Skip to main content
SpringerLink
Log in

Measuring Disagreement in Argumentation Graphs

  • Conference paper
  • First Online:
Scalable Uncertainty Management (SUM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10564))

Included in the following conference series:

Abstract

The aim of this paper is to evaluate to what extent an argumentation graph (a set of arguments and attacks between them) is conflicting. For that purpose, we introduce the novel notion of disagreement measure as well as a set of principles that such a measure should satisfy. We propose some intuitive measures and show that they fail to satisfy some of the principles. Then, we come up with a more discriminating measure which satisfies them all. Finally, we relate some measures to those quantifying inconsistency in knowledge bases.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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 symbol \(\vdash \) stands for propositional inference relation.

  2. 2.

    The symbol \(\equiv \) stands for logical equivalence.

References

  1. Besnard, P., Hunter, A.: A logic-based theory of deductive arguments. Artif. Intell. J. 128(1–2), 203–235 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bonzon, E., Maudet, N.: On the outcomes of multiparty persuasion. In: 10th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2011), pp. 47–54 (2011)

    Google Scholar 

  3. 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 

  4. Pollock, J.: How to reason defeasibly. Artif. Intell. 57(1), 1–42 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  5. Elvang-Gøransson, M., Krause, P.J., Fox, J.: Acceptability of arguments as ‘logical uncertainty’. In: Clarke, M., Kruse, R., Moral, S. (eds.) ECSQARU 1993. LNCS, vol. 747, pp. 85–90. Springer, Heidelberg (1993). doi:10.1007/BFb0028186

    Chapter  Google Scholar 

  6. Hunter, A., Konieczny, S.: On the measure of conflicts: shapley inconsistency values. Artif. Intell. 174(14), 1007–1026 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Grant, J., Hunter, A.: Distance-based measures of inconsistency. In: Gaag, L.C. (ed.) ECSQARU 2013. LNCS (LNAI), vol. 7958, pp. 230–241. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39091-3_20

    Chapter  Google Scholar 

  8. Jabbour, S., Ma, Y., Raddaoui, B.: Inconsistency measurement thanks to MUS decomposition. In: International Conference on Autonomous Agents and Multi-Agent Systems, AAMAS 2014, pp. 877–884 (2014)

    Google Scholar 

  9. Thimm, M.: Towards large-scale inconsistency measurement. In: Lutz, C., Thielscher, M. (eds.) KI 2014. LNCS (LNAI), vol. 8736, pp. 195–206. Springer, Cham (2014). doi:10.1007/978-3-319-11206-0_19

    Google Scholar 

  10. Jabbour, S., Ma, Y., Raddaoui, B., Sais, L., Salhi, Y.: On structure-based inconsistency measures and their computations via closed set packing. In: Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2015, pp. 1749–1750 (2015)

    Google Scholar 

  11. Jabbour, S., Sais, L.: Exploiting MUS structure to measure inconsistency of knowledge bases. In: 22nd European Conference on Artificial Intelligence, ECAI 2016, pp. 991–998 (2016)

    Google Scholar 

  12. Shapley, L.: A values for n-person games. In: Kuhn, H.W., Tucker, A.W. (eds.) Contributions to the Theory of Games, vol. II. Annal of Mathematics Studies (AM-28) (1953)

    Google Scholar 

  13. Amgoud, L., Ben-Naim, J.: Axiomatic foundations of acceptability semantics. In: Proceedings of the Fifteenth International Conference Principles of Knowledge Representation and Reasoning, KR 2016, pp. 2–11 (2016)

    Google Scholar 

  14. Grant, J., Hunter, A.: Measuring consistency gain and information loss in stepwise inconsistency resolution. In: Liu, W. (ed.) ECSQARU 2011. LNCS, vol. 6717, pp. 362–373. Springer, Heidelberg (2011). doi:10.1007/978-3-642-22152-1_31

    Chapter  Google Scholar 

  15. Amgoud, L., Besnard, P.: Logical limits of abstract argumentation frameworks. J. Appl. Non-Class. Logics 23(3), 229–267 (2013)

    Article  MathSciNet  Google Scholar 

  16. Booth, R., Caminada, M., Podlaszewski, M., Rahwan, I.: Quantifying disagreement in argument-based reasoning. In: International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2012, pp. 493–500 (2012)

    Google Scholar 

Download references

Acknowledgments

This work was supported by ANR-13-BS02-0004 and ANR-11-LABX-0040-CIMI.

Author information

Authors and Affiliations

  1. IRIT – CNRS, Toulouse, France

    Leila Amgoud & Jonathan Ben-Naim

Authors
  1. Leila Amgoud
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jonathan Ben-Naim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Leila Amgoud .

Editor information

Editors and Affiliations

  1. University of Granada, Granada, Spain

    Serafín Moral

  2. University of Rennes I, Lannion, France

    Olivier Pivert

  3. University of Granada, Granada, Spain

    Daniel Sánchez

  4. University of Granada, Granada, Spain

    Nicolás Marín

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Amgoud, L., Ben-Naim, J. (2017). Measuring Disagreement in Argumentation Graphs. In: Moral, S., Pivert, O., Sánchez, D., Marín, N. (eds) Scalable Uncertainty Management. SUM 2017. Lecture Notes in Computer Science(), vol 10564. Springer, Cham. https://doi.org/10.1007/978-3-319-67582-4_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-67582-4_15

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67581-7

  • Online ISBN: 978-3-319-67582-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation