Skip to main content

Topology and Epistemic Logic

  • Chapter

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   329.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Aiello, Marco, van Benthem, Johan, and Bezhanishvili, Guram (2003). Reasoning about space: the modal way. J. Log. Comput., 13(6):889–920.

    Article  Google Scholar 

  • Barwise, Jon (1988). Three views of common knowledge. In Vardi, M., editor, Proceedings of the Second Conference on Theoretical Aspects of Reasoning about Knowledge, pages 365–379. Morgan Kaufmann, San Francisco.

    Google Scholar 

  • Bezhanishvili, Guram, Esakia, Leo, and Gabelaia, David (2005). Some results on modal axiomatization and definability for topological spaces. Studia Logica, 81(3):325–355.

    Article  Google Scholar 

  • Dabrowski, Andrew, Moss, Lawrence S., and Parikh, Rohit (1996). Topological reasoning and the logic of knowledge. Annals of Pure and Applied Logic, 78(1–3):73–110. Papers in honor of the Symposium on Logical Foundations of Computer Science, “Logic at St. Petersburg” (St. Petersburg, 1994).

    Article  Google Scholar 

  • Davoren, J. M. (1999). Topologies, continuity and bisimulations. Theoretical Informatics and Applications, 33(4/5):357–381.

    Article  Google Scholar 

  • Davoren, Jen M. and Gore, Rajeev P. (2002). Bimodal logics for reasoning about continuous dynamics. In Advances in Modal Logic (Leipzig, 2000), volume 3, pages 91–111. World Sci. Publishing, River Edge, NJ.

    Google Scholar 

  • Esakia, Leo (1981). Diagonal construction, Loeb’s formula and Cantor’s scattered spaces. In Logical And Semantical Investigations, pages 128–143. Academy Press, Tbilisi. In Russian.

    Google Scholar 

  • Esakia, Leo (2001). Weak transitivity—a restitution. Logical Investigations, 8:244–255. In Russian.

    Google Scholar 

  • Gabelaia, David (2001). Modal definability in topology. Master’s thesis, ILLC, University of Amsterdam.

    Google Scholar 

  • Georgatos, Konstantinos (1993). Modal Logics for Topological Spaces. PhD thesis, CUNY Graduate Center.

    Google Scholar 

  • Georgatos, Konstantinos (1994a). Knowledge theoretic properties of topological spaces. In Masuch, Michael and Laszlo, Polos, editors, Knowledge Representation and Uncertainty, Lecture Notes in Comput. Sci. Springer, Berlin.

    Google Scholar 

  • Georgatos, Konstantinos (1994b). Reasoning about knowledge on computation trees. In Logics in artificial intelligence (York, 1994), volume 838 of Lecture Notes in Comput. Sci., pages 300–315. Springer, Berlin.

    Chapter  Google Scholar 

  • Georgatos, Konstantinos (1997). Knowledge on treelike spaces. Studia Logica, 59:271–301.

    Article  Google Scholar 

  • Heinemann, Bernhard (1997). A topological generalization of propositional linear time temporal logic. In Mathematical Foundations of Computer Science 1997 (Bratislava), volume 1295 of Lecture Notes in Comput. Sci., pages 289–297. Springer, Berlin.

    Google Scholar 

  • Heinemann, Bernhard (1998). Topological modal logics satisfying finite chain conditions. Notre Dame Journal of Formal Logic, 39(3):406–421.

    Article  Google Scholar 

  • Heinemann, Bernhard (1999a). The complexity of certain modal formulas on binary ramified subset trees. Fundamenta Informaticae, 39(3):259–272.

    Google Scholar 

  • Heinemann, Bernhard (1999b). Temporal aspects of the modal logic of subset spaces. Theoret. Comput. Sci., 224(1–2):135–155. Logical foundations of computer science (Yaroslavl, 1997).

    Article  Google Scholar 

  • Heinemann, Bernhard (2001). Modelling change with the aid of knowledge and time. In Fundamentals of computation theory (Riga, 2001), volume 2138 of Lecture Notes in Comput. Sci., pages 150–161. Springer, Berlin.

    Chapter  Google Scholar 

  • Heinemann, Bernhard (2006). Regarding overlaps in “topologic”. In Hodkinson, I. and Venema, Y., editors, Advances in Modal Logic, AiML 2006, Noosa, Queensland, Australia, volume 6. King’s College Publications, London.

    Google Scholar 

  • Kozen, Dexter and Parikh, Rohit (1981). An elementary proof of the completeness of PDL. Theoretical Computer Science, pages 113–118.

    Google Scholar 

  • Krommes, G. (2003). A new proof of decidability for the modal logic of subset spaces. In Eighth ESSLLI Student Session, pages 137–148.

    Google Scholar 

  • Kudinov, Andrey (2006). Topological modal logics with difference modality. In Hodkinson, I. and Venema, Y., editors, Advances in Modal Logic, AiML 2006, Noosa, Queensland, Australia, volume 6. King’s College Publications, London.

    Google Scholar 

  • McKinsey, J. C. C. (1941). A solution of the decision problem for the lewis systems S2 and S4, with an application to topology. J. Symbolic Logic, 6: 117–134.

    Article  Google Scholar 

  • McKinsey, J. C. C. and A. Tarski (1944). The algebra of topology. Annals of Mathematics, 45:141–191.

    Article  Google Scholar 

  • Moss, Lawrence S. and Parikh, Rohit (1992). Topological reasoning and the logic of knowledge. In Moses, Y., editor, Theoretical Aspects of Reasoning About Knowledge, pages 95–105. Morgan Kaufmann.

    Google Scholar 

  • Pacuit, Eric and Parikh, Rohit (2005). The logic of communication graphs. In Leite, J., Omicini, A., Torroni, P., and Yolum, P., editors, Declarative Agent Languages and Technologies II: Second International Workshop, DALT 2004, volume 3476 of Lecture Notes in Artificial Intelligence. Springer, Berlin.

    Google Scholar 

  • Shehtman, V. (1990). Derived sets in euclidean spaces and modal logic. Technical Report X-90-05, University of Amsterdam.

    Google Scholar 

  • Steinsvold, Chris (2006). Topological Models of Belief Logics. PhD thesis, CUNY Graduate Center.

    Google Scholar 

  • van Benthem, Johan, Bezhanishvili, Guram, ten Cate, Balder, and Sarenac, Darko (2007). Multimodal logics of products of topologies. Studia Logica. to appear.

    Google Scholar 

  • van Benthem, Johan and Sarenac, Darko (2004). The geometry of knowledge. Technical Report PP-2004-20, ILLC.

    Google Scholar 

  • Vickers, Steven (1989). Topology via Logic. Cambridge University Press, Cambridge.

    Google Scholar 

  • Weiss, M. A. (1999). Completeness of Certain Bimodal Logics. PhD thesis, CUNY Graduate Center.

    Google Scholar 

  • Weiss, M. A. and Parikh, R. (2002). Completeness of certain bimodal logics for subset spaces. Studia Logica, 71(1):1–30.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer

About this chapter

Cite this chapter

Parikh, R., Moss, L., Steinsvold, C. (2007). Topology and Epistemic Logic. In: Aiello, M., Pratt-Hartmann, I., Van Benthem, J. (eds) Handbook of Spatial Logics. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5587-4_6

Download citation

Publish with us

Policies and ethics