Decomposition-Guided Reductions for Argumentation and Treewidth

Argumentation is a widely applied framework for modeling and evaluating arguments and its reasoning with various applications. Popular frameworks are abstract argumentation (Dung’s framework) or logic-based argumentation (BesnardHunter’s framework). Their computational complexity has been studied quite in-depth. Incorporating treewidth into the complexity analysis is particularly interesting, as solvers oftentimes employ SAT-based solvers, which can solve instances of low treewidth fast. In this paper, we address whether one can design reductions from argumentation problems to SAT-problems while linearly preserving the treewidth, which results in decomposition-guided (DG) reductions. It turns out that the linear treewidth overhead caused by our DG reductions, cannot be significantly improved under reasonable assumptions. Finally, we consider logic-based argumentation and establish new upper bounds using DG reductions and lower bounds.

[1]  Nadia Creignou,et al.  Complexity Classifications for Logic-Based Argumentation , 2014, TOCL.

[2]  Arne Meier,et al.  Counting Complexity for Reasoning in Abstract Argumentation , 2018, AAAI.

[3]  Rina Dechter,et al.  Bucket Elimination: A Unifying Framework for Reasoning , 1999, Artif. Intell..

[4]  Markus Hecher,et al.  Treewidth-aware Reductions of Normal ASP to SAT - Is Normal ASP Harder than SAT after All? , 2020, KR.

[5]  Editors , 2003 .

[6]  M. Ziegler.  Volume 152 of Graduate Texts in Mathematics , 1995 .

[7]  Toniann Pitassi,et al.  Algorithms and complexity results for #SAT and Bayesian inference , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[8]  Michael Lampis,et al.  Treewidth with a Quantifier Alternation Revisited , 2018, IPEC.

[9]  Thomas Linsbichler,et al.  Abstract Solvers for Dung's Argumentation Frameworks , 2015, TAFA.

[10]  R. Lathe.  Phd by thesis , 1988, Nature.

[11]  Michael J. Maher.  Resistance to Corruption of Strategic Argumentation , 2016, AAAI.

[12]  Stefan Woltran,et al.  Expansion-based QBF Solving on Tree Decompositions , 2017, RCRA@AI*IA.

[13]  S Hancocks,et al.  I go to a friend , 2001, British dental journal.

[14]  Stefan Woltran,et al.  On the Complexity of Enumerating the Extensions of Abstract Argumentation Frameworks , 2017, IJCAI.

[15]  Russell Impagliazzo,et al.  Which problems have strongly exponential complexity? , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[16]  Nicholas Pippenger,et al.  Theories of computability , 1997 .

[17]  Stefan Woltran,et al.  Methods for solving reasoning problems in abstract argumentation – A survey , 2015, Artif. Intell..

[18]  Anthony Hunter,et al.  Elements of Argumentation , 2007, ECSQARU.

[19]  Johannes Klaus Fichte,et al.  Clause-Learning Algorithms with Many Restarts and Bounded-Width Resolution , 2011, J. Artif. Intell. Res..

[20]  Stefan Woltran,et al.  Towards fixed-parameter tractable algorithms for abstract argumentation , 2012, Artif. Intell..

[21]  Francesca Toni,et al.  Argumentation-Based Recommendations: Fantastic Explanations and How to Find Them , 2018, IJCAI.

[22]  Stefan Mengel,et al.  QBF as an Alternative to Courcelle's Theorem , 2018, SAT.

[23]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[24]  Michal Pilipczuk,et al.  Parameterized Algorithms , 2015, Springer International Publishing.

[25]  Phan Minh Dung,et al.  On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming and n-Person Games , 1995, Artif. Intell..

[26]  Stefan Woltran,et al.  Complexity of logic-based argumentation in Post's framework , 2011, Argument Comput..

[27]  Stefan Woltran,et al.  Taming High Treewidth with Abstraction, Nested Dynamic Programming, and Database Technology , 2020, SAT.

[28]  Andreas Pfandler,et al.  Lower Bounds for QBFs of Bounded Treewidth , 2019, LICS.