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A Logical Analysis of the Interplay Between Social Influence and Friendship Selection

  • Sonja Smets
  • Fernando R. Velázquez-QuesadaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12005)

Abstract

This paper is part of a series of proposals for using logic to analyse social networks. It studies the intertwining of two forms of information dynamics: social influence, through which an agent’s behaviour, opinions or features are affected by those of her social connections, and friendship selection, through which an agent chooses her social connections based on their common behaviour, opinions or features. The text provides a logical analysis of the two forms of dynamics (the main ingredients in the phenomenon known as homophily) as well as of their interaction, discussing also some of their variations.

References

  1. 1.
    Baltag, A., Moss, L.S., Solecki, S.: The logic of public announcements, common knowledge, and private suspicions. In: Gilboa, I. (ed.) Proceedings of TARK 1998, pp. 43–56 (1998)Google Scholar
  2. 2.
    van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Synthese Library Series, vol. 337. Springer, Dordrecht (2008).  https://doi.org/10.1007/978-1-4020-5839-4CrossRefzbMATHGoogle Scholar
  3. 3.
    van Benthem, J.: Logical Dynamics of Information and Interaction. Cambridge University Press, Cambridge (2011)CrossRefGoogle Scholar
  4. 4.
    Seligman, J., Liu, F., Girard, P.: Logic in the community. In: Banerjee, M., Seth, A. (eds.) ICLA 2011. LNCS (LNAI), vol. 6521, pp. 178–188. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-18026-2_15CrossRefzbMATHGoogle Scholar
  5. 5.
    Zhen, L., Seligman, J.: A logical model of the dynamics of peer pressure. Electron. Notes Theor. Comput. Sci. 278, 275–288 (2011)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Baltag, A., Christoff, Z., Hansen, J.U., Smets, S.: Logical models of informational cascades. In: van Benthem, J., Liu, F. (eds.) Proceedings of the Tsinghua Logic Conference, Logic Across the University: Foundations and Applications, Beijing of Studies in Logic, London, vol. 47, pp. 405–432. College Publications (2013)Google Scholar
  7. 7.
    Liu, F., Seligman, J., Girard, P.: Logical dynamics of belief change in the community. Synthese 191(11), 2403–2431 (2014)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Christoff, Z., Hansen, J.U., Proietti, C.: Reflecting on social influence in networks. J. Logic Lang. Inform. 25(3–4), 299–333 (2016)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Baltag, A., Christoff, Z., Rendsvig, R.K., Smets, S.: Dynamic epistemic logics of diffusion and prediction in social networks (extended abstract). In: Bonanno, G., van der Hoek, W., Perea, A. (eds.) Proceedings of LOFT 2016 (2016)Google Scholar
  10. 10.
    Velázquez-Quesada, F.R.: Reliability-based preference dynamics: lexicographic upgrade. J. Log. Comput. 27(8), 2341–2381 (2017)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Smets, S., Velázquez-Quesada, F.R.: How to make friends: a logical approach to social group creation. In: Baltag, A., Seligman, J., Yamada, T. (eds.) LORI 2017. LNCS, vol. 10455, pp. 377–390. Springer, Heidelberg (2017).  https://doi.org/10.1007/978-3-662-55665-8_26CrossRefGoogle Scholar
  12. 12.
    Smets, S., Velázquez-Quesada, F.R.: The creation and change of social networks: a logical study based on group size. In: Madeira, A., Benevides, M. (eds.) DALI 2017. LNCS, vol. 10669, pp. 171–184. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-73579-5_11CrossRefzbMATHGoogle Scholar
  13. 13.
    Smets, S., Velázquez-Quesada, F.R.: A closeness- and priority-based logical study of social network creation. Under submission (2018)Google Scholar
  14. 14.
    Smets, S., Velázquez-Quesada, F.R.: A logical study of group-size based social network creation. J. Log. Algebr. Methods Program. 106, 117–140 (2019)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Easley, D., Kleinberg, J.: Networks, Crowds and Markets: Reasoning about a Highly Connected World. Cambridge University Press, New York (2010)CrossRefGoogle Scholar
  16. 16.
    McPherson, M., Smith-Lovin, L., Cook, J.M.: Birds of a feather: homophily in social networks. Annu. Rev. Sociol. 27, 415–444 (2001)CrossRefGoogle Scholar
  17. 17.
    Bramoullé, Y., Currarini, S., Jackson, M.O., Pin, P., Rogers, B.W.: Homophily and long-run integration in social networks. J. Econ. Theory 147(5), 1754–1786 (2012)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Kim, K., Altmann, J.: Effect of homophily on network formation. Commun. Nonlinear Sci. Numer. Simul. 44, 482–494 (2017)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Baltag, A., Christoff, Z., Rendsvig, R.K., Smets, S.: Dynamic epistemic logics of diffusion and prediction in social networks. Stud. Logica 107, 489–531 (2019)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Christoff, Z., Hansen, J.U.: A logic for diffusion in social networks. J. Appl. Log. 13(1), 48–77 (2015)MathSciNetCrossRefGoogle Scholar
  21. 21.
    DeGroot, M.H.: Reaching a consensus. J. Am. Stat. Assoc. 69(345), 118–121 (1974)CrossRefGoogle Scholar
  22. 22.
    Holliday, W.H.: Dynamic testimonial logic. In: He, X., Horty, J., Pacuit, E. (eds.) LORI 2009. LNCS (LNAI), vol. 5834, pp. 161–179. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-642-04893-7_13CrossRefzbMATHGoogle Scholar
  23. 23.
    Seligman, J., Liu, F., Girard, P.: Facebook and the epistemic logic of friendship. In: Schipper, B.C. (ed.) Proceedings of the 14th Conference on Theoretical Aspects of Rationality and Knowledge (TARK 2013), Chennai, India, 7–9 January 2013 (2013)Google Scholar
  24. 24.
    Granovetter, M.: Threshold models of collective behavior. Am. J. Sociol. 83(6), 1420–1443 (1978)CrossRefGoogle Scholar
  25. 25.
    Wang, Y., Cao, Q.: On axiomatizations of public announcement logic. Synthese 190(Suppl.-1), 103–134 (2013)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Smets, S., Velázquez-Quesada, F.R.: A logical perspective on social group creation. In: Arazim, P., Lávička, T. (eds.) The Logica Yearbook 2017, pp. 271–288. College Publications, London (2018a)Google Scholar
  27. 27.
    Blackburn, P., de Rijke, M., Venema, Y.: Modal logic. Number 53 in Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge (2001)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute for Logic, Language and ComputationUniversiteit van AmsterdamAmsterdamThe Netherlands

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