Advertisement

Topo-Logic as a Dynamic-Epistemic Logic

  • Alexandru Baltag
  • Aybüke ÖzgünEmail author
  • Ana Lucia Vargas Sandoval
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10455)

Abstract

We extend the ‘topologic’ framework [13] with dynamic modalities for ‘topological public announcements’ in the style of Bjorndahl [5]. We give a complete axiomatization for this “Dynamic Topo-Logic”, which is in a sense simpler than the standard axioms of topologic. Our completeness proof is also more direct (making use of a standard canonical model construction). Moreover, we study the relations between this extension and other known logical formalisms, showing in particular that it is co-expressive with the simpler (and older) logic of interior and global modality [1, 4, 10, 14]. This immediately provides an easy decidability proof (both for topologic and for our extension).

References

  1. 1.
    Aiello, M.: Theory and practice. Ph.D. thesis, ILLC, Univerisity of Amsterdam (2002)Google Scholar
  2. 2.
    Balbiani, P., Baltag, A., van Ditmarsch, H., Herzig, A., Hoshi, T., Lima, T.D.: ‘Knowable’ as ‘Known after an announcement’. Rew. Symb. Logic 1, 305–334 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Baltag, A.: To know is to know the value of a variable. In: Proceedings of the 11th Advances in Modal Logic, pp. 135–155 (2016)Google Scholar
  4. 4.
    Bennett, B.: Modal logics for qualitative spatial reasoning. Logic J. IGPL 4, 23–45 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bjorndahl, A.: Topological subset space models for public announcements. In: Trends in Logic, Outstanding Contributions: Jaakko Hintikka (2016, to appear)Google Scholar
  6. 6.
    Dabrowski, A., Moss, L.S., Parikh, R.: Topological reasoning and the logic of knowledge. Ann. Pure Appl. Logic 78, 73–110 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Engelking, R.: General Topology, vol. 6, 2nd edn. Heldermann Verlag, Berlin (1989)zbMATHGoogle Scholar
  8. 8.
    Georgatos, K.: Modal logics for topological spaces. Ph.D. thesis, City University of New York (1993)Google Scholar
  9. 9.
    Georgatos, K.: Knowledge theoretic properties of topological spaces. In: Masuch, M., Pólos, L. (eds.) Logic at Work 1992. LNCS, vol. 808, pp. 147–159. Springer, Heidelberg (1994). doi: 10.1007/3-540-58095-6_11 CrossRefGoogle Scholar
  10. 10.
    Goranko, V., Passy, S.: Using the universal modality: gains and questions. J. Log. Comput. 2, 5–30 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Kelly, K.T.: The Logic of Reliable Inquiry. Oxford University Press, Oxford (1996)zbMATHGoogle Scholar
  12. 12.
    McKinsey, J.C.C., Tarski, A.: The algebra of topology. Ann. Math. 2(45), 141–191 (1944)CrossRefzbMATHGoogle Scholar
  13. 13.
    Moss, L.S., Parikh, R.: Topological reasoning and the logic of knowledge. In: Proceedings of the 4th TARK, pp. 95–105. Morgan Kaufmann (1992)Google Scholar
  14. 14.
    Shehtman, V.B.: “Everywhere” and “Here”. J. Appl. Non Class. Logics 9, 369–379 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Ditmarsch, H., Knight, S., Özgün, A.: Arbitrary announcements on topological subset spaces. In: Bulling, N. (ed.) EUMAS 2014. LNCS (LNAI), vol. 8953, pp. 252–266. Springer, Cham (2015). doi: 10.1007/978-3-319-17130-2_17 Google Scholar
  16. 16.
    Vickers, S.: Topology via Logic. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge (1989)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Alexandru Baltag
    • 1
  • Aybüke Özgün
    • 1
    • 2
    Email author
  • Ana Lucia Vargas Sandoval
    • 1
  1. 1.ILLCUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.LORIA-CNRS, Université de LorraineNancyFrance

Personalised recommendations