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A Branching Time Logic with Two Types of Probability Operators

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Scalable Uncertainty Management (SUM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6929))

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Abstract

We introduce a propositional logic whose formulas are built using the language of CTL *, enriched by two types of probability operators: one speaking about probabilities on branches, and one speaking about probabilities of sets of branches with the same initial state. An infinitary axiomatization for the logic, which is shown to be sound and strongly complete with respect to the corresponding class of models, is proposed.

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References

  1. Abadi, M.: The power of temporal proofs. Theoretical Computer Science 65, 35–83 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  2. Aziz, A., Singhal, V., Balarin, F., Brayton, R.K., Sangiovanni-Vincentelli, A.L.: It usually works: The temporal logic of stochastic systems. In: Wolper, P. (ed.) CAV 1995. LNCS, vol. 939, Springer, Heidelberg (1995)

    Google Scholar 

  3. Bianco, A., de Alfaro, L.: Model checking of probabilistic and nondeterministic systems. In: Thiagarajan, P.S. (ed.) FSTTCS 1995. LNCS, vol. 1026, pp. 499–512. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  4. Burgess, J.: Axioms for tense logic. I. “Since” and “until”. Notre Dame Journal of Formal Logic 23(4), 367–374 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  5. Burgess, J.: Logic and time. The Journal of Symbolic Logic 44(4), 566–582 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  6. Burgess, J.: Basic tense logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. II, pp. 89–133. D. Reidel Publishing Compaany, Dordrecht (1984); Kopetz, H., Kakuda, Y. (eds.) Dependable Computing and Fault-Tolerant Systems. Responsive Computer Systems, Vol. 7 pp. 30–52. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  7. Doder, D., Ognjanović, Z., Marković, Z.: An Axiomatization of a First-order Branching Time Temporal Logic. Journal of Universal Computer Science 16(11), 1439–1451 (2010)

    MathSciNet  MATH  Google Scholar 

  8. Doder, D., Marković, Z., Ognjanović, Z., Perović, A., Rašković, M.: A Probabilistic Temporal Logic That Can Model Reasoning about Evidence. In: Link, S., Prade, H. (eds.) FoIKS 2010. LNCS, vol. 5956, pp. 9–24. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  9. Doder, D., Marinković, B., Maksimović, P., Perović, A.: A Logic with Conditional Probability Operators. Publications de l’Institut Mathématique, Nouvelle Série, Beograd 87(101), 85–96 (2010)

    MathSciNet  MATH  Google Scholar 

  10. Emerson, E., Clarke, E.: Using branching time logic to synthesize synchronization skeletons. Sci. Comput. Program. 2, 241–266 (1982)

    Article  MATH  Google Scholar 

  11. Emerson, E.: Temporal and Modal Logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics, pp. 995–1072. North-Holland Pub. Co./MIT Press (1990)

    Google Scholar 

  12. Fagin, R., Halpern, J., Megiddo, N.: A logic for reasoning about probabilities. Information and Computation 87(1–2), 78–128 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  13. Feldman, Y.: A decidable propositional dynamic logic with explicit probabilities. Information and Control 63, 11–38 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  14. Guelev, D.P.: A propositional dynamic logic with qualitative probabilities. Journal of Philosophical Logic 28(6), 575–605 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  15. Guelev, D.P.: Probabilistic neighbourhood logic. In: Joseph, M. (ed.) FTRTFT 2000. LNCS, vol. 1926, pp. 264–275. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  16. Guelev, D.P.: Probabilistic Interval Temporal Logic and Duration Calculus with Infinite Intervals: Complete Proof Systems. Logical Methods in Computer Science 3(3), 1–43 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  17. Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspect of Computing 6(5), 512–535 (1994)

    Article  MATH  Google Scholar 

  18. Hart, S., Sharir, M.: Probabilistic temporal logics for finite and bounded models. In: 16th ACM Symposium on Theory of Computing, pp. 1–13. ACM, New York (1984): Extended version In: Information and Control 70 (2/3), 97-155 (1986)

