Skip Navigation


Logic Journal of IGPL Advance Access originally published online on September 25, 2007
Logic Journal of IGPL 2008 16(2):105-120; doi:10.1093/jigpal/jzm031
This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Ognjanovic, Z.
Right arrow Articles by Raskovic, M.
Social Bookmarking
 Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Logics with the Qualitative Probability Operator

Zoran Ognjanovic

Matematicki institut SANU, Kneza Mihaila 35, 11000 Beograd, Serbia. E-mail: zorano{at}mi.sanu.ac.yu

Aleksandar Perovic

Saobracajni fakultet, Vojvode Stepe 305, 11000 Beograd, Serbia. E-mail: pera{at}sf.bg.ac.yu

Miodrag Raskovic

Matematicki institut SANU, Kneza Mihaila 35, 11000 Beograd, Serbia. E-mail: miodragm{at}mi.sanu.ac.yu

The paper presents several strongly complete axiomatizations of qualitative probability within the framework of probabilistic logic. We show that in the proposed semantics qualitative probabilities are characterized by probability functions, so they also are comparative probabilities.

Key Words: probability logic • qualitative probability • strong completeness • decidability

Received for publication 25 October 2006.

References

  1. Dubois D, Prade H. Qualitative possibility functions and integrals. In: Handbook of measure theory.—Pap E, ed. (2002) North-Holland. 1499–1522.

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

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

  4. Heifetz A, Mongin P. Probability logic for