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Analyzing Echo Chambers: A Logic of Strong and Weak Ties

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 11813)

Abstract

Echo chamber is a widely used term describing a situation where certain information is reinforced within a closed network. To reason about echo chambers, we introduce a two-sorted hybrid logic of strong and weak ties based on a logic of positive and negative relations known from the literature. We show that some classical property definitions can be formalized and that a known claim from social network analysis is a validity. We also prove that the logic is axiomatizable, sound and strongly complete. We combine our results with research on homophily and social group formation to represent relations between similar agents. Lastly, we add a knowledge modality and dynamic operators to analyze change in these networks.

Keywords

  • Strong and weak ties
  • Echo chamber
  • Friendship logic
  • Hybrid logic
  • Logic for social epistemic networks
  • Homophily

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Fig. 1.

Notes

  1. 1.

    For further details on hybrid logics beyond the scope of this paper, we recommend turning to [1].

  2. 2.

    See [7] for details.

  3. 3.

    For proof of the claim see Granovetter’s original paper [13].

References

  1. Areces, C., ten Cate, B.: Hybrid logics. In: van Benthem, J., Blackburn, P., Wolter, F. (eds.) Handbook of Modal Logic. Elsevier, Amsterdam (2006)

    Google Scholar 

  2. Aucher, G., van Benthem, J., Grossi, D.: Modal logics of sabotage revisited. J. Log. Comput. 28(2), 269–303 (2017)

    MathSciNet  CrossRef  Google Scholar 

  3. Baltag, A., Boddy, R., Smets, S.: Group knowledge in interrogative epistemology. In: van Ditmarsch, H., Sandu, G. (eds.) Jaakko Hintikka on Knowledge and Game-Theoretical Semantics. Outstanding Contributions to Logic, vol. 12, pp. 131–164. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-62864-6_5

    CrossRef  Google Scholar 

  4. Baltag, A., Christoff, Z., Rendsvig, R.K., Smets, S.: Dynamic epistemic logics of diffusion and prediction in social networks. Stud. Logica 107(3), 1–43 (2018)

    MathSciNet  CrossRef  Google Scholar 

  5. Baltag, A., Moss, L.S., Solecki, S.: The logic of public announcements, common knowledge, and private suspicions. In: Arló-Costa, H., Hendricks, V., van Benthem, J. (eds.) Readings in Formal Epistemology. Springer Graduate Texts in Philosophy, vol. 1, pp. 773–812. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-20451-2_38

    CrossRef  Google Scholar 

  6. Blackburn, P., ten Cate, B.: Pure extensions, proof rules, and hybrid axiomatics. Stud. Logica 84(2), 277–322 (2006)

    MathSciNet  CrossRef  Google Scholar 

  7. Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001)

    CrossRef  Google Scholar 

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

    MathSciNet  CrossRef  Google Scholar 

  9. van Ditmarsch, H., van Der Hoek, W., Kooi, B.: Dynamic Epistemic Logic, vol. 337. Springer, Dordrecht (2007). https://doi.org/10.1007/978-1-4020-5839-4

    CrossRef  MATH  Google Scholar 

  10. Li, D.: Losing Connection: the Modal Logic of Definable Link Deletion, ILLC Technical Notes Series (X-2019-01) (2019)

    Google Scholar 

  11. Easley, D., Kleinberg, J.: Networks, Crowds and Markets. Cambridge University Press, Cambridge (2010)

    CrossRef  Google Scholar 

  12. Geschke, D., Lorenz, J., Holtz, P.: The triple-filter bubble: using agent-based modelling to test a meta-theoretical framework for the emergence of filter bubbles and echo chambers. Br. J. Soc. Psychol. 58(1), 129–149 (2019)

    CrossRef  Google Scholar 

  13. Granovetter, M.S.: The Strength of Weak Ties. Social Networks, pp. 347–367. Academic Press, New York (1977)

    Google Scholar 

  14. Hendricks, V.F., Hansen, P.G.: Infostorms. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-32765-5

    CrossRef  Google Scholar 

  15. Seligman, J., Liu, F., Girard, P.: Facebook and the epistemic logic of friendship. In: Proceedings of the TARK conference on Theoretical Aspects of Rationality and Knowledge, pp. 229–238 (2013)

    Google Scholar 

  16. 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

    CrossRef  MATH  Google Scholar 

  17. 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

    CrossRef  MATH  Google Scholar 

  18. 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

    CrossRef  Google Scholar 

  19. Xiong, Z., Ågotnes, T.: On the logic of balance in social networks. J. Log. Lang. Inf. (2019, to appear)

    Google Scholar 

  20. Xiong, Z.: On the logic of multicast messaging and balance in social networks. Doctoral dissertation, University of Bergen (2017)

    Google Scholar 

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Correspondence to Mina Young Pedersen , Sonja Smets or Thomas Ågotnes .

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Pedersen, M.Y., Smets, S., Ågotnes, T. (2019). Analyzing Echo Chambers: A Logic of Strong and Weak Ties. In: Blackburn, P., Lorini, E., Guo, M. (eds) Logic, Rationality, and Interaction. LORI 2019. Lecture Notes in Computer Science(), vol 11813. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-60292-8_14

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  • DOI: https://doi.org/10.1007/978-3-662-60292-8_14

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