Advertisement

Dynamic Topological Logic

  • Philip Kremer
  • Grigori Mints

Keywords

Topological Space Modal Logic Propositional Variable Kripke Model Alexandrov Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aiello, M., van Benthem, J., and Bezhanishvili, G. (2003). Reasoning about Space: the Modal Way. Journal of Logic and Computation, 13 (6): 889–920.CrossRefGoogle Scholar
  2. Aiken, E. (1993). The General Topology of Dynamical Systems. American Mathematical Society.Google Scholar
  3. Alexandrov, P. (1937). Diskrete Räume. Matematicheskii Sbornik, 2:501–518.Google Scholar
  4. Artemov, S., Davoren, J., and Nerode, A. (1997). Modal Logics and Topological Semantics for Hybrid Systems. Technical Report MSI 97-05, Cornell University. Available at http://web.cs.gc.cuny.edu/~sartemov/.
  5. Bezhanishvili, G. and Gehrke, M. (2005). A New Proof of Completeness of S4 with Respect to Real Line. Annals of Pure and Applied Logic, 133(1–3): 287–301.CrossRefGoogle Scholar
  6. Brown, J. (1976). Ergodic Theory and Topological Dynamics. Academic Press, New York.Google Scholar
  7. Davoren, J. (1998). Modal Logics for Continuous Dynamics. PhD thesis, Cornell University.Google Scholar
  8. Fernandez, D. (2006). Completeness of S4C for KMR 2.Google Scholar
  9. Furstenberg, H. (1981). Recurrence in Ergodic Theory and Combinatorial Number Theory. Princeton University Press, Princeton.Google Scholar
  10. Goldblatt, R. (1992). Logics of Time and Computation, volume 7 of Center for the Study of Language and Information Lecture Notes. Stanford University Press, Stanford, 2nd edition edition.Google Scholar
  11. Konev, B., Kontchakov, R., Tishovsky, D., Wolter, F., and Zakharyaschev, M. (2006a). On Dynamic Topological and Metric Logics. Studia Logica. to be published.Google Scholar
  12. Konev, B., Kontchakov, R., Wolter, F., and Zakharyaschev, M. (2006b). Dynamic Topological Logics over Spaces with Continuous Functions. Google Scholar
  13. Kremer, P. (1997). Temporal Logic over S4: an Axiomatizable Fragment of Dynamic Topological Logic. Bulletin of Symbolic Logic, 3:375–376.Google Scholar
  14. Kremer, P. (2004). The Modal Logic of Continuous Functions on Cantor Space. Availble at http://individual.utoronto.ca/philipkremer/online papers/cantor.pdf.
  15. Kremer, P. and Mints, G. (1997). Dynamic Topological Logic. Bulletin of Symbolic Logic, 3:371–372.Google Scholar
  16. Kremer, P., Mints, G., and Rybakov, V. (1997). Axiomatizing the Next-Interior Fragment of Dynamic Topological Logic. Bulletin of Symbolic Logic, 3: 376–377.Google Scholar
  17. Kripke, S. (1963). Semantical Analysis of Modal Logic I, Normal Propositional Calculi. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 9:67–96.CrossRefGoogle Scholar
  18. McKinsey, J. C. C. and Tarski, A. (1944). The Algebra of Topology. Annals of Mathematics, 45:141–191.CrossRefGoogle Scholar
  19. Mints, G. (1999). A Completeness Proof for Propositional S4 in Cantor Space. In Orlowska, E., editor, Logic at work. Essays dedicated to the memory of Helena Rasiowa., Stud. Fuzziness Soft Comput., chapter 24, pages 79–88. Heidelberg: Physica-Verlag.Google Scholar
  20. Mints, G. and Zhang, T. (2005a). A Proof of Topological Completeness for S4 in (0,1). Annals of Pure and Applied. Logic, 133(1–3):231–246.CrossRefGoogle Scholar
  21. Mints, G. and Zhang, T. (2005b). Propositional Logic of Continuous Transformation in Cantor Space. Archive for Mathematical Logic, 44(6):783–799.CrossRefGoogle Scholar
  22. Rasiowa, H. and Sikorski, R. (1963). The Mathematics of Metamathematics. Państowowe Wydawnictwo Naukowe, Warsaw.Google Scholar
  23. Segerberg, K. (1976). Discrete Linear Future Time Without Axioms. Studia Logica, 35:273–278.CrossRefGoogle Scholar
  24. Slavnov, S. (2003). Two Counterexamples in the Logic of Dynamic Topological Systems. Technical report, Cornell University.Google Scholar
  25. Slavnov, S. A. (2005). On Completeness of Dynamical Topological Logic. Moscow Mathematical Journal, 5(5).Google Scholar
  26. van Benthem, J. (1995). Temporal Logic. In Gabbay, D. M., Hogger, C. J., and Robinson, J. A., editors, Handbook of Logic in Artificial Intelligence and Logic Programming, volume 4, pages 241–350. Clarendon Press, Oxford.Google Scholar
  27. Walters, P. (1982). An Introduction to Ergodic Theory. Springer-Verlag, Berlin.Google Scholar

Copyright information

© Springer 2007

Authors and Affiliations

  • Philip Kremer
    • 1
  • Grigori Mints
    • 2
  1. 1.University of TorontoCanada
  2. 2.Stanford UniversityStanford

Personalised recommendations