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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.
Aiken, E. (1993). The General Topology of Dynamical Systems. American Mathematical Society.
Alexandrov, P. (1937). Diskrete Räume. Matematicheskii Sbornik, 2:501–518.
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.
Brown, J. (1976). Ergodic Theory and Topological Dynamics. Academic Press, New York.
Davoren, J. (1998). Modal Logics for Continuous Dynamics. PhD thesis, Cornell University.
Fernandez, D. (2006). Completeness of S4C for KMR 2.
Furstenberg, H. (1981). Recurrence in Ergodic Theory and Combinatorial Number Theory. Princeton University Press, Princeton.
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.
Konev, B., Kontchakov, R., Tishovsky, D., Wolter, F., and Zakharyaschev, M. (2006a). On Dynamic Topological and Metric Logics. Studia Logica. to be published.
Konev, B., Kontchakov, R., Wolter, F., and Zakharyaschev, M. (2006b). Dynamic Topological Logics over Spaces with Continuous Functions.
Kremer, P. (1997). Temporal Logic over S4: an Axiomatizable Fragment of Dynamic Topological Logic. Bulletin of Symbolic Logic, 3:375–376.
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.
Kremer, P., Mints, G., and Rybakov, V. (1997). Axiomatizing the Next-Interior Fragment of Dynamic Topological Logic. Bulletin of Symbolic Logic, 3: 376–377.
Kripke, S. (1963). Semantical Analysis of Modal Logic I, Normal Propositional Calculi. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 9:67–96.
McKinsey, J. C. C. and Tarski, A. (1944). The Algebra of Topology. Annals of Mathematics, 45:141–191.
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.
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.
Mints, G. and Zhang, T. (2005b). Propositional Logic of Continuous Transformation in Cantor Space. Archive for Mathematical Logic, 44(6):783–799.
Rasiowa, H. and Sikorski, R. (1963). The Mathematics of Metamathematics. Państowowe Wydawnictwo Naukowe, Warsaw.
Segerberg, K. (1976). Discrete Linear Future Time Without Axioms. Studia Logica, 35:273–278.
Slavnov, S. (2003). Two Counterexamples in the Logic of Dynamic Topological Systems. Technical report, Cornell University.
Slavnov, S. A. (2005). On Completeness of Dynamical Topological Logic. Moscow Mathematical Journal, 5(5).
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.
Walters, P. (1982). An Introduction to Ergodic Theory. Springer-Verlag, Berlin.
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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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