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Completeness theorem for propositional probabilistic models whose measures have only finite ranges

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Abstract.

A propositional logic is defined which in addition to propositional language contains a list of probabilistic operators of the form P ≥s (with the intended meaning ‘‘the probability is at least s’’). The axioms and rules syntactically determine that ranges of probabilities in the corresponding models are always finite. The completeness theorem is proved. It is shown that completeness cannot be generalized to arbitrary theories.

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References

  1. Barwise, K.J.: Admissible sets and structures. Springer-Verlag, Berlin, 1975

  2. Bhaskara Rao, K.P.S., Bhaskara Rao, M.: Theory of charges. Academic Press, 1983

  3. Fagin, R., Halpern, J.Y., Megiddo, N.: A logic for reasoning about probabilities. Information and Computation 8, 78–128 (1990)

    MathSciNet  MATH  Google Scholar 

  4. Fagin, R., Halpern, J.Y.: Reasoning about knowledge and probability. Journal of the ACM 41 (2), 340–367 (1994)

    Article  MATH  Google Scholar 

  5. Fattorosi-Barnaba, M., Amati, G.: Modal operators with probabilistic interpretations I. Studia Logica 46 (4), 383–393 (1989)

    MATH  Google Scholar 

  6. Keisler, H.J.: Model theory for infinitary logic. North-Holland, Amsterdam, 1971

  7. Nilsson, N.: Probabilistic logic. Artificial Intelligence 28, 71–87 (1986)

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  9. Rašković , M.: Completeness theorem for biprobability models. J. Symbolic Logic 51 (3), 586–590 (1986)

    Google Scholar 

  10. Rašković , M.: Classical logic with some probability operators. Publ. Inst. Math. (NS) 53 (67), 1–3 (1993)

    Google Scholar 

  11. van der Hoek, W.: Some considerations on the logic P F D: a logic combining modality and probability. Journal of Applied Non-Classical Logics 7 (3), 287–307 (1997)

    Google Scholar 

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Authors and Affiliations

  1. Prirodno-matematički fakultet, R. Domanović a, 12, 34000, Kragujevac, Yugoslavia

    Radosav Dordević

  2. Učiteljski fakultet, Narodnog fronta 43, 11000, Beograd, Yugoslavia

    Miodrag Rašković

  3. Matematički institut, Kneza Mihaila 35, 11000, Beograd, Yugoslavia

    Zoran Ognjanović

Authors
  1. Radosav Dordević
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  2. Miodrag Rašković
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  3. Zoran Ognjanović
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Corresponding author

Correspondence to Zoran Ognjanović.

Additional information

This research was supported by Ministarstvo za nauku, tehnologije i razvoj Republike Srbije, through Matematički institut, under grant 1379

Mathematics Subject Classification (2000): 03C70, 03B48

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Dordević, R., Rašković, M. & Ognjanović, Z. Completeness theorem for propositional probabilistic models whose measures have only finite ranges. Arch. Math. Logic 43, 557–563 (2004). https://doi.org/10.1007/s00153-004-0217-3

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  • DOI: https://doi.org/10.1007/s00153-004-0217-3

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