Skip to main content
SpringerLink
Log in

A Dynamic Hybrid Logic for Followership

  • Conference paper
  • First Online:
Book cover Logic, Rationality, and Interaction (LORI 2019)

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

Included in the following conference series:

Abstract

This paper formalises the followership in networks that agents following or unfollowing each other dynamically. The semantics is based on the basic hybrid logic and we extend the logic with a propositional action modality \([{a}\uparrow {\theta }]\) for the changes of followership. The main contribution of this paper is the completeness result. Moreover, we have proved that all pure axiomatic extensions have completeness and discussed some possible future works and extensions, in particular, some features of the extended action modality \([{a}\uparrow {\varphi }]\), like repetition regrets are discussed.

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.

    Our action here is a little bit in difference, agents will follow and only all the agents satisfied by the claimed property. Action itself does not preserving the old relations.

  2. 2.

    In the later section, when we talk about the extended languages, the set of Agt will then be substituted by the extended set as well.

  3. 3.

    The converse of \([\overrightarrow{a}]\) is \([\overleftarrow{a}]\) which is defined by \([{a_n}\uparrow {\theta _n}]\ldots [{a_2}\uparrow {\theta _2}][{a_1}\uparrow {\theta _1}]\).

  4. 4.

    It means that agents are dropping p-property, if they update with q-property.

  5. 5.

    \(@_b\theta \rightarrow @_a[{a}\uparrow {\theta }]\Diamond {b}\) indicates that if b satisfies \(\theta \), then b will be followed by a after the executing \([{a}\uparrow {\theta }]\). \(@_a[{a}\uparrow {\theta }]\Diamond {b}\rightarrow @_b\theta \) says that since agent a is following b after executing \([{a}\uparrow {\theta }]\), then agent b satisfies \(\theta \).

  6. 6.

    As the propositional case is trivial, and it’s also a technical reason why we need to restrict our actions into propositional formulas.

  7. 7.

    Due to the property of \(\Diamond {}\), it is not possible to interpret the action that “agent a chooses to follow all agents that are followed by b”, actions like \([{a}\uparrow {(i\wedge @_b\Diamond {i})}]\) only means that “agent a chooses to follow agent i and b is following i”.

References

  1. Areces, C., Fervari, R., Hoffmann, G.: Relation-changing modal operators. Log. J. IGPL 23(4), 601–627 (2015)

    Article  MathSciNet  Google Scholar 

  2. Aucher, G., Balbiani, P., Cerro, L.F.D., Herzig, A.: Global and local graph modifiers. Electron. Notes Theor. Comput. Sci. 231, 293–307 (2009)

    Article  MathSciNet  Google Scholar 

  3. Aucher, G., van Benthem, J., Grossi, D.: Sabotage modal logic: some model and proof theoretic aspects. In: van der Hoek, W., Holliday, W.H., Wang, W. (eds.) LORI 2015. LNCS, vol. 9394, pp. 1–13. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48561-3_1

    Chapter  MATH  Google Scholar 

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

    Book  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  6. Renardel De Lavalette, G.R.: Changing modalities. J. Log. Comput. 14(2), 251–275 (2004)

    Article  MathSciNet  Google Scholar 

  7. Harel, D., Tiuryn, J., Kozen, D.: Dynamic Logic. MIT Press, Cambridge (2000)

    Book  Google Scholar 

  8. Kooi, B.: Expressivity and completeness for public update logics via reduction axioms. J. Appl. Non-Class. Log. 17(2), 231–253 (2007)

    Article  MathSciNet  Google Scholar 

  9. Kooi, B., Renne, B.: Arrow update logic. Rev. Symbolic Log. 4(4), 536–559 (2011)

    Article  MathSciNet  Google Scholar 

  10. Kooi, B., Renne, B.: Generalized arrow update logic. In: Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge, TARK XIII, pp. 205–211. ACM, New York (2011)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  12. 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 

  13. 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, pp. 229–238, Chennai (2013)

    Google Scholar 

  14. van Benthem, J.: Dynamic logic for belief revision. J. Appl. Non-Class. Log. 17, 129–156 (2007)

    Article  MathSciNet  Google Scholar 

  15. Benthem, J.: An essay on sabotage and obstruction. In: Hutter, D., Stephan, W. (eds.) Mechanizing Mathematical Reasoning. LNCS (LNAI), vol. 2605, pp. 268–276. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-32254-2_16

    Chapter  Google Scholar 

  16. van Benthem, J., Liu, F.: The dynamics of preference upgrade. J. Appl. Non-Class. Log. 17(2), 157–182 (2007)

    Article  MathSciNet  Google Scholar 

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

    Book  MATH  Google Scholar 

  18. Xiong, Z.: On the logic of multicast messaging and balance in social networks. Ph.D. thesis, University of Bergen (2017). ISBN 978-82-308-3928-7

    Google Scholar 

  19. Xiong, Z., Ågotnes, T., Seligman, J., Zhu, R.: Towards a logic of tweeting. In: Baltag, A., Seligman, J., Yamada, T. (eds.) LORI 2017. LNCS, vol. 10455, pp. 49–64. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-55665-8_4

    Chapter  MATH  Google Scholar 

Download references

Acknowledgment

We thank anonymous reviewers of LORI-2019 for many helpful comments, and in particular, for the contribution of related works. The first author is supported by the Fundamental Research Funds for the Central Universities under research no. SWU1809669, and by the Key Research Funds for the Key Liberal Science Research Base of Chongqing under research no. 18SK045.

Author information

Authors and Affiliations

  1. Institute of Logic and Intelligence, Southwest University, Chongqing, China

    Zuojun Xiong & Meiyun Guo

Authors
  1. Zuojun Xiong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Meiyun Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zuojun Xiong .

Editor information

Editors and Affiliations

  1. Roskilde University, Roskilde, Denmark

    Patrick Blackburn

  2. Université Paul Sabatier, IRIT-CNRS, Toulouse, France

    Emiliano Lorini

  3. Southwest University, Chongqing, China

    Meiyun Guo

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer-Verlag GmbH Germany, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Xiong, Z., Guo, M. (2019). A Dynamic Hybrid Logic for Followership. 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_31

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-60292-8_31

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-60291-1

  • Online ISBN: 978-3-662-60292-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation