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Subset Space Public Announcement Logic

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Logic and Its Applications (ICLA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7750))

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Abstract

The logic of public announcements has received great interest in recent years. In this paper we give an account of public announcements in terms of the semantics of subset space logic (SSL). In particular, we give a natural interpretation of the language of public announcement logic (PAL) in subset models, and show that it embeds PAL. We give sound and complete axiomatisations of different variants of the logic. Unlike in other work combining PAL and SSL, the goal is not to import PAL operators with update semantics into SSL, but to give an alternative semantics for PAL: using neighborhoods instead of model updates.

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References

  1. Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning About Knowledge. The MIT Press, Cambridge (1995)

    MATH  Google Scholar 

  2. Meyer, J.J.C., van der Hoek, W.: Epistemic Logic for AI and Computer Science. Cambridge University Press, Cambridge (1995)

    Book  MATH  Google Scholar 

  3. van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Springer (2007)

    Google Scholar 

  4. Plaza, J.A.: Logics of public communications. In: Emrich, M.L., Pfeifer, M.S., Hadzikadic, M., Ras, Z.W. (eds.) Proc. of ISMIS, pp. 201–216 (1989)

    Google Scholar 

  5. Moss, L.S., Parikh, R.: Topological reasoning and the logic of knowledge. In: Moses, Y. (ed.) Proc. of TARK, pp. 95–105 (1992)

    Google Scholar 

  6. McKinsey, J.C.C.: A solution of the decision problem for the lewis systems s2 and s4, with an application to topology. Journal of Symbolic Logic 6(4), 117–134 (1941)

    Article  MathSciNet  Google Scholar 

  7. McKinsey, J.C.C., Tarski, A.: The algebra of topology. Ann. Math. 45(1), 141–191 (1944)

    Article  MathSciNet  MATH  Google Scholar 

  8. Başkent, C.: Public announcement logic in geometric frameworks. Fundamenta Informaticae 114, 1–17 (2012)

    MathSciNet  Google Scholar 

  9. Başkent, C.: Topics in subset space logic. Master’s thesis, ILLC, UvA (2007)

    Google Scholar 

  10. Balbiani, P., van Ditmarsch, H., Kudinov, A.: Subset Space Logic with Arbitrary Announcements. In: Lodaya, K. (ed.) ICLA 2013. LNCS, vol. 7750, pp. 232–243. Springer, Heidelberg (2013)

    Google Scholar 

  11. Kooi, B., van Benthem, J.: Reduction axioms for epistemic actions. In: Schmidt, R., Pratt-Hartmann, I., Reynolds, M., Wansing, H. (eds.) Proc. of AiML 2004, pp. 197–211 (2004)

    Google Scholar 

  12. Kooi, B.: Expressivity and completeness for public update logics via reduction axioms. Journal of Applied Non-Classical Logics 17(2), 231–253 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Parikh, R., Moss, L.S., Steinsvold, C.: Topology and epistemic logic. In: Aiello, M., Pratt-Hartmann, I.E., van Benthem, J.F. (eds.) Handbook of Spatial Logics, pp. 299–341 (2007)

    Google Scholar 

  14. Dabrowski, A., Moss, L.S., Parikh, R.: Topological reasoning and the logic of knowledge. Annals of Pure and Applied Logic 78(1-3), 73–110 (1996)

    Article  MathSciNet  Google Scholar 

  15. Balbiani, P., Baltag, A., van Ditmarsch, H., Herzig, A., Hoshi, T., de Lima, T.: ‘knowable’ as ‘known after an announcement’. Review of Symbolic Logic 1(3), 305–334 (2008)

    Article  MATH  Google Scholar 

  16. Ågotnes, T., Balbiani, P., van Ditmarsch, H., Seban, P.: Group announcement logic. Journal of Applied Logic (2009)

    Google Scholar 

  17. Baltag, A., Moss, L.S.: Logics for epistemic programs. Synthese 139, 165–224 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  18. van Benthem, J., Gerbrandy, J., Pacuit, E.: Merging frameworks for interaction: Del and etl. In: Proc. of TARK 2007, pp. 72–81 (2007)

    Google Scholar 

  19. van Benthem, J., Gerbrandy, J., Hoshi, T., Pacuit, E.: Merging frameworks for interaction. Journal of Philosophical Logic 38(5), 491–526 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  20. Hoshi, T.: Merging DEL and ETL. JOLLI 19(4), 413–430 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  22. Heinemann, B.: Topology and Knowledge of Multiple Agents. In: Geffner, H., Prada, R., Machado Alexandre, I., David, N. (eds.) IBERAMIA 2008. LNCS (LNAI), vol. 5290, pp. 1–10. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  23. Heinemann, B.: Logics for multi-subset spaces. JANCL 20(3), 219–240 (2010)

    MathSciNet  MATH  Google Scholar 

  24. Wen, X., Liu, H., Huang, F.: An Alternative Logic for Knowability. In: van Ditmarsch, H., Lang, J., Ju, S. (eds.) LORI 2011. LNCS, vol. 6953, pp. 342–355. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computing, Mathematics and Physics, Bergen University College, Norway

    Yì N. Wáng & Thomas Ågotnes

  2. Institute of Logic and Intelligence, Southwest University, China

    Thomas Ågotnes

  3. Department of Information Science and Media Studies, University of Bergen, Norway

    Yì N. Wáng & Thomas Ågotnes

Authors
  1. Yì N. Wáng
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  2. Thomas Ågotnes
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Editor information

Editors and Affiliations

  1. The Institute of Mathematical Sciences, CIT Campus, 600113, Chennai, India

    Kamal Lodaya

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Wáng, Y.N., Ågotnes, T. (2013). Subset Space Public Announcement Logic. In: Lodaya, K. (eds) Logic and Its Applications. ICLA 2013. Lecture Notes in Computer Science, vol 7750. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36039-8_22

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  • DOI: https://doi.org/10.1007/978-3-642-36039-8_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36038-1

  • Online ISBN: 978-3-642-36039-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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