Journal of Philosophical Logic

, Volume 28, Issue 6, pp 575–604 | Cite as

A Propositional Dynamic Logic with Qualitative Probabilities

  • Dimitar P. Guelev
Article

Abstract

This paper presents an ω-completeness theorem for a new propositional probabilistic logic, namely, the dynamic propositional logic of qualitative probabilities (D Q P), which has been introduced by the author as a dynamic extension of the logic of qualitative probabilities (Q P) introduced by Segerberg.

dynamic logic probabilistic logic propositional logic stochastic processes 

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REFERENCES

  1. 1.
    Alechina, N., Logic with probabilistic operators, Report ML-94-10, ILLC, University of Amsterdam, 1994.Google Scholar
  2. 2.
    Baeten, J. C. M., Bergstra, J. A. and Smolka, S. A., Axiomatizing Probabilistic Processes: ACP with Generative Probabilities, Eindhoven University of Technology, Computing Science Note 92/19, Eindhoven, September 1992.Google Scholar
  3. 3.
    Van Benthem, J. A. F. K. and Humberstone, I. L., Halldén completeness by gluing of Kripke frames, Notre Dame J. Formal Logic 24(4) (1983), 426–430.Google Scholar
  4. 4.
    Van Benthem, J. A. F. K., Modal Logic and Classical Logic, Chapter VI, Bibliopolis, Naples, 1983.Google Scholar
  5. 5.
    Chanqui, R., Truth, Possibility and Probability. New Logical Foundations of Probability and Statistical Inference, Math. Studies 166, North-Holland, 1991.Google Scholar
  6. 6.
    Dang Van Hung and Zhou Chaochen, Probabilistic duration calculus for continuous time, Research Report 25, UNU/IIST, P.O. Box 3058, Macau, May 1994.Google Scholar
  7. 7.
    Fagin, R., Halpern, J. Y. and Megiddo, N., A logic for reasoning about probabilities, Inform. Comput. 87(1-2) (July/August 1990), 78–128.Google Scholar
  8. 8.
    Gärdenfors, P., Qualitative probability as an intentional logic, J. Philos. Logic 4 (1975), 171–185.Google Scholar
  9. 9.
    Gelev, D. P., Introducing some classical elements of modal logic to the propositional logics of qualitative probabilities, Report LP-94-01, ILLC, University of Amsterdam, 1994.Google Scholar
  10. 10.
    Gelev, D. P., A strong completeness theorem for the probabilistic logic of Segerberg, Master's thesis, Sofia University, 1994 (in Bulgarian).Google Scholar
  11. 11.
    Guelev, D. P., Probabilistic interval temporal logic, Technical Report 144, UNU/IIST, P.O. Box 3058, Macau, August 1998, Draft.Google Scholar
  12. 12.
    Goldblatt, R., Logics of Time and Computation, Chapter 10, CSLI Lecture Notes 7, Stanford, 1987.Google Scholar
  13. 13.
    Van der Hoek, W., Modalities for Reasoning About Knowledge and Quantities, Chapter 7, Ph.D. Thesis, Vrije Universiteit van Amsterdam, 1992.Google Scholar
  14. 14.
    Hughes, G. E. and Cresswell, M. J., A Companion to Modal Logic, Methuen, London, 1984.Google Scholar
  15. 15.
    Kapitonova, Iu. V. and Letichevsky, A. A., Matematicheskaya Teoriya Proektirovaniya Vyichislitel'nyih Sistem, Nauka, Moskow, 1988 (in Russian).Google Scholar
  16. 16.
    Kozen, D., A probabilistic PDL, J. Comput. System Sci. 30 (1985), 162–178.Google Scholar
  17. 17.
    Zhiming Liu, Ravn, A. P., Sørensen, E. V. and Zhou Chaochen, A probabilistic duration calculus, in Proceedings of the Second International Workshop on Responsive Computer Systems, KDD Research and Development Laboratories, Saitama, Japan, 1992, also in Zhou Chaochen, (ed.), Duration Calculus. Compendium, 3, UNU/IIST, P.O. Box 3058, Macau, March 1993.Google Scholar
  18. 18.
    Sahlqvist, H., Completeness and correspondence in the first-and second-order semantics for modal logic, in S. Kanger (ed.), Proceedings of the Third Scandinavian Logic Symposium, North-Holland, Amsterdam, 1975.Google Scholar
  19. 19.
    Sarymsakov, T. A., Foundations of the Theory of Markov Processes, Chapter I, Fan, Tashkent, 1988 (in Russian).Google Scholar
  20. 20.
    Segerberg, K., Qualitative probability in a modal setting, in J. E. Fenstad (ed.), Proceedings of the Second Scandinavian Logic Symposium, North-Holland, Amsterdam, 1971.Google Scholar
  21. 21.
    Skordev, D., Combinatory Spaces and Recursiveness in Them, Chapter III, §§5.3-5.6, Publishing House of the Bulgarian Academy of Sciences, Sofia, 1980 (in Russian).Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Dimitar P. Guelev
    • 1
  1. 1.Department of Mathematical Logic and Its Applications, Faculty of Mathematics and InformaticsSofia UniversitySofiaBulgaria

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