Skip to main content
SpringerLink
Log in

Abstract Argumentation with Qualitative Uncertainty: An Analysis in Dynamic Logic

  • Conference paper
  • First Online:
Logic and Argumentation (CLAR 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13040))

Included in the following conference series:

Abstract

We extend the existing encoding of abstract argumentation frameworks in DL-PA (Dynamic Logic of Propositional Assignments) in order to capture different formalisms for arguing with qualitative forms of uncertainty. More in particular, we encode the main reasoning tasks of (rich) incomplete argumentation frameworks and control argumentation frameworks. After that, and inspired by our encoding, we define and study a new class of structures that are shown to be maximally expressive: constrained incomplete argumentation frameworks.

Andreas Herzig is partially supported by the EU ICT-48 2020 project TAILOR (No. 952215). Antonio Yuste-Ginel gratefully acknowledges funding received from the PhD grant No. MECDFPU 2016/04113. We thank Sylvie Doutre and Jean-Guy Mailly for previous discussions on the topic of this paper, specially for triggering the idea of constrained incomplete argumentation frameworks.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    As \(A\subseteq \mathcal {U}\), we actually focus on finite AFs, as most of the literature does. This is an essential limitation of our approach, as our encodings use formulas parametrised by \(\mathcal {U}\), which makes finiteness of \(\mathcal {U}\) necessary. Capturing some argumentation semantics for the general case has been shown to require powerful logical languages, such as modal \(\mu \)-calculus for the grounded semantics [25].

  2. 2.

    Symmetry and irreflexivity of \(R^{\leftrightarrow }\) are not assumed in the original paper [18], but as pointed out by [30, 31], both assumptions can be made without loss of generality.

  3. 3.

    Note that \(\mathsf {vary}\) is noted \(\mathsf {flipSome}\) in [21].

References

  1. Amgoud, L., Vesic, S.: A new approach for preference-based argumentation frameworks. Ann. Math. Artif. Intell. 63(2), 149–183 (2011). https://doi.org/10.1007/s10472-011-9271-9

    Article  MathSciNet  MATH  Google Scholar 

  2. Atkinson, K., et al.: Towards artificial argumentation. AI Mag. 38(3), 25–36 (2017). https://doi.org/10.1609/aimag.v38i3.2704

    Article  Google Scholar 

  3. Balbiani, P., Herzig, A., Schwarzentruber, F., Troquard, N.: DL-PA and DCL-PC: model checking and satisfiability problem are indeed in PSPACE. CoRR abs/1411.7825 (2014). http://arxiv.org/abs/1411.7825

  4. Balbiani, P., Herzig, A., Troquard, N.: Dynamic logic of propositional assignments: a well-behaved variant of PDL. In: 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science, pp. 143–152. IEEE (2013). https://doi.org/10.1109/LICS.2013.20

  5. Baroni, P., Caminada, M., Giacomin, M.: Abstract argumentation frameworks and their semantics. In: Handbook of Formal Argumentation, pp. 159–236. College Publications (2018)

    Google Scholar 

  6. Baroni, P., Cerutti, F., Giacomin, M., Guida, G.: Encompassing attacks to attacks in abstract argumentation frameworks. In: Sossai, C., Chemello, G. (eds.) ECSQARU 2009. LNCS (LNAI), vol. 5590, pp. 83–94. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02906-6_9

    Chapter  MATH  Google Scholar 

  7. Baumann, R., Brewka, G.: Expanding argumentation frameworks: enforcing and monotonicity results. In: Baroni, P., Cerutti, F., Giacomin, M., Simari, G.R. (eds.) Proceedings of the COMMA 2010, vol. 216, pp. 75–86. IOS Press (2010). https://doi.org/10.3233/978-1-60750-619-5-75

  8. Baumeister, D., Järvisalo, M., Neugebauer, D., Niskanen, A., Rothe, J.: Acceptance in incomplete argumentation frameworks. Artif. Intell. 295, 103470 (2021). https://doi.org/10.1016/j.artint.2021.103470

    Article  MathSciNet  MATH  Google Scholar 

  9. Baumeister, D., Neugebauer, D., Rothe, J.: Credulous and skeptical acceptance in incomplete argumentation frameworks. In: Proceedings of the COMMA 2018. Frontiers in AI and Applications, vol. 305, pp. 181–192. IOS Press (2018). https://doi.org/10.3233/978-1-61499-906-5-181

  10. Baumeister, D., Neugebauer, D., Rothe, J., Schadrack, H.: Complexity of verification in incomplete argumentation frameworks. In: McIlraith, S.A., Weinberger, K.Q. (eds.) Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence, (AAAI 2018), pp. 1753–1760. AAAI Press (2018)

    Google Scholar 

  11. Baumeister, D., Neugebauer, D., Rothe, J., Schadrack, H.: Verification in incomplete argumentation frameworks. Artif. Intell. 264, 1–26 (2018). https://doi.org/10.1016/j.artint.2018.08.001

    Article  MathSciNet  MATH  Google Scholar 

  12. Bench-Capon, T.J., Dunne, P.E.: Argumentation in artificial intelligence. Artif. Intell. 171(10–15), 619–641 (2007). https://doi.org/10.1016/j.artint.2007.05.001

    Article  MathSciNet  MATH  Google Scholar 

  13. Besnard, P., Cayrol, C., Lagasquie-Schiex, M.C.: Logical theories and abstract argumentation: a survey of existing works. Argument Comput. 11(1–2), 41–102 (2020). https://doi.org/10.3233/AAC-190476

    Article  Google Scholar 

  14. Besnard, P., et al.: Introduction to structured argumentation. Argument Comput. 5(1), 1–4 (2014). https://doi.org/10.1080/19462166.2013.869764

    Article  Google Scholar 

  15. Caminada, M.: Rationality postulates: applying argumentation theory for non-monotonic reasoning. J. Appl. Log. 4(8), 2707–2734 (2017)

    MathSciNet  Google Scholar 

  16. Cayrol, C., Lagasquie-Schiex, M.C.: On the acceptability of arguments in bipolar argumentation frameworks. In: Godo, L. (ed.) ECSQARU 2005. LNCS (LNAI), vol. 3571, pp. 378–389. Springer, Heidelberg (2005). https://doi.org/10.1007/11518655_33

    Chapter  Google Scholar 

  17. Coste-Marquis, S., Devred, C., Marquis, P.: Constrained argumentation frameworks. In: Proceedings of the Tenth International Conference on Principles of Knowledge Representation and Reasoning, pp. 112–122. AAAI Press (2006)

    Google Scholar 

  18. Dimopoulos, Y., Mailly, J., Moraitis, P.: Control argumentation frameworks. In: McIlraith, S.A., Weinberger, K.Q. (eds.) Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence, (AAAI 2018), The 30th innovative Applications of Artificial Intelligence (IAAI 2018), and the 8th AAAI Symposium on Educational Advances in Artificial Intelligence (EAAI 2018), New Orleans, Louisiana, USA, 2–7 February 2018, pp. 4678–4685. AAAI Press (2018). https://www.aaai.org/ocs/index.php/AAAI/AAAI18/paper/view/16639

  19. Dimopoulos, Y., Mailly, J.G., Moraitis, P.: Argumentation-based negotiation with incomplete opponent profiles. In: 13èmes Journées d’Intelligence Artificielle Fondamentale (JIAF 2019), pp. 91–100 (2019)

    Google Scholar 

  20. Doutre, S., Herzig, A., Perrussel, L.: A dynamic logic framework for abstract argumentation. In: Baral, C., De Giacomo, G., Eiter, T. (eds.) Fourteenth International Conference on the Principles of Knowledge Representation and Reasoning. AAAI Press (2014)

    Google Scholar 

  21. Doutre, S., Herzig, A., Perrussel, L.: Abstract argumentation in dynamic logic: representation, reasoning and change. In: Liao, B., Ågotnes, T., Wang, Y.N. (eds.) CLAR 2018. LASLL, pp. 153–185. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-7791-4_8

    Chapter  MATH  Google Scholar 

  22. Doutre, S., Maffre, F., McBurney, P.: A dynamic logic framework for abstract argumentation: adding and removing arguments. In: Benferhat, S., Tabia, K., Ali, M. (eds.) IEA/AIE 2017. LNCS (LNAI), vol. 10351, pp. 295–305. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-60045-1_32

    Chapter  Google Scholar 

  23. 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), 321–357 (1995). https://doi.org/10.1016/0004-3702(94)00041-X

    Article  MathSciNet  MATH  Google Scholar 

  24. Fazzinga, B., Flesca, S., Furfaro, F.: Revisiting the notion of extension over incomplete abstract argumentation frameworks. In: Proceedings of IJCAI 2020, pp. 1712–1718. IJCAI Organization, July 2020. https://doi.org/10.24963/ijcai.2020/237

  25. Grossi, D.: On the logic of argumentation theory. In: Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems, pp. 409–416. IFAMA (2010)

    Google Scholar 

  26. Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press, Cambridge (2000)

    Book  Google Scholar 

  27. Herzig, A., Yuste-Ginel, A.: On the epistemic logic of incomplete argumentation frameworks. In: Proceedings of International Conference on Principles of Knowledge Representation and Reasoning. AAAI Press (2021)

    Google Scholar 

  28. Li, H., Oren, N., Norman, T.J.: Probabilistic argumentation frameworks. In: Modgil, S., Oren, N., Toni, F. (eds.) TAFA 2011. LNCS (LNAI), vol. 7132, pp. 1–16. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29184-5_1

    Chapter  Google Scholar 

  29. Mailly, J.G.: A note on rich incomplete argumentation frameworks. arXiv preprint arXiv:2009.04869 (2020)

  30. Niskanen, A.: Computational approaches to dynamics and uncertainty in abstract argumentation. Ph.D. thesis, Helsingin yliopisto (2020)

    Google Scholar 

  31. Niskanen, A., Neugebauer, D., Järvisalo, M., et al.: Controllability of control argumentation frameworks. In: Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence (IJCAI 2020). IJCAI Organization (2021). https://doi.org/10.24963/ijcai.2020/257

  32. Proietti, C., Yuste-Ginel, A.: Dynamic epistemic logics for abstract argumentation. Synthese 1–60 (2021). https://doi.org/10.1007/s11229-021-03178-5

Download references

Author information

Authors and Affiliations

  1. IRIT, Toulouse, France

    Andreas Herzig

  2. Departamento de Filosofía, Universidad de Málaga, Málaga, Spain

    Antonio Yuste-Ginel

Authors
  1. Andreas Herzig
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Antonio Yuste-Ginel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Information Engineering, University of Brescia, Brescia, Italy

    Pietro Baroni

  2. Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany

    Christoph Benzmüller

  3. Department of Philosophy (Zhuhai), Sun Yat-sen University, Zhuhai, China

    Yὶ N. Wáng

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Herzig, A., Yuste-Ginel, A. (2021). Abstract Argumentation with Qualitative Uncertainty: An Analysis in Dynamic Logic. In: Baroni, P., Benzmüller, C., Wáng, Y.N. (eds) Logic and Argumentation. CLAR 2021. Lecture Notes in Computer Science(), vol 13040. Springer, Cham. https://doi.org/10.1007/978-3-030-89391-0_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-89391-0_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-89390-3

  • Online ISBN: 978-3-030-89391-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation