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Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation pp 249–264Cite as

Reduction-Based Approaches to Implement Modgil’s Extended Argumentation Frameworks

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9060))

Abstract

This paper reconsiders Modgil’s Extended Argumentation Frameworks (EAFs) that extend Dung’s abstract argumentation frameworks by attacks on attacks. This allows to encode preferences directly in the framework and thus also to reason about the preferences themselves. As a first step to reduction-based approaches to implement EAFs, we give an alternative (but equivalent) characterization of acceptance in EAFs. Then we use this characterization to provide EAF encodings for answer set programming and propositional logic. Moreover, we address an open complexity question and the expressiveness of EAFs.

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References

  1. Amgoud, L., Cayrol, C.: A reasoning model based on the production of acceptable arguments. Ann. Math. Artif. Intell. 34(1-3), 197–215 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Baroni, P., Caminada, M.W.A., Giacomin, M.: An introduction to argumentation semantics. Knowledge Eng. Review 26(4), 365–410 (2011)

    Article  Google Scholar 

  3. Bench-Capon, T.J.M.: Persuasion in practical argument using value-based argumentation frameworks. J. Log. Comput. 13(3), 429–448 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Besnard, P., Doutre, S.: Checking the acceptability of a set of arguments. In: Proc. NMR, pp. 59–64 (2004)

    Google Scholar 

  5. Brewka, G., Woltran, S.: Abstract Dialectical Frameworks. In: Proc. KR 2010, pp. 102–111. AAAI Press (2010)

    Google Scholar 

  6. Brewka, G., Eiter, T., Truszczyński, M.: Answer set programming at a glance. Commun. ACM 54(12), 92–103 (2011)

    Article  Google Scholar 

  7. Brewka, G., Ellmauthaler, S., Strass, H., Wallner, J.P., Woltran, S.: Abstract Dialectical Frameworks Revisited. In: Proc. IJCAI, pp. 803–809. AAAI Press / IJCAI (2013)

    Google Scholar 

  8. Cerutti, F., Dunne, P.E., Giacomin, M., Vallati, M.: Computing preferred extensions in abstract argumentation: A SAT-based approach. In: Black, E., Modgil, S., Oren, N. (eds.) TAFA 2013. LNCS, vol. 8306, pp. 176–193. Springer, Heidelberg (2014)

    Google Scholar 

  9. 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 

  10. Dunne, P.E., Bench-Capon, T.J.M.: Coherence in finite argument systems. Artif. Intell. 141(1/2), 187–203 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Dunne, P.E., Dvořák, W., Linsbichler, T., Woltran, S.: Characteristics of multiple viewpoints in abstract argumentation. In: Proc. KR, pp. 72–81. AAAI Press (2014)

    Google Scholar 

  12. Dunne, P.E., Modgil, S., Bench-Capon, T.J.M.: Computation in extended argumentation frameworks. In: Proc. ECAI, pp. 119–124. IOS Press (2010)

    Google Scholar 

  13. Dvořák, W., Järvisalo, M., Wallner, J.P., Woltran, S.: Complexity-sensitive decision procedures for abstract argumentation. Artif. Intell. 206, 53–78 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  14. Dvořák, W., Szeider, S., Woltran, S.: Abstract argumentation via monadic second order logic. In: Hüllermeier, E., Link, S., Fober, T., Seeger, B. (eds.) SUM 2012. LNCS, vol. 7520, pp. 85–98. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  15. Egly, U., Gaggl, S.A., Woltran, S.: Answer-Set Programming Encodings for Argumentation Frameworks. Argument and Computation 1(2), 147–177 (2010)

    Article  MATH  Google Scholar 

  16. Egly, U., Woltran, S.: Reasoning in argumentation frameworks using Quantified Boolean Formulas. In: Proc. COMMA, pp. 133–144. IOS Press (2006)

    Google Scholar 

  17. Gebser, M., Kaminski, R., Kaufmann, B., Ostrowski, M., Schaub, T., Schneider, M.: Potassco: The Potsdam Answer Set Solving Collection. AI Communications 24(2), 105–124 (2011)

    MathSciNet  MATH  Google Scholar 

  18. Modgil, S.: Reasoning about preferences in argumentation frameworks. Artif. Intell. 173(9-10), 901–934 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  19. Modgil, S., Prakken, H.: A general account of argumentation with preferences. Artif. Intell. 195, 361–397 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  20. Niemelä, I.: Logic Programming with Stable Model Semantics as a Constraint Programming Paradigm. Ann. Math. Artif. Intell. 25(3-4), 241–273 (1999)

    Article  MATH  Google Scholar 

  21. Nofal, S., Dunne, P.E., Atkinson, K.: Towards experimental algorithms for abstract argumentation. In: Proc. COMMA, pp. 217–228. IOS Press (2012)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Computer Science, University of Vienna, Austria

    Wolfgang Dvořák

  2. Computational Logic Group, Technische Universität Dresden, Germany

    Sarah Alice Gaggl

  3. Institute of Information Systems, Vienna University of Technology, Austria

    Thomas Linsbichler & Johannes Peter Wallner

Authors
  1. Wolfgang Dvořák
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  2. Sarah Alice Gaggl
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  3. Thomas Linsbichler
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  4. Johannes Peter Wallner
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Editor information

Editors and Affiliations

  1. Institut für Informationssysteme, Technische Universität Wien, 184/3, Abteilung für wissensbasierte Systeme, Favoritenstraße 9-11, 1040, Wien, Austria

    Thomas Eiter

  2. Institut für Informatik, Abteilung Intelligente Systeme, Universität Leipzig, PF 100920, 04009, Leipzig, Germany

    Hannes Strass

  3. Department of Computer Science, University of Kentucky, 309 Davis Marksbury Building, 329 Rose Street, 40506-0633, Lexington, KY, USA

    Mirosław Truszczyński

  4. Institut für Informationssysteme, Technische Universität Wien, 184/2, Abteilung für Datenbanken und Artificial Intelligence, Favoritenstraße 9-11, 1040, Wien, Austria

    Stefan Woltran

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Dvořák, W., Gaggl, S.A., Linsbichler, T., Wallner, J.P. (2015). Reduction-Based Approaches to Implement Modgil’s Extended Argumentation Frameworks. In: Eiter, T., Strass, H., Truszczyński, M., Woltran, S. (eds) Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation. Lecture Notes in Computer Science(), vol 9060. Springer, Cham. https://doi.org/10.1007/978-3-319-14726-0_17

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  • DOI: https://doi.org/10.1007/978-3-319-14726-0_17

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-14725-3

  • Online ISBN: 978-3-319-14726-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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