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Dynamic Topological Logic

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References

  • Aiello, M., van Benthem, J., and Bezhanishvili, G. (2003). Reasoning about Space: the Modal Way. Journal of Logic and Computation, 13 (6): 889–920.

    Article  Google Scholar 

  • Aiken, E. (1993). The General Topology of Dynamical Systems. American Mathematical Society.

    Google Scholar 

  • Alexandrov, P. (1937). Diskrete Räume. Matematicheskii Sbornik, 2:501–518.

    Google Scholar 

  • 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/.

  • 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.

    Article  Google Scholar 

  • Brown, J. (1976). Ergodic Theory and Topological Dynamics. Academic Press, New York.

    Google Scholar 

  • Davoren, J. (1998). Modal Logics for Continuous Dynamics. PhD thesis, Cornell University.

    Google Scholar 

  • Fernandez, D. (2006). Completeness of S4C for KMR 2.

    Google Scholar 

  • Furstenberg, H. (1981). Recurrence in Ergodic Theory and Combinatorial Number Theory. Princeton University Press, Princeton.

    Google Scholar 

  • 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 

  • 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 

  • Konev, B., Kontchakov, R., Wolter, F., and Zakharyaschev, M. (2006b). Dynamic Topological Logics over Spaces with Continuous Functions.

    Google Scholar 

  • Kremer, P. (1997). Temporal Logic over S4: an Axiomatizable Fragment of Dynamic Topological Logic. Bulletin of Symbolic Logic, 3:375–376.

    Google Scholar 

  • Kremer, P. (2004). The Modal Logic of Continuous Functions on Cantor Space. Availble at http://individual.utoronto.ca/philipkremer/online papers/cantor.pdf.

  • Kremer, P. and Mints, G. (1997). Dynamic Topological Logic. Bulletin of Symbolic Logic, 3:371–372.

    Google Scholar 

  • 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 

  • Kripke, S. (1963). Semantical Analysis of Modal Logic I, Normal Propositional Calculi. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 9:67–96.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • Mints, G. and Zhang, T. (2005b). Propositional Logic of Continuous Transformation in Cantor Space. Archive for Mathematical Logic, 44(6):783–799.

    Article  Google Scholar 

  • Rasiowa, H. and Sikorski, R. (1963). The Mathematics of Metamathematics. Państowowe Wydawnictwo Naukowe, Warsaw.

    Google Scholar 

  • Segerberg, K. (1976). Discrete Linear Future Time Without Axioms. Studia Logica, 35:273–278.

    Article  Google Scholar 

  • Slavnov, S. (2003). Two Counterexamples in the Logic of Dynamic Topological Systems. Technical report, Cornell University.

    Google Scholar 

  • Slavnov, S. A. (2005). On Completeness of Dynamical Topological Logic. Moscow Mathematical Journal, 5(5).

    Google Scholar 

  • 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 

  • Walters, P. (1982). An Introduction to Ergodic Theory. Springer-Verlag, Berlin.

    Google Scholar 

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Kremer, P., Mints, G. (2007). Dynamic Topological 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_10

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