{"type":"ScholarlyArticle","title":"Quantitative Reasoning and Structural Complexity for Claim-Centric Argumentation","authors":[{"name":"Johannes K. Fichte","slug":"johannes-k-fichte","given":"Johannes K.","family":"Fichte","affiliation":"Linköping University , Sweden"},{"name":"Markus Hecher","slug":"markus-hecher","given":"Markus","family":"Hecher","affiliation":"Massachusetts Institute of Technology , USA"},{"name":"Yasir Mahmood","slug":"yasir-mahmood","given":"Yasir","family":"Mahmood","affiliation":"DICE group , Paderborn University , Germany"},{"name":"Arne Meier","slug":"arne-meier","given":"Arne","family":"Meier","affiliation":"Institut für Theoretische Informatik , Leibniz Universität Hannover , Germany"}],"abstract":"Argumentation is a well-established formalism for nonmonotonic reasoning and a vibrant area of research in AI. Claim-augmented argumentation frameworks (CAFs) have been introduced to deploy a conclusion-oriented perspective. CAFs expand argumentation frameworks by an additional step which involves retaining claims for an accepted set of arguments. We introduce a novel concept of a justification status for claims, a quantitative measure of extensions supporting a particular claim. The well-studied problems of credulous and skeptical reasoning can then be seen as simply the two endpoints of the spectrum when considered as a justification level of a claim. Furthermore, we explore the parameterized complexity of various reasoning problems for CAFs, including the quantitative reasoning for claim assertions. We begin by presenting a suitable graph representation that includes arguments and their associated claims. Our analysis includes the parameter treewidth, and we present decomposition-guided reductions between reasoning problems in CAF and the validity problem for QBF.","doi":"10.24963/ijcai.2023/358","url":"https://ijcai.org/proceedings/2023/358","pdf":"https://ijcai.org/proceedings/2023/0358.pdf","markdown":"https://ijcai.org/proceedings/2023/358.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/358","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Knowledge Representation and Reasoning","track":"Main Track","number":358,"pages":{"first":3212,"last":3220},"keywords":["Knowledge Representation and Reasoning: KRR: Computational complexity of reasoning","Knowledge Representation and Reasoning: KRR: Argumentation"],"videos":[],"references":[{"position":1,"raw":"[Alfano et al., 2020] Gianvincenzo Alfano, Marco Calautti, Sergio Greco, Francesco Parisi, and Irina Trubitsyna. Ex- plainable acceptance in probabilistic abstract argumenta- tion: Complexity and approximation. In KR'20, pages 33-43. IJCAI Organization, 2020.","title":"Explainable acceptance in probabilistic abstract argumentation: Complexity and approximation","authors":"Alfano","year":"2020","venue":"KR'20","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Alviano, 2018] Mario Alviano. The Pyglaf Argumentation Reasoner. In ICLP'17, volume 58, pages 2:1-2:3. Dagstuhl Publishing, 2018.","title":"The Pyglaf Argumentation Reasoner","authors":"Mario Alviano","year":"2018","venue":"ICLP'17","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Amgoud and Prade, 2009] Leila Amgoud and Henri Prade. Using arguments for making and explaining decisions. Ar- tificial Intelligence, 173(3-4):413-436, 2009.","title":"Leila Amgoud and Henri Prade. Using arguments for making and explaining decisions","authors":"Prade Amgoud","year":"2009","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Atkinson et al., 2017] Katie Atkinson, Pietro Baroni, Massi- miliano Giacomin, Anthony Hunter, Henry Prakken, Chris Reed, Guillermo Ricardo Simari, Matthias Thimm, and Serena Villata. Towards artificial argumentation. AI Mag., 38(3):25-36, 2017.","title":"Towards artificial argumentation","authors":"Katie Atkinson, Pietro Baroni, Massimiliano Giacomin, Anthony Hunter, Henry Prakken, Chris Reed, Guillermo Ricardo Simari, Matthias Thimm, Serena Villata","year":"2017","venue":"AI Mag","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Atserias et al., 2011] Albert Atserias, Johannes Klaus Fichte, and Marc Thurley. Clause-learning algorithms with many restarts and bounded-width resolution. Journal of Artificial Intelligence Research, 40:353-373, 2011.","title":"Clause-learning algorithms with many restarts and bounded-width resolution","authors":"Atserias","year":"2011","venue":"Journal of Artificial Intelligence Research","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Bacchus et al., 2003] Fahiem Bacchus, Shannon Dalmao, and Toniann Pitassi. Algorithms and complexity results for #SAT and Bayesian inference. In FOCS'03, pages 340-351, 2003.","title":"Algorithms and complexity results for #SAT and Bayesian inference","authors":"Bacchus","year":"2003","venue":"FOCS'03","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Baroni and Riveret, 2019] Pietro Baroni and Régis Riveret. Enhancing statement evaluation in argumentation via multi- labelling systems. J. Artif. Intell. Res., 66:793-860, 2019.","title":"Enhancing statement evaluation in argumentation via multilabelling systems","authors":"Pietro Baroni, Régis Riveret","year":"2019","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Baroni et al., 2016] Pietro Baroni, Guido Governatori, Ho- Pun Lam, and Régis Riveret. On the justification of state- ments in argumentation-based reasoning. In KR'16, pages 521-524. The AAAI Press, 2016.","title":"On the justification of statements in argumentation-based reasoning","authors":"Pietro Baroni, Guido Governatori, Ho-Pun, Régis Lam, Riveret","year":"2016","venue":"KR'16","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Baroni et al., 2018] Pietro Baroni, Dov Gabbay, Massimil- iano Giacomin, and Leendert van der Torre, editors. Hand- book of Formal Argumentation. College Publications, 2018.","title":"Handbook of Formal Argumentation","authors":null,"year":"2018","venue":null,"doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Besnard and Hunter, 2008] Philippe Besnard and Anthony Hunter. Elements of Argumentation. MIT Press, 2008.","title":"Elements of Argumentation","authors":"Philippe Besnard, Anthony Hunter","year":"2008","venue":null,"doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Biere et al., 2021] Armin Biere, Marijn Heule, Hans van Maaren, and Toby Walsh, editors. Handbook of Satisfiabil- ity -Second Edition, volume 336 of Frontiers in Artificial Intelligence and Applications. IOS Press, 2021.","title":"Handbook of Satisfiability -Second Edition","authors":"Biere","year":"2021","venue":"Frontiers in Artificial Intelligence and Applications","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Bodlaender and Koster, 2008] Hans L. Bodlaender and Arie M. C. A. Koster. Combinatorial optimization on graphs of bounded treewidth. Comput. J., 51(3):255-269, 2008.","title":"Combinatorial optimization on graphs of bounded treewidth","authors":"L Hans, Arie M C A Bodlaender, Koster","year":"2008","venue":"Comput. J","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Bodlaender, 1996] Hans L. Bodlaender. A linear-time algo- rithm for finding tree-decompositions of small treewidth. SIAM J. Comput., 25(6):1305-1317, 1996.","title":"A linear-time algorithm for finding tree-decompositions of small treewidth","authors":"L Hans, Bodlaender","year":"1996","venue":"SIAM J. Comput","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Bondy and Murty, 2008] J. Adrian Bondy and Uppaluri S. R. Murty. Graph Theory. Graduate Texts in Mathematics. Springer, 2008.","title":"Graph Theory","authors":"J, Adrian Bondy, S R Uppaluri, Murty","year":"2008","venue":"Graduate Texts in Mathematics","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Bonzon et al., 2018] Elise Bonzon, Jérôme Delobelle, Sébastien Konieczny, and Nicolas Maudet. Combining extension-based semantics and ranking-based semantics for abstract argumentation. In KR'18, pages 118-127. The AAAI Press, 2018.","title":"Combining extension-based semantics and ranking-based semantics for abstract argumentation","authors":"Elise Bonzon, Jérôme Delobelle, Sébastien Konieczny, Nicolas Maudet","year":"2018","venue":"KR'18","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Brochenin et al., 2018] Remia Brochenin, Thomas Linsbich- ler, Marcoa Maratea, Johannes P. Wallner, and Stefan Woltran. Abstract solvers for Dung's argumentation frame- works. Argument & Computation, 9(1):41-72, 2018.","title":"Abstract solvers for Dung's argumentation frameworks","authors":"Brochenin","year":"2018","venue":"Argument & Computation","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Charwat et al., 2015] Günther Charwat, Wolfgang Dvořák, Sarah A. Gaggl, Johannes P. Wallner, and Stefan Woltran. Methods for solving reasoning problems in abstract argu- mentation -a survey. Artificial Intelligence, 220:28-63, 2015.","title":"Methods for solving reasoning problems in abstract argumentation -a survey","authors":"Günther Charwat, Wolfgang Dvořák, Sarah A Gaggl, Johannes P Wallner, Stefan Woltran","year":"2015","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Chen, 2004] Hubie Chen. Quantified constraint satisfaction and bounded treewidth. In ECAI'04, pages 161-165. IOS Press, 2004.","title":"Quantified constraint satisfaction and bounded treewidth","authors":"Hubie Chen","year":"2004","venue":"ECAI'04","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Dewoprabowo et al., 2022] Ridhwan Dewoprabowo, Jo- hannes Klaus Fichte, Piotr Jerzy Gorczyca, and Markus Hecher. A practical account into counting dung's exten- sions by dynamic programming. In LPNMR'22, pages 387-400. Springer Verlag, 2022.","title":"A practical account into counting dung's extensions by dynamic programming","authors":"Dewoprabowo","year":"2022","venue":"LPNMR'22","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Dung, 1995] Phan Minh Dung. On the acceptability of argu- ments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelli- gence, 77(2):321-357, 1995.","title":"On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games","authors":"Phan Minh, Dung","year":"1995","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Dunne and Bench-Capon, 2002] Paul E. Dunne and Trevor J. M. Bench-Capon. Coherence in finite argument systems. Artificial Intelligence, 141(1/2):187-203, 2002.","title":"Coherence in finite argument systems","authors":"Paul E Dunne, Trevor J M Bench-Capon","year":"2002","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Dvorák and Woltran, 2020] Wolfgang Dvorák and Stefan Woltran. Complexity of abstract argumentation under a claim-centric view. Artificial Intelligence, 285:1-22, 2020.","title":"Complexity of abstract argumentation under a claim-centric view","authors":"Woltran Dvorák, Wolfgang Dvorák, Stefan Woltran","year":"2020","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Dvorák et al., 2020] Wolfgang Dvorák, Anna Rapberger, and Stefan Woltran. Argumentation semantics under a claim-centric view: Properties, expressiveness and relation to setafs. In KR'20, pages 341-350, 2020.","title":"Argumentation semantics under a claim-centric view: Properties, expressiveness and relation to setafs","authors":"Dvorák","year":"2020","venue":"KR'20","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Dvorák et al., 2021] Wolfgang Dvorák, Alexander Greßler, Anna Rapberger, and Stefan Woltran. The complexity land- scape of claim-augmented argumentation frameworks. In AAAI'21, pages 6296-6303. The AAAI Press, 2021.","title":"The complexity landscape of claim-augmented argumentation frameworks","authors":"Dvorák","year":"2021","venue":"AAAI'21","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Dvorák et al., 2022] Wolfgang Dvorák, Markus Hecher, Matthias König, André Schidler, Stefan Szeider, and Stefan Woltran. Tractable Abstract Argumentation via Backdoor- Treewidth. In AAAI, pages 5608-5615. AAAI Press, 2022.","title":"Tractable Abstract Argumentation via Backdoor-Treewidth","authors":"Dvorák","year":"2022","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Dvořák, 2012] Wolfgang Dvořák. Computational aspects of abstract argumentation. PhD thesis, TU Wien, 2012.","title":"Computational aspects of abstract argumentation","authors":"Wolfgang Dvořák, Dvořák","year":"2012","venue":null,"doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Dvořák and Woltran, 2010] W. Dvořák and S. Woltran. Complexity of semi-stable and stage semantics in argu- mentation frameworks. Information Processing Letters, 110(11):425-430, 2010.","title":"Complexity of semi-stable and stage semantics in argumentation frameworks","authors":"W Dvořák, S Woltran","year":"2010","venue":"Information Processing Letters","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Dvořák et al., 2012] W. Dvořák, R. Pichler, and S. Woltran. Towards fixed-parameter tractable algorithms for abstract argumentation. Artificial Intelligence, 186:1-37, 2012.","title":"Towards fixed-parameter tractable algorithms for abstract argumentation","authors":"W Dvořák, R Pichler, S Woltran","year":"2012","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Eiter et al., 2021] Thomas Eiter, Markus Hecher, and Rafael Kiesel. Treewidth-aware cycle breaking for algebraic an- swer set counting. In KR'21, pages 269-279. IJCAI Orga- nization, 2021.","title":"Treewidth-aware cycle breaking for algebraic answer set counting","authors":"Thomas Eiter, Markus Hecher, Rafael Kiesel","year":"2021","venue":"KR'21","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Fazzinga et al., 2015] Bettina Fazzinga, Sergio Flesca, and Francesco Parisi. On the complexity of probabilistic ab- stract argumentation frameworks. ACM Trans. Comput. Log., 16(3):22:1-22:39, 2015.","title":"On the complexity of probabilistic abstract argumentation frameworks","authors":"Bettina Fazzinga, Sergio Flesca, Francesco Parisi","year":"2015","venue":"ACM Trans. Comput. Log","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Fichte et al., 2019] Johannes K. Fichte, Markus Hecher, and Arne Meier. Counting complexity for reasoning in abstract argumentation. In AAAI'19, pages 2827-2834. The AAAI Press, 2019.","title":"Counting complexity for reasoning in abstract argumentation","authors":"Johannes K Fichte, Markus Hecher, Arne Meier","year":"2019","venue":"AAAI'19","doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Fichte et al., 2020] Johannes Klaus Fichte, Markus Hecher, and Andreas Pfandler. Lower Bounds for QBFs of Bounded Treewidth. In LICS, pages 410-424. ACM, 2020.","title":"Lower Bounds for QBFs of Bounded Treewidth","authors":"Fichte","year":"2020","venue":"LICS","doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Fichte et al., 2021a] Johannes Klaus Fichte, Markus Hecher, and Florim Hamiti. The Model Counting Competition 2020. ACM J. Exp. Algorithmics, 26:13:1-13:26, 2021.","title":"The Model Counting Competition 2020","authors":"Fichte","year":"2021","venue":"ACM J. Exp. Algorithmics","doi":null,"url":null,"internal_url":null},{"position":34,"raw":"[Fichte et al., 2021b] Johannes Klaus Fichte, Markus Hecher, Yasir Mahmood, and Arne Meier. Decomposition-guided reductions for argumentation and treewidth. In IJCAI'21, pages 1880-1886. IJCAI Organization, 2021.","title":"Decomposition-guided reductions for argumentation and treewidth","authors":"Fichte","year":"2021","venue":"IJCAI'21","doi":null,"url":null,"internal_url":"/proceedings/2021/259"},{"position":35,"raw":"[Fichte et al., 2022a] Johannes K Fichte, Markus Hecher, Mo- hamed A Nadeem, and TU Dresden. Plausibility reasoning via projected answer set counting-a hybrid approach. In IJCAI'22, pages 2620-2626. IJCAI Organization, 2022.","title":"Plausibility reasoning via projected answer set counting-a hybrid approach","authors":"Fichte","year":"2022","venue":"IJCAI'22","doi":null,"url":null,"internal_url":"/proceedings/2022/363"},{"position":36,"raw":"[Fichte et al., 2022b] Johannes Klaus Fichte, Sarah Alice Gaggl, and Dominik Rusovac. Rushing and strolling among answer sets -navigation made easy. Proceedings of the AAAI Conference on Artificial Intelligence, 36(5):5651- 5659, Jun. 2022.","title":"Rushing and strolling among answer sets -navigation made easy","authors":"Fichte","year":"2022","venue":"Proceedings of the AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":37,"raw":"[Fichte et al., 2023a] Johannes K. Fichte, Robert Ganian, Markus Hecher, Sebastian Ordyniak, and Friedrich Slivovsky. Structure-aware lower bounds and broaden- ing the horizon of tractability for QBF. In LICS'23. ACM, 2023.","title":"Structure-aware lower bounds and broadening the horizon of tractability for QBF","authors":"Fichte","year":"2023","venue":"LICS'23","doi":null,"url":null,"internal_url":null},{"position":38,"raw":"[Fichte et al., 2023b] Johannes K. Fichte, Markus Hecher, Michael Morak, Patrick Thier, and Stefan Woltran. Solv- ing projected model counting by utilizing treewidth and its limits. Artificial Intelligence, 314:103810, 2023.","title":"Solving projected model counting by utilizing treewidth and its limits","authors":"Fichte","year":"2023","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":39,"raw":"[Hecher, 2022] Markus Hecher. Treewidth-aware reductions of normal ASP to SAT -is normal ASP harder than SAT after all? Artif. Intell., 304:103651, 2022.","title":"Treewidth-aware reductions of normal ASP to SAT -is normal ASP harder than SAT after all?","authors":"Markus Hecher","year":"2022","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":40,"raw":"[Hossain and Laroussinie, 2021] Akash Hossain and Franc ¸ois Laroussinie. QCTL model-checking with QBF solvers. Inf. Comput., 280:104642, 2021.","title":"QCTL model-checking with QBF solvers","authors":"Akash Hossain, Franc ¸ois Laroussinie","year":"2021","venue":"Inf. Comput","doi":null,"url":null,"internal_url":null},{"position":41,"raw":"[Hunter and Thimm, 2017] Anthony Hunter and Matthias Thimm. Probabilistic reasoning with abstract argumen- tation frameworks. J. Artif. Intell. Res., 59:565-611, 2017.","title":"Probabilistic reasoning with abstract argumentation frameworks","authors":"Anthony Hunter, Matthias Thimm","year":"2017","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":42,"raw":"[Impagliazzo et al., 2001] Russell Impagliazzo, Ramamohan Paturi, and Francis Zane. Which problems have strongly exponential complexity? J. Comput. Syst. Sci., 63(4):512- 530, 2001.","title":"Which problems have strongly exponential complexity?","authors":"Russell Impagliazzo, Ramamohan Paturi, Francis Zane","year":"2001","venue":"J. Comput. Syst. Sci","doi":null,"url":null,"internal_url":null},{"position":43,"raw":"[Jung et al., 2022] Jean Christoph Jung, Valentin Mayer- Eichberger, and Abdallah Saffidine. QBF Programming with the Modeling Language Bule. In SAT'22, volume 236 of Leibniz International Proceedings in Informatics (LIPIcs), pages 31:1-31:14. Dagstuhl Publishing, 2022.","title":"QBF Programming with the Modeling Language Bule","authors":"Jung","year":"2022","venue":"Leibniz International Proceedings in Informatics (LIPIcs)","doi":null,"url":null,"internal_url":null},{"position":44,"raw":"[Lagniez et al., 2021] Jean-Marie Lagniez, Emmanuel Lonca, Jean-Guy Mailly, and Julien Rossit. Design and results of ICCMA 2021. CoRR, abs/2109.08884, 2021.","title":"Design and results of ICCMA","authors":"Jean-Marie Lagniez, Emmanuel Lonca, Jean-Guy Mailly, Julien Rossit","year":"2021","venue":null,"doi":null,"url":null,"internal_url":null},{"position":45,"raw":"[Lampis et al., 2018] Michael Lampis, Stefan Mengel, and Valia Mitsou. QBF as an alternative to Courcelle's theorem. In SAT'18, pages 235-252. Springer Verlag, 2018.","title":"QBF as an alternative to Courcelle's theorem","authors":"Michael Lampis, Stefan Mengel, Valia Mitsou","year":"2018","venue":"SAT'18","doi":null,"url":null,"internal_url":null},{"position":46,"raw":"[Maher, 2016] Michael J Maher. Resistance to corruption of strategic argumentation. In Dale Schuurmans and Michael Wellman, editors, AAAI'16, pages 1030-1036. The AAAI Press, 2016.","title":"Resistance to corruption of strategic argumentation","authors":"J Michael, Maher","year":"2016","venue":"AAAI'16","doi":null,"url":null,"internal_url":null},{"position":47,"raw":"[Pan and Vardi, 2006] Guoqiang Pan and Moshe Y. Vardi. Fixed-parameter hierarchies inside PSPACE. In LICS, pages 27-36. IEEE Computer Society, 2006.","title":"Fixed-parameter hierarchies inside PSPACE","authors":"Pan, ; ] Guoqiang Vardi, Moshe Y Pan, Vardi","year":"2006","venue":"LICS","doi":null,"url":null,"internal_url":null},{"position":48,"raw":"[Pippenger, 1997] Nicholas Pippenger. Theories of com- putability. Cambridge University Press, 1997.","title":"Theories of computability","authors":"Nicholas Pippenger","year":"1997","venue":null,"doi":null,"url":null,"internal_url":null},{"position":49,"raw":"[Prakken and Vreeswijk, 2002] Henry Prakken and Gerard Vreeswijk. Logics for Defeasible Argumentation, pages 219-318. Springer Verlag, 2002.","title":"Logics for Defeasible Argumentation","authors":"Vreeswijk Prakken","year":"2002","venue":null,"doi":null,"url":null,"internal_url":null},{"position":50,"raw":"[Rago et al., 2018] Antonio Rago, Oana Cocarascu, and Francesca Toni. Argumentation-based recommendations: Fantastic explanations and how to find them. In IJCAI'18, pages 1949-1955. IJCAI Organization, 2018.","title":"Argumentation-based recommendations: Fantastic explanations and how to find them","authors":"Rago","year":"2018","venue":"IJCAI'18","doi":null,"url":null,"internal_url":"/proceedings/2018/269"},{"position":51,"raw":"[Robertson and Seymour, 1986] Neil Robertson and Paul D. Seymour. Graph minors. II. algorithmic aspects of tree- width. J. Algorithms, 7(3):309-322, 1986.","title":"Graph minors. II. algorithmic aspects of treewidth","authors":"Neil Robertson, Paul D Seymour","year":"1986","venue":"J. Algorithms","doi":null,"url":null,"internal_url":null},{"position":52,"raw":"[Sanjay Modgil, 2018] Henry Prakken Sanjay Modgil. Hand- book of Formal Argumentation, chapter Abstract rule-based argumentation, pages 286-361. College Publications, 2018.","title":"Handbook of Formal Argumentation, chapter Abstract rule-based argumentation","authors":"Henry Prakken, Sanjay Modgil","year":"2018","venue":null,"doi":null,"url":null,"internal_url":null},{"position":53,"raw":"[Shaik and van de Pol, 2022] Irfansha Shaik and Jaco van de Pol. Classical Planning as QBF without Grounding. In ICAPS'22, pages 329-337. The AAAI Press, 2022.","title":"Irfansha Shaik and Jaco van de Pol. Classical Planning as QBF without Grounding","authors":"Van Shaik, De Pol","year":"2022","venue":"ICAPS'22","doi":null,"url":null,"internal_url":null},{"position":54,"raw":"[Shukla et al., 2019] Ankit Shukla, Armin Biere, Luca Pulina, and Martina Seidl. A survey on applications of quantified boolean formulas. In ICTAI, pages 78-84. IEEE, 2019.","title":"A survey on applications of quantified boolean formulas","authors":"Ankit Shukla, Armin Biere, Luca Pulina, Martina Seidl","year":"2019","venue":"ICTAI","doi":null,"url":null,"internal_url":null},{"position":55,"raw":"[Wrathall, 1976] Celia Wrathall. Complete sets and the polynomial-time hierarchy. Theor. Comput. Sci., 3(1):23- 33, 1976.","title":"Complete sets and the polynomial-time hierarchy","authors":"Celia Wrathall","year":"1976","venue":"Theor. Comput. Sci","doi":null,"url":null,"internal_url":null},{"position":56,"raw":"[Wu and Caminada, 2010] Yining Wu and Martin Caminada. A labelling based justification status of arguments. Studies in Logic, 3:12-29, 01 2010.","title":"A labelling based justification status of arguments","authors":"Caminada Wu, Yining Wu, Martin Caminada","year":"2010","venue":"Studies in Logic","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}