Skip to main content
SpringerLink
Log in

Boolean Matrix Approach for Abstract Argumentation

  • Conference paper
  • First Online:
Multi-Agent Systems and Agreement Technologies (EUMAS 2016, AT 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10207))

  • 787 Accesses

Abstract

In this paper, we propose a Boolean matrix approach to encode Dung’s acceptability semantics. Each semantics is encoded into one or more Boolean constraint models, which can be solved by Boolean constraint solvers. In addition, based on our Boolean matrix representations, we also propose a bit-vector-based approach to compute the grounded semantics, and the experimental results show that this approach can achieve a good performance.

The research reported here was supported by the Fund NSFC61572279.

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.

    Here, we consider \(\mathcal {R}^+(\mathbf {s})\) and \(\mathcal {R}^-(\mathbf {s})\) as Boolean functions, which map a Boolean vector to another Boolean vector.

  2. 2.

    http://www.boost.org/.

  3. 3.

    http://www.dmi.unipg.it/conarg/.

  4. 4.

    http://argumentationcompetition.org/.

  5. 5.

    http://swish.swi-prolog.org/p/argmat-clpb.pl.

References

  1. Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. J. Artif. Intell. 77(2), 321–357 (1995)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  3. Givant, S., Halmos, P.: Introduction to Boolean Algebras. Springer Science & Business Media, Berlin (2008)

    MATH  Google Scholar 

  4. Pu, F., Luo, J., Luo, G.: Some supplementaries to the counting semantics for abstract argumentation. In: 2015 IEEE 27th International Conference on Tools with Artificial Intelligence (ICTAI), pp. 242–249. IEEE (2015)

    Google Scholar 

  5. Hadjisoteriou, E.: Computing argumentation with matrices. In: Schulz, C., Liew, D. (eds.) 2015 Imperial College Computing Student Workshop (ICCSW 2015). OpenAccess Series in Informatics (OASIcs), vol. 49, pp. 29–36. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl (2015)

    Google Scholar 

  6. Bistarelli, S., Rossi, F., Santini, F.: Benchmarking hard problems in random abstract AFs: the stable semantics. In: COMMA (2014)

    Google Scholar 

  7. Lagniez, J.M., Lonca, E., Mailly, J.G.: CoQuiAAS: a constraint-based quick abstract argumentation solver. In: 2015 IEEE 27th International Conference on Tools with Artificial Intelligence (ICTAI), pp. 928–935. IEEE (2015)

    Google Scholar 

  8. Cerutti, F., Giacomin, M., Vallati, M.: ArgSemSAT: solving argumentation problems using SAT. COMMA 14, 455–456 (2014)

    Google Scholar 

  9. Xu, Y.: A matrix approach for computing extensions of argumentation frameworks. CoRR abs/1209.1899 (2012)

    Google Scholar 

  10. Hadjisoteriou, E., Georgiou, M.: ASSA: computing stable extensions with matrices. In: System Descriptions of the First International Competition on Computational Models of Argumentation (ICCMA 2015) (2015)

    Google Scholar 

  11. Triska, M.: The boolean constraint solver of SWI-Prolog: system description. In: Kiselyov, O., King, A. (eds.) FLOPS 2016. LNCS, vol. 9613, pp. 45–61. Springer, Cham (2016). doi:10.1007/978-3-319-29604-3_4

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Software, Tsinghua University, Beijing, China

    Fuan Pu, Guiming Luo & Yucheng Chen

Authors
  1. Fuan Pu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guiming Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yucheng Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fuan Pu .

Editor information

Editors and Affiliations

  1. King’s College London, London, United Kingdom

    Natalia Criado Pacheco

  2. Polytechnic University of Valencia, Valencia, Portugal

    Carlos Carrascosa

  3. Artificial Intelligence Research Institute (IIIA-CSIC), Barcelona, Spain

    Nardine Osman

  4. Polytechnic University of Valencia, Valencia, Spain

    Vicente Julián Inglada

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Pu, F., Luo, G., Chen, Y. (2017). Boolean Matrix Approach for Abstract Argumentation. In: Criado Pacheco, N., Carrascosa, C., Osman, N., Julián Inglada, V. (eds) Multi-Agent Systems and Agreement Technologies. EUMAS AT 2016 2016. Lecture Notes in Computer Science(), vol 10207. Springer, Cham. https://doi.org/10.1007/978-3-319-59294-7_38

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-59294-7_38

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59293-0

  • Online ISBN: 978-3-319-59294-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation