Skip to main content
SpringerLink
Log in

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

  • Conference paper
  • First Online:
Dynamic Logic. New Trends and Applications (DALI 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12005))

Included in the following conference series:

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.

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.

    For an overview on the topic we refer to [16] (see also [17, 18]), where the authors discuss the main developments in the literature and indicate that homophily exists on a wide array of sociodemographic and behavioral and value-based dimensions.

  2. 2.

    It will be useful to consider the ‘dual’ function , returning the set of positions each agent \(\mathtt {i}\in \varvec{\mathcal {A}}\) holds on topic \(T \in \varvec{\mathcal {T}}\), and defined as .

  3. 3.

    Definition 4.3 presents an alternative in which an agent’s new stance on topic T depends on the stances of all the agents to which she is socially connected, regardless of whether it is on topic T or on another.

  4. 4.

    For contrast, [11] proposes an operation through which two agents become socially connected if and only if they are similar enough and some agent can act as the middleman. See Definition 4.4 for an alternative that restricts the pool of candidates for friendship.

  5. 5.

    The labels of the diagrams are as in Item (i) through the whole Example.

  6. 6.

    Consider a one-topic case with positions \(\{ p,q \}\) and agents \(\{ \mathtt {a}, \mathtt {b}, \mathtt {c} \}\), their initial positions being and the initial network being just reflexive edges. The repetition of(i) social influence with \(\tau \,{=}\,1\) (no effect), (ii) friendship selection with (adding only symmetric edges between \(\mathtt {b}\) and both \(\mathtt {a}\) and \(\mathtt {c}\)), (iii) social influence now with (no effect) and (iv) friendship selection now with \(\theta \,{=}\,1\) (removing the just added edges) does not stabilise.

  7. 7.

    For contrast, a parallel composition, affecting both agents and social networks at once, would require a new modality.

  8. 8.

    In modal languages cases, one could work directly with a semantic characterisation of the language’s expressivity, i.e., with some form of bisimulation [27, Section 2.2].

  9. 9.

    Again, although not shown, the labels of the diagrams are as in Item (ii) through the whole Example.

References

  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. van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Synthese Library Series, vol. 337. Springer, Dordrecht (2008). https://doi.org/10.1007/978-1-4020-5839-4

    Book  MATH  Google Scholar 

  3. van Benthem, J.: Logical Dynamics of Information and Interaction. Cambridge University Press, Cambridge (2011)

    Book  Google Scholar 

  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_15

    Chapter  MATH  Google Scholar 

  5. Zhen, L., Seligman, J.: A logical model of the dynamics of peer pressure. Electron. Notes Theor. Comput. Sci. 278, 275–288 (2011)

    Article  MathSciNet  Google Scholar 

  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. Liu, F., Seligman, J., Girard, P.: Logical dynamics of belief change in the community. Synthese 191(11), 2403–2431 (2014)

    Article  MathSciNet  Google Scholar 

  8. Christoff, Z., Hansen, J.U., Proietti, C.: Reflecting on social influence in networks. J. Logic Lang. Inform. 25(3–4), 299–333 (2016)

    Article  MathSciNet  Google Scholar 

  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. Velázquez-Quesada, F.R.: Reliability-based preference dynamics: lexicographic upgrade. J. Log. Comput. 27(8), 2341–2381 (2017)

    Article  MathSciNet  Google Scholar 

  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_26

    Chapter  Google Scholar 

  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_11

    Chapter  MATH  Google Scholar 

  13. Smets, S., Velázquez-Quesada, F.R.: A closeness- and priority-based logical study of social network creation. Under submission (2018)

    Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  15. Easley, D., Kleinberg, J.: Networks, Crowds and Markets: Reasoning about a Highly Connected World. Cambridge University Press, New York (2010)

    Book  Google Scholar 

  16. McPherson, M., Smith-Lovin, L., Cook, J.M.: Birds of a feather: homophily in social networks. Annu. Rev. Sociol. 27, 415–444 (2001)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  18. Kim, K., Altmann, J.: Effect of homophily on network formation. Commun. Nonlinear Sci. Numer. Simul. 44, 482–494 (2017)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  20. Christoff, Z., Hansen, J.U.: A logic for diffusion in social networks. J. Appl. Log. 13(1), 48–77 (2015)

    Article  MathSciNet  Google Scholar 

  21. DeGroot, M.H.: Reaching a consensus. J. Am. Stat. Assoc. 69(345), 118–121 (1974)

    Article  Google Scholar 

  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_13

    Chapter  MATH  Google Scholar 

  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. Granovetter, M.: Threshold models of collective behavior. Am. J. Sociol. 83(6), 1420–1443 (1978)

    Article  Google Scholar 

  25. Wang, Y., Cao, Q.: On axiomatizations of public announcement logic. Synthese 190(Suppl.-1), 103–134 (2013)

    Article  MathSciNet  Google Scholar 

  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. 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 

Download references

Author information

Authors and Affiliations

  1. Institute for Logic, Language and Computation, Universiteit van Amsterdam, Amsterdam, The Netherlands

    Sonja Smets & Fernando R. Velázquez-Quesada

Authors
  1. Sonja Smets
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fernando R. Velázquez-Quesada
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fernando R. Velázquez-Quesada .

Editor information

Editors and Affiliations

  1. University of Minho, Braga, Portugal

    Luís Soares Barbosa

  2. Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, Noord-Holland, The Netherlands

    Alexandru Baltag

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Smets, S., Velázquez-Quesada, F.R. (2020). A Logical Analysis of the Interplay Between Social Influence and Friendship Selection. In: Soares Barbosa, L., Baltag, A. (eds) Dynamic Logic. New Trends and Applications. DALI 2019. Lecture Notes in Computer Science(), vol 12005. Springer, Cham. https://doi.org/10.1007/978-3-030-38808-9_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-38808-9_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-38807-2

  • Online ISBN: 978-3-030-38808-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation