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Incremental Computation of Grounded Semantics for Dynamic Abstract Argumentation Frameworks

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Conflict Resolution in Decision Making (COREDEMA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10238))

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Abstract

Abstract argumentation has emerged as a central field in Artificial Intelligence. Although the underlying idea is very simple and intuitive, most of the semantics proposed so far suffer from a high computational complexity. For this reason, in recent years, an increasing amount of work has been done to define efficient algorithms. However, so far, the research has concentrated on the definition of algorithms for static frameworks, whereas argumentation frameworks (AFs) are highly dynamic in practice. Surprisingly, the definition of evaluation algorithms taking into account such dynamic aspects has been mostly neglected. In this paper, we address the problem of efficiently recomputing the extensions of AFs which are updated by adding/deleting arguments or attacks. In particular, after identifying some properties that hold for updates of AFs under several well-known semantics, we focus on the most popular unique-status semantics (namely, the grounded semantics) and present an algorithm for its incremental computation, well-suited to dynamic applications where updates to an initial AF are frequently performed to take into account new available knowledge.

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Notes

  1. 1.

    Similarly to the characteristic function F of an AF [20], function G infers new arguments that can be labelled \({\textsc {in}}\). But it is more efficient as it only uses arguments labelled in the last step.

  2. 2.

    http://argumentationcompetition.org.

  3. 3.

    Data points with the same x-axis value are due to AFs in the datasets having the same number of arguments.

References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. Baroni, P., Boella, G., Cerutti, F., Giacomin, M., van der Torre, L.W.N., Villata, S.: On the input/output behavior of argumentation frameworks. Artif. Intell. 217, 144–197 (2014)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  4. Baroni, P., Giacomin, M., Liao, B.: 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 (2014)

    Article  MATH  Google Scholar 

  5. Baumann, R.: Splitting an argumentation framework. In: Delgrande, J.P., Faber, W. (eds.) LPNMR 2011. LNCS (LNAI), vol. 6645, pp. 40–53. Springer, Heidelberg (2011). doi:10.1007/978-3-642-20895-9_6

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. Baumann, R.: Context-free and context-sensitive kernels: update and deletion equivalence in abstract argumentation. In: Proceedings of European Conference on Artificial Intelligence (ECAI), pp. 63–68 (2014)

    Google Scholar 

  8. Baumann, R., Brewka, G.: Expanding argumentation frameworks: enforcing and monotonicity results. In: Proceedings of International Conference Computational Models of Argument (COMMA), pp. 75–86 (2010)

    Google Scholar 

  9. Baumann, R., Brewka, G., Dvořák, W., Woltran, S.: Parameterized splitting: a simple modification-based approach. In: Erdem, E., Lee, J., Lierler, Y., Pearce, D. (eds.) Correct Reasoning. LNCS, vol. 7265, pp. 57–71. Springer, Heidelberg (2012). doi:10.1007/978-3-642-30743-0_5

    Chapter  Google Scholar 

  10. Bench-Capon, T.J.M., Dunne, P.E.: Argumentation in artificial intelligence. Artif. Intell. 171(1015), 619–641 (2007). argumentation in Artificial Intelligence

    Google Scholar 

  11. Bisquert, P., Cayrol, C., de Saint-Cyr, F.D., Lagasquie-Schiex, M.: Characterizing change in abstract argumentation systems. Trends Belief Revision Argumentation Dyn. 48, 75–102 (2013)

    MathSciNet  MATH  Google Scholar 

  12. Boella, G., Kaci, S., Torre, L.: Dynamics in argumentation with single extensions: abstraction principles and the grounded extension. In: Sossai, C., Chemello, G. (eds.) ECSQARU 2009. LNCS (LNAI), vol. 5590, pp. 107–118. Springer, Heidelberg (2009). doi:10.1007/978-3-642-02906-6_11

    Chapter  Google Scholar 

  13. Boella, G., Kaci, S., Torre, L.: Dynamics in argumentation with single extensions: attack refinement and the grounded extension (extended version). In: McBurney, P., Rahwan, I., Parsons, S., Maudet, N. (eds.) ArgMAS 2009. LNCS (LNAI), vol. 6057, pp. 150–159. Springer, Heidelberg (2010). doi:10.1007/978-3-642-12805-9_9

