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Stability in Binary Opinion Diffusion

Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10455)

Abstract

The paper studies the stabilization of the process of diffusion of binary opinions on networks. It first shows how such dynamics can be modeled and studied via techniques from binary aggregation, which directly relate to neighborhood frames. It then characterizes stabilization in terms of such neighborhood structures, and shows how the monotone \(\mu \)-calculus can express relevant properties of them. Finally, it illustrates the scope of these results by applying them to specific diffusion models.

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Notes

Acknowledgments

Zoé Christoff and Davide Grossi acknowledge support for this research by EPSRC (grant EP/M015815/1, “Foundations of Opinion Formation in Autonomous Systems”). Zoé Christoff also acknowledges support from the Deutsche Forschungsgemeinschaft (DFG) and Grantová agentura České republiky (GAČR) joint project RO 4548/6–1.

References

  1. 1.
    Azimipour, S., Naumov, P.: Lighthouse principle for diffusion in social networks. J. Appl. Logic. (2017, to appear)Google Scholar
  2. 2.
    Baltag, A., Christoff, Z., Rendsvig, R.K., Smets, S.: Dynamic epistemic logic of diffusion and prediction in social networks. In: Twelfth Conference on Logic and the Foundations of Game and Decision Theory (LOFT 2016) (2016)Google Scholar
  3. 3.
    Baltag, A., Sonja, S.: Logic goes viral - modalities for social networks. Presented at the workshop Trends in Logic - Presenting the Tsinghua-UvA Joint Research Center, Tsinghua University, 2 July 2014Google Scholar
  4. 4.
    van Benthem, J.: Oscillations, logic, and dynamical systems. In: Ghosh, S., Szymanik, J. (eds.) The Facts Matter. Essays on Logic and Cognition in Honour of Rineke Verbrugge, pp. 9–22. College Publications (2015)Google Scholar
  5. 5.
    van Benthem, J., Bezhanishvili, N., Enqvist, S., Junhua, Y.: Instantial neighbourhood logic. Rev. Symbol. Logic 10(1), 116144 (2017)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Botan, S.: Propositional opinion diffusion with constraints. ILLC Master of Logic Thesis (2016)Google Scholar
  7. 7.
    Chellas, B.F.: Modal Logic. An Introduction. Cambridge University Press, Cambridge (1980)CrossRefzbMATHGoogle Scholar
  8. 8.
    Cholvy, L.: Influence-based opinion diffusion (extended abstract). In: Proceedings of AAMAS 2016, pp. 1355–1356. IFAAMAS (2016)Google Scholar
  9. 9.
    Christoff, Z.: Dynamic logics of networks: information flow and the spread of opinion. Ph.D thesis, Institute for logic, Language and Computation, University of Amsterdam, Amsterdam, The Netherlands. ILLC Dissertation Series DS-2016-02 (2016)Google Scholar
  10. 10.
    Christoff, Z., Grossi, D.: Binary aggregation with delegable proxy: an analysis of liquid democracy. In: Proceedings of TARK 2017, EPTCS, vol. 251 (2017)Google Scholar
  11. 11.
    Degroot, M.H.: Reaching a consensus. J. Am. Stat. Assoc. 69(345), 118–121 (1974)CrossRefzbMATHGoogle Scholar
  12. 12.
    Dokow, E., Holzman, R.: Aggregation of binary evaluations. J. Econ. Theory 145(2), 495–511 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Endriss, U.: Judgment aggregation. In: Brandt, F., Conitzer, V., Endriss, U., Lang, J., Procaccia, A.D. (eds.) Handbook of Computational Social Choice, chap. 17. Cambridge University Press (2016)Google Scholar
  14. 14.
    Enqvist, S., Seifan, F., Venema, Y.: Expressiveness of the modal mu-calculus on monotone neighborhood structures. Technical report, arXiv: 1502.07889 (2015)
  15. 15.
    Friedkin, N.E., Proskurnikov, A.V., Tempo, R., Parsegov, S.E.: Network science on belief system dynamics under logic constraints. Science 354(6310), 321–326 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Goles, E.: Periodic behavior of generalized threshold functions. Discrete Math. 30, 187–189 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Grandi, U., Endriss, U.: Lifting integrity constraints in binary aggregation. Artif. Intell. 199, 45–66 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Grandi, U., Lorini, E., Perrussel, L.: Propositional opinion diffusion. In: Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2015, pp. 989–997. International Foundation for Autonomous Agents and Multiagent Systems, Richland (2015)Google Scholar
  19. 19.
    Granovetter, M.: Threshold models of collective behavior. Am. J. Sociol. 83(6), 1420–1443 (1978)CrossRefGoogle Scholar
  20. 20.
    Grossi, D., Pigozzi, G.: Judgment aggregation: a primer. Synth. Lect. Artif. Intell. Mach. Learn. 8(2), 1–151 (2014)CrossRefGoogle Scholar
  21. 21.
    Hansen, H.H.: Monotonic modal logics. Technical Report PP-2003-24, ILLC (2003)Google Scholar
  22. 22.
    Jackson, M.O.: Social and Economic Networks. Princeton University Press, Princeton (2008)zbMATHGoogle Scholar
  23. 23.
    Liu, F., Seligman, J., Girard, P.: Logical dynamics of belief change in the community. Synthese 191(11), 2403–2431 (2014)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of BayreuthBayreuthGermany
  2. 2.Department of Computer ScienceUniversity of LiverpoolLiverpoolEngland

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