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An Incremental Algorithm for Computing the Grounded Extension of Dynamic Abstract Argumentation Frameworks

Abstract

Several formalisms have been introduced to model disputes between agents. Abstract argumentation is a simple, yet powerful formalism for modeling disputes by abstracting from the internal structure of arguments. Much work has been done to characterize fast algorithms for ‘static’ argumentation frameworks which are assumed to be fixed, in the sense that they do not change during a dispute. However, argumentation frameworks are highly dynamic in practice. For instance, applications of argumentation for negotiation and persuasion are usually based on protocols where agents state their arguments and attacks one after the other in a dynamic process during which the outcome of the debate evolves. We focus on one of the most popular argumentation semantics, namely the grounded semantics, and deal with the problem of recalculating the extensions of argumentation frameworks after adding or deleting attacks or arguments. In particular, we propose an incremental algorithm for the efficient computation of the grounded semantics, useful in dynamic contexts where argumentation frameworks are continuously updated to consider new information. We report on experiments showing that our incremental algorithm is on average faster than CoQuiAAS, the solver that won the last edition of the international competition on computational models of argumentation for the task of computing the grounded extension of an argumentation framework.

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Notes

  1. 1.

    A detailed list of the differences between (Greco and Parisi 2017) and this paper is reported in the last paragraph of the related work section.

  2. 2.

    Available at http://argumentationcompetition.org/2015/iccma15_testcases.zip.

  3. 3.

    Available at http://argumentationcompetition.org/2015/iccma2015_benchmarks.zip.

References

  1. Alfano G, Greco S, Parisi F (2017a) Efficient computation of extensions for dynamic abstract argumentation frameworks: an incremental approach. In: Proceedings of the twenty-sixth international joint conference on artificial intelligence (IJCAI), pp 49–55

  2. Alfano G, Greco S, Parisi F (2017b) Computing stable and preferred extensions of dynamic bipolar argumentation frameworks. In: Proceedings of the 1st workshop on advances in argumentation in artificial intelligence co-located with XVI international conference of the Italian Association for artificial intelligence (\(AI{^3}@AI*IA\)), pp 28–42

  3. Alfano G, Greco S, Parisi F (2018a) A meta-argumentation approach for the efficient computation of stable and preferred extensions in dynamic bipolar argumentation frameworks. Intell Artif 12(2):193–211

    Google Scholar 

  4. Alfano G, Greco S, Parisi F (2018b) Computing extensions of dynamic abstract argumentation frameworks with second-order attacks. In: Proceedings of the 22nd international database engineering & applications symposium (IDEAS), pp 183–192

  5. Alfano G, Greco S, Parisi F, Simari GI, Simari GR (2018c) Incremental computation of warranted arguments in dynamic defeasible argumentation: the rule addition case. In: Proceedings of the 33rd annual ACM symposium on applied computing (SAC), pp 911–917

  6. Alfano G, Greco S, Parisi F, Simari GI, Simari GR (2018d) An incremental approach to structured argumentation over dynamic knowledge bases. In: Proceedings of the sixteenth international conference of principles of knowledge representation and reasoning (KR), pp 78–87

  7. Alfano G, Greco S, Parisi F (2019) An efficient algorithm for skeptical preferred acceptance in dynamic argumentation frameworks. In: Proceedings of international joint conference on artificial intelligence (IJCAI)

  8. Amgoud L, Vesic S (2012) Revising option status in argument-based decision systems. J Logic Comput 22(5):1019–1058

    Article  Google Scholar 

  9. Baroni P, Caminada M, Giacomin M (2011) An introduction to argumentation semantics. Knowl Eng Rev 26(4):365–410

    Article  Google Scholar 

  10. Baroni P, Giacomin M, Liao B (2014) On topology-related properties of abstract argumentation semantics. A correction and extension to dynamics of argumentation systems: a division-based method. Artif Intell 212:104–115

    Article  Google Scholar 

  11. Bastos MT, Puschmann C, Travitzki R (2013) Tweeting across hashtags: overlapping users and the importance of language, topics, and politics. In: 24th ACM conference on hypertext and social media (part of ECRC) (HT), pp 164–168

  12. Baumann R (2011) Splitting an argumentation framework. In: Proceedings of international conference on logic programming and nonmonotonic reasoning (LPNMR), pp 40–53

  13. Baumann R (2012) Normal and strong expansion equivalence for argumentation frameworks. Artif Intell 193:18–44

    Article  Google Scholar 

  14. Baumann R (2014) Context-free and context-sensitive kernels: update and deletion equivalence in abstract argumentation. In: Proceedings of the European conference on artificial intelligence (ECAI), pp 63–68

  15. Baumann R, Brewka G (2010) Expanding argumentation frameworks: enforcing and monotonicity results. In: Proceedings of international conference computational models of argument (COMMA), pp 75–86

  16. Baumann R, Brewka G, Dvorák W, Woltran S (2012) Parameterized splitting: a simple modification-based approach. In: Correct reasoning—essays on logic-based AI in honour of Vladimir Lifschitz, pp 57–71

  17. Bench-Capon TJM, Dunne Paul E (2007) Argumentation in artificial intelligence. Artif Intell 171(1015):619–641

    Article  Google Scholar 

  18. Bentahar J, Labban J (2011) An argumentation-driven model for flexible and efficient persuasive negotiation. Group Decis Negot 20(4):411–435

    Article  Google Scholar 

  19. Bisquert P, Cayrol C, de Saint-Cyr FD, Lagasquie-Schiex M-C (2013) Characterizing change in abstract argumentation systems. In: Trends in belief revision and argumentation dynamics, vol 48, pp 75–102

  20. Bistarelli S, Rossi F, Santini F (2017) A conarg-based library for abstract argumentation. In: 29th IEEE international conference on tools with artificial intelligence (ICTAI), pp 374–381

  21. Boella G, Kaci S, van der Torre LWN (2009a) Dynamics in argumentation with single extensions: attack refinement and the grounded extension (extended version). In: Proceedings of the international workshop on argumentation in multi-agent systems (ArgMAS), pp 150–159

  22. Boella G, Kaci S, van der Torre LWN (2009b) Dynamics in argumentation with single extensions: abstraction principles and the grounded extension. In: Proceedings of the European conference on symbolic and quantitative approaches to reasoning with uncertainty (ECSQARU), pp 107–118

  23. Caminada M (2006) Semi-stable semantics. In: Proceedings of the international conference on computational models of argument (COMMA), pp 121–130

  24. Cayrol C, de Saint-Cyr FD, Lagasquie-Schiex M-C (2008) Revision of an argumentation system. In: Proceedings of the international conference on principles of knowledge represent and reasoning (KR), pp 124–134

  25. Cayrol C, de Saint-Cyr FD, Lagasquie-Schiex M-C (2010) Change in abstract argumentation frameworks: adding an argument. J Artif Intell Res 38:49–84

    Article  Google Scholar 

  26. Charwat G, Dvorák W, Gaggl SA, Wallner JP, Woltran S (2015) Methods for solving reasoning problems in abstract argumentation—a survey. Artif Intell 220:28–63

    Article  Google Scholar 

  27. de Saint-Cyr FD, Bisquert P, Cayrol C, Lagasquie-Schiex M-C (2016) Argumentation update in YALLA (yet another logic language for argumentation). Int J Approx Reason 75:57–92

    Article  Google Scholar 

  28. Doutre S, Herzig A, Perrussel L (2014) A dynamic logic framework for abstract argumentation. In: Proceedings of the fourteenth international conference of principles of knowledge representation and reasoning (KR)

  29. Dung PM (1995) On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif Intell 77(2):321–358

    Article  Google Scholar 

  30. Dung PM, Mancarella P, Toni F (2007) Computing ideal sceptical argumentation. Artif Intell 171(10–15):642–674

    Article  Google Scholar 

  31. Dunne PE (2009) The computational complexity of ideal semantics. Artif Intell 173(18):1559–1591

    Article  Google Scholar 

  32. Dunne PE, Wooldridge M (2009) Complexity of abstract argumentation. In: Argumentation in artificial intelligence, pp 85–104

  33. Dvorák W, Woltran S (2010) Complexity of semi-stable and stage semantics in argumentation frameworks. Inf Process Lett 110(11):425–430

    Article  Google Scholar 

  34. Dvorák W, Pichler R, Woltran S (2010) Towards fixed-parameter tractable algorithms for argumentation. In: Proceedings of the international conference on principles of knowledge representation and reasoning (KR)

  35. Eiter T, Strass H, Truszczynski M, Woltran S (eds) (2015) Advances in knowledge representation, logic programming, and abstract argumentation, volume 9060 of lecture notes in computer science. Springer, Berlin

    Google Scholar 

  36. Falappa MA, Garcia AJ, Kern-Isberner G, Simari GR (2011) On the evolving relation between belief revision and argumentation. Knowl Eng Rev 26(1):35–43

    Article  Google Scholar 

  37. Fazzinga B, Flesca S, Parisi F (2015) On the complexity of probabilistic abstract argumentation frameworks. ACM Trans Comput Logic 16(3):22

    Article  Google Scholar 

  38. Fazzinga B, Flesca S, Parisi F (2016) On efficiently estimating the probability of extensions in abstract argumentation frameworks. Int J Approx Reason 69:106–132

    Article  Google Scholar 

  39. Greco S, Parisi F (2016a) Efficient computation of deterministic extensions for dynamic abstract argumentation frameworks. In: Proceedings of the European conference on artificial intelligence (ECAI), pp 1668–1669

  40. Greco S, Parisi F (2016b) Incremental computation of deterministic extensions for dynamic argumentation frameworks. In: Proceedings of the European conference on logics in artificial intelligence (JELIA), pp 288–304

  41. Greco S, Parisi F (2017) Incremental computation of grounded semantics for dynamic abstract argumentation frameworks. In: Second international workshop on conflict resolution in decision making (COREDEMA 2016), revised selected papers, pp 66–81

  42. Kökciyan N, Yaglikci N, Yolum P (2017) An argumentation approach for resolving privacy disputes in online social networks. ACM Trans Internet Technol 17(3):27:1–27:22

    Article  Google Scholar 

  43. Lagniez J-M, Lonca E, Mailly J-G (2015) CoQuiAAS: a constraint-based quick abstract argumentation solver. In: ICTAI, pp 928–935

  44. Liao BS, Jin L, Koons RC (2011) Dynamics of argumentation systems: a division-based method. Artif Intell 175(11):1790–1814

    Article  Google Scholar 

  45. Lifschitz V, Turner H (1994) Splitting a logic program. In: Proceedings of the international conference on logic programming (ICLP), pp 23–37

  46. Modgil S, Prakken H (2011) Revisiting preferences and argumentation. In: Proceedings of the international joint conference on artificial intelligence (IJCAI), pp 1021–1026

  47. Oikarinen E, Woltran S (2011) Characterizing strong equivalence for argumentation frameworks. Artif Intell 175(14–15):1985–2009

    Article  Google Scholar 

  48. Parsons S, McBurney P (2003) Argumentation-based dialogues for agent co-ordination. Group Decis Negot 12(5):415–439

    Article  Google Scholar 

  49. Pollock JL (1998) Perceiving and reasoning about a changing world. Comput Intell 14(4):498–562

    Article  Google Scholar 

  50. Rahwan I, Simari GR (2009) Argumentation in artificial intelligence, 1st edn. Springer, Berlin

    Google Scholar 

  51. Thimm M, Villata S (2017) The first international competition on computational models of argumentation: results and analysis. Artif Intell 252:267–294

    Article  Google Scholar 

  52. Thimm M, Villata S, Cerutti F, Oren N, Strass H, Vallati M (2016) Summary report of the first international competition on computational models of argumentation. AI Mag 37(1):102

    Article  Google Scholar 

  53. Xu Y, Cayrol C (2015) The matrix approach for abstract argumentation frameworks. In: Proceedings of the international workshop on theory and applications of formal argumentation (TAFA), pp 243–259

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Correspondence to Francesco Parisi.

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Alfano, G., Greco, S. & Parisi, F. An Incremental Algorithm for Computing the Grounded Extension of Dynamic Abstract Argumentation Frameworks. Group Decis Negot 28, 935–960 (2019). https://doi.org/10.1007/s10726-019-09627-4

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Keywords

  • Abstract argumentation
  • Dynamic argumentation
  • Grounded semantics