    Chapter  Google Scholar 

  14. Calautti, M., Greco, S., Trubitsyna, I.: Detecting decidable classes of finitely ground logic programs with function symbols. In: Proceedings of International Symposium on Principles and Practice of Declarative Programming (PPDP), pp. 239–250 (2013)

    Google Scholar 

  15. Caminada, M.: Semi-stable semantics. In: Proceedings of International Conference on Computational Models of Argument (COMMA), pp. 121–130 (2006)

    Google Scholar 

  16. Caminada, M., Sá, S., Alcântara, J., Dvorák, W.: On the equivalence between logic programming semantics and argumentation semantics. Int. J. Approx. Reasoning 58, 87–111 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  17. Cayrol, C., de Saint-Cyr, F.D., Lagasquie-Schiex, M.: Revision of an argumentation system. In: Proceedings of International Conference on Principles of Knowledge Represent and Reasoning (KR), pp. 124–134 (2008)

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  19. Charwat, G., Dvorák, W., Gaggl, S.A., Wallner, J.P., Woltran, S.: Methods for solving reasoning problems in abstract argumentation - a survey. Artif. Intell. 220, 28–63 (2015)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  22. Dunne, P.E.: The computational complexity of ideal semantics. Artif. Intell. 173(18), 1559–1591 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  23. Dunne, P.E., Wooldridge, M.: Complexity of abstract argumentation. In: Simari, G., Rahwan, I. (eds.) Argumentation in Artificial Intelligence, pp. 85–104. Springer, USA (2009)

    Chapter  Google Scholar 

  24. Dvorák, W., Pichler, R., Woltran, S.: Towards fixed-parameter tractable algorithms for argumentation. In: Proceedings of International Conference on Principles of Knowledge Representation and Reasoning (KR) (2010)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  26. Eiter, T., Strass, H., Truszczyński, M., Woltran, S. (eds.): Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation. LNCS (LNAI), vol. 9060. Springer, Cham (2015)

    Google Scholar 

  27. Falappa, M.A., Garcia, A.J., Kern-Isberner, G., Simari, G.R.: On the evolving relation between belief revision and argumentation. Knowl. Eng. Rev. 26(1), 35–43 (2011)

    Article  Google Scholar 

  28. Fazzinga, B., Flesca, S., Parisi, F.: Efficiently estimating the probability of extensions in abstract argumentation. In: Proceedings of International Conference on Scalable Uncertainty Management (SUM), pp. 106–119 (2013)

    Google Scholar 

  29. Fazzinga, B., Flesca, S., Parisi, F.: On the complexity of probabilistic abstract argumentation. In: Proceedings of International Joint Conference on Artificial Intelligence (IJCAI), pp. 898–904 (2013)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  32. Fazzinga, B., Flesca, S., Parisi, F., Pietramala, A.: PARTY: a mobile system for efficiently assessing the probability of extensions in a debate. In: Chen, Q., Hameurlain, A., Toumani, F., Wagner, R., Decker, H. (eds.) DEXA 2015. LNCS, vol. 9261, pp. 220–235. Springer, Cham (2015). doi:10.1007/978-3-319-22849-5_16

    Chapter  Google Scholar 

  33. Flesca, S., Furfaro, F., Parisi, F.: Preferred database repairs under aggregate constraints. In: Proceedings of First International Conference Scalable Uncertainty Management (SUM), pp. 215–229 (2007)

    Google Scholar 

  34. Flesca, S., Furfaro, F., Parisi, F.: Range-consistent answers of aggregate queries under aggregate constraints. In: Proceedings of International Conference Scalable Uncertainty Management (SUM), pp. 163–176 (2010)

    Google Scholar 

  35. Greco, S., Molinaro, C., Trubitsyna, I.: Logic programming with function symbols: checking termination of bottom-up evaluation through program adornments. TPLP 13(4–5), 737–752 (2013)

    MathSciNet  MATH  Google Scholar 

  36. Greco, S., Molinaro, C., Trubitsyna, I., Zumpano, E.: NP datalog: a logic language for expressing search and optimization problems. TPLP 10(2), 125–166 (2010)

    MATH  Google Scholar 

  37. Greco, S., Parisi, F.: Efficient computation of deterministic extensions for dynamic abstract argumentation frameworks. In: Proceedings of European Conference on Artificial Intelligence (ECAI), pp. 1668–1669 (2016)

    Google Scholar 

  38. Greco, S., Parisi, F.: Incremental computation of deterministic extensions for dynamic argumentation frameworks. In: Michael, L., Kakas, A. (eds.) JELIA 2016. LNCS (LNAI), vol. 10021, pp. 288–304. Springer, Cham (2016). doi:10.1007/978-3-319-48758-8_19

    Chapter  Google Scholar 

  39. Liao, B.S., Jin, L., Koons, R.C.: Dynamics of argumentation systems: a division-based method. Artif. Intell. 175(11), 1790–1814 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  40. Lifschitz, V., Turner, H.: Splitting a logic program. In: Proceedings of International Conference on Logic Programming (ICLP), pp. 23–37 (1994)

    Google Scholar 

  41. Martinez, M.V., Parisi, F., Pugliese, A., Simari, G.I., Subrahmanian, V.S.: Policy-based inconsistency management in relational databases. Int. J. Approx. Reasoning 55(2), 501–528 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  42. Modgil, S., Prakken, H.: Revisiting preferences and argumentation. In: Proceedings of International Joint Conference on Artificial Intelligence (IJCAI), pp. 1021–1026 (2011)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  44. Pollock, J.L.: Perceiving and reasoning about a changing world. Comput. Intell. 14(4), 498–562 (1998)

    Article  MathSciNet  Google Scholar 

  45. Rahwan, I., Simari, G.R.: Argumentation in Artificial Intelligence, 1st edn. Springer Publishing Company, Incorporated (2009)

    Google Scholar 

  46. Santos, E., Martins, J.P., Galhardas, H.: An argumentation-based approach to database repair. In: Proceedings of European Conference on Artificial Intelligence (ECAI), pp. 125–130 (2010)

    Google Scholar 

  47. Thimm, M.: Tweety: A comprehensive collection of java libraries for logical aspects of artificial intelligence and knowledge representation. In: Proceedings of International Conference on Principles of Knowledge Representation and Reasoning (KR) (2014)

    Google Scholar 

  48. Xu, Y., Cayrol, C.: The matrix approach for abstract argumentation frameworks. In: Black, E., Modgil, S., Oren, N. (eds.) TAFA 2015. LNCS (LNAI), vol. 9524, pp. 243–259. Springer, Cham (2015). doi:10.1007/978-3-319-28460-6_15

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Department of Informatics Modeling, Electronics and System Engineering, University of Calabria, Rende, Italy

    Sergio Greco & Francesco Parisi

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  1. Sergio Greco
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  2. Francesco Parisi
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Correspondence to Francesco Parisi .

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Editors and Affiliations

  1. Özyeğin University, Istanbul, Turkey

    Reyhan Aydoğan

  2. Centrum Wiskunde and Informatica (CWI), Amsterdam, The Netherlands

    Tim Baarslag

  3. University of Southampton, Southampton, United Kingdom

    Enrico Gerding

  4. Interactive Intelligence, Delft University of Technology, Delft, Zuid-Holland, The Netherlands

    Catholijn M. Jonker

  5. Department of Computer Systems and Computation, Technical University of Valencia, Valencia, Spain

    Vicente Julian

  6. Coventry University, West Midlands, United Kingdom

    Victor Sanchez-Anguix

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Greco, S., Parisi, F. (2017). Incremental Computation of Grounded Semantics for Dynamic Abstract Argumentation Frameworks. In: Aydoğan, R., Baarslag, T., Gerding, E., Jonker, C., Julian, V., Sanchez-Anguix, V. (eds) Conflict Resolution in Decision Making. COREDEMA 2016. Lecture Notes in Computer Science(), vol 10238. Springer, Cham. https://doi.org/10.1007/978-3-319-57285-7_5

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