Skip to main content
SpringerLink
Log in

How Can You Resolve a Trilemma? - A Topological Approach -

  • 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

This paper discusses how to escape a state in which argumentation can reach no conclusion, by offering a new argument. We formalize our approach based on Dung’s abstract argumentation framework (AF). When an AF has no stable extension, we have no meaningful conclusion. We address the problem of whether it is possible to revise this situation by adding an argument that attacks an existing one. If possible, how many solutions can we generate and at what position should it be added? We discuss this problem using an AF consisting of a trilemma and show conditions depending on the topology of the AF. We also address the point that a specific argument can be accepted or not by this action. We extend the discussion into two possible directions: a general N-lemma case and a set of AFs, each of which consists of several trilemmas. It follows that when a large argumentation becomes stuck in a practical situation, the position to which a counter-argument should be added can be detected by a check of the topology of the AF.

This work was supported by JSPS KAKENHI Grant Number JP17H06103.

T. Okubo—Currently, Fuji Soft Incorporated.

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.

    The meaning of “repair” is not exactly the same as that used in [4].

References

  1. Alfaso, G., Greco, S., Parisi, F.: Incremental computation in dynamic argumentation frameworks. IEEE Intell. Syst. 36(2), 6–12 (2021)

    Article  Google Scholar 

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

    Article  Google Scholar 

  3. 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  Google Scholar 

  4. Baumann, R., Brewka, G.: Expanding argumentation frameworks: enforcing and monotonicity results. In: COMMA 2010, pp. 75–86 (2010)

    Google Scholar 

  5. Baumann, R., Ulbricht, M.: If nothing is accepted - repairing argumentation frameworks. In: KR 2018, pp. 108–117 (2018)

    Google Scholar 

  6. Baumann, R., Brewka, G.: Extension removal in abstract argumentation - an axiomatic approach. In: AAAI 2019, pp. 2670–2677 (2019)

    Google Scholar 

  7. Baumann, R., Gabbay, D.M., Rodrigues, O.: Forgetting an argument. In: AAAI 2020, pp. 2750–2757 (2020)

    Google Scholar 

  8. Boella, G., Kaci, S., van der 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). https://doi.org/10.1007/978-3-642-02906-6_11

    Chapter  MATH  Google Scholar 

  9. Boella, G., Kaci, S., van der Torre, L.W.N.: Dynamics in argumentation with single extensions: attack refinement and the grounded extension. In: AAMAS 2009, pp. 1213–1214 (2009)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  11. Cayrol, C., de Saint-Cyr, F.D., Lagasquie-Schiex, M.-C.: Revision of an argumentation system. In: KR 2008, pp. 124–134 (2011)

    Google Scholar 

  12. Cayrol, C., Lagasquie-Schiex, M.-C.: Weighted argumentation systems: a tool for merging argumentation systems. In: ICAI 2011, pp. 629–632 (2011)

    Google Scholar 

  13. Coste-Marquis, S., Konieczny, S., Mailly, J.-G., Marquis, P.: Extension enforcement in abstract argumentation as an optimization problem. In: IJCAI 2015, pp. 2876–2882 (2015)

    Google Scholar 

  14. Doutre, S., Mailly, J.-G.: Constraints and changes: a survey of abstract argumentation dynamics. Argum. Comput. 9(3), 223–248 (2018)

    Article  Google Scholar 

  15. Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif. Intell. 77, 321–357 (1995)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  17. Rahwan, I., Simari, G.R. (eds.): Argumentation in Artificial Intelligence. Springer, Heidelberg (2009)

    Google Scholar 

  18. Šefránek, J.: Updates of argumentation frameworks. In: NMR 2012 (2012)

    Google Scholar 

  19. Wallner, J.P., Niskanen, A., Järvisalo, M.: Complexity results and algorithms for extension enforcement in abstract argumentation. J. Artif. Intell. Res. 60, 1–40 (2017)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kwansei Gakuin University, 2-1, Gakuen, Sanda, 669-1338, Japan

    Kazuko Takahashi & Tamon Okubo

Authors
  1. Kazuko Takahashi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tamon Okubo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kazuko Takahashi .

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 BenzmĂĽller

  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

Takahashi, K., Okubo, T. (2021). How Can You Resolve a Trilemma? - A Topological Approach -. 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_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-89391-0_22

  • 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