    Google Scholar 

  19. Hung, D.V., Chaochen, Z.: Probabilistic Duration Calculus for Continuous Time. Formal Aspects of Computing 11(1), 21–44 (1999)

    Article  MATH  Google Scholar 

  20. Kozen, D.: A probabilistic PDL. Journal of Computer and System Sciences 30, 162–178 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  21. Lehmann, D., Shelah, S.: Reasoning with time and chance. Information and Control 53, 165–198 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  22. Liu, Z., Ravn, A.P., Sorensen, E.V., Chaochen, Z.: A Probabilistic Duration Calculus. In: Kopetz, H., Kakuda, Y. (eds.) Dependable Computing and Fault-Tolerant Systems. Responsive Computer Systems, vol. 7, pp. 30–52. Springer, Heidelberg (1993)

    Google Scholar 

  23. Marković, Z., Ognjanović, Z., Rašković, M.: A Probabilistic Extension of Intuitionistic Logic. Mathematical Logic Quarterly 49, 415–424 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  24. Ognjanović, Z., Rašković, M.: Some probability logics with new types of probability operators. Journal of Logic and Computation 9(2), 181–195 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  25. Ognjanović, Z., Rašković, M.: Some first-order probability logics. Theoretical Computer Science 247(1-2), 191–212 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  26. Ognjanović, Z.: Discrete Linear-time Probabilistic Logics: Completeness, Decidability and Complexity. Journal of Logic Computation 16(2), 257–285 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  27. Ognjanović, Z., Perović, A., Rašković, M.: Logics with the Qualitative Probability Operator. Logic Journal of IGPL 16(2), 105–120 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  28. Perović, A., Ognjanović, Z., Rašković, M., Marković, Z.: A Probabilistic Logic with Polynomial Weight Formulas. In: Hartmann, S., Kern-Isberner, G. (eds.) FoIKS 2008. LNCS, vol. 4932, pp. 239–252. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  29. Pnueli, A.: The Temporal Logic of Programs. In: Proceedings of the 18th IEEE Symposium Foundations of Computer Science (FOCS 1977), pp. 46–57 (1977)

    Google Scholar 

  30. Prior, A.: Time and Modality. Oxford University Press, Oxford (1957)

    MATH  Google Scholar 

  31. Rašković, M., Marković, Z., Ognjanović, Z.: A Logic with Approximate Conditional Probabilities that can Model Default Reasoning. International Journal of Approximate Reasoning 49(1), 52–66 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  32. Reynolds, M.: An axiomatization of full computation tree logic. The Journal of Symbolic Logic 66(3), 1011–1057 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  33. Segerberg, K.: Qualitative probability in a modal setting. In: Fenstad, J.E. (ed.) Proceedings of the Second Scandinavian Logic Symposium. North-Holland, Amsterdam (1971)

    Google Scholar 

  34. Stirling, C.: Modal and temporal logic. Handbook of Logic in Computer Science 2, 477–563 (1992)

    MathSciNet  Google Scholar 

  35. Tzanis, E., Hirsch, R.: Probabilistic Logic over Paths. Electronic Notes in Theoretical Computer Science 220(3), 79–96 (2008)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Matematički institut SANU, Kneza Mihaila 36, 11000, Beograd, Serbia

    Zoran Ognjanović & Zoran Marković

  2. Mašinski fakultet, Kraljice Marije 16, 11120, Beograd, Serbia

    Dragan Doder

Authors
  1. Zoran Ognjanović
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  2. Dragan Doder
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  3. Zoran Marković
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Editor information

Editors and Affiliations

  1. CRIL-CNRS, University of Artois, 62307, France

    Salem Benferhat

  2. Department of Mathematics, Towson University, 21252, Towson, MD, USA

    John Grant

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Ognjanović, Z., Doder, D., Marković, Z. (2011). A Branching Time Logic with Two Types of Probability Operators. In: Benferhat, S., Grant, J. (eds) Scalable Uncertainty Management. SUM 2011. Lecture Notes in Computer Science(), vol 6929. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23963-2_18

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  • DOI: https://doi.org/10.1007/978-3-642-23963-2_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23962-5

  • Online ISBN: 978-3-642-23963-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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