP 2020. LNCS, vol. 12333, pp. 248–266. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-58475-7_15
Fichte, J.K., Hecher, M., Meier, A.: Knowledge-base degrees of inconsistency: complexity and counting. In: AAA 2021, pp. 6349–6357. No. 7, The AAAI Press (2021)
Fichte, J.K., Hecher, M., Nadeem, M.A.: Plausibility reasoning via projected answer set counting–a hybrid approach. In: IJCAI 2022 (2022, to appear)
Fichte, J.K., Hecher, M., Pfandler, A.: Lower bounds for QBFs of bounded treewidth. In: LICS 2020, pp. 410–424. Associating for Computing Machinery, New York (2020)
Fichte, J.K., Hecher, M., Roland, V.: Parallel model counting with CUDA: algorithm engineering for efficient hardware utilization. In: CP 2021, pp. 24:1–24:20 (2021)
Fichte, J.K., Hecher, M., Roland, V.: Proofs for propositional model counting. In: SAT 2022 (2022, to appear)
Fichte, J.K., Hecher, M., Thier, P., Woltran, S.: Exploiting database management systems and treewidth for counting. TPLP 22(1), 128–157 (2022)
Fichte, J.K., Gaggl, S.A., Rusovac, D.: Rushing and strolling among answer sets - navigation made easy. In: Proceedings of the 36th AAAI Conference on Artificial Intelligence (AAAI 2022). The AAAI Press (2022, to appear)
Fichte, J.K., Hecher, M., McCreesh, C., Shahab, A.: Complications for computational experiments from modern processors. In: CP 2021, pp. 25:1–25:21 (2021)
Hecher, M., Thier, P., Woltran, S.: Taming high treewidth with abstraction, nested dynamic programming, and database technology. In: Pulina, L., Seidl, M. (eds.) SAT 2020. LNCS, vol. 12178, pp. 343–360. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-51825-7_25
Lagniez, J., Lonca, E., Mailly, J., Rossit, J.: Design and results of ICCMA 2021. CoRR abs/2109.08884 (2021). https://arxiv.org/abs/2109.08884
Niskanen, A., Järvisalo, M.: \(\rm \mu \)-toksia: an efficient abstract argumentation reasoner. In: KR 2020, pp. 800–804 (2020)
Rago, A., Cocarascu, O., Toni, F.: Argumentation-based recommendations: fantastic explanations and how to find them. In: IJCAI 2018, pp. 1949–1955 (2018)
Ullman, J.D.: Principles of Database and Knowledge-Base Systems, vol. II. Computer Science Press, New York (1989)
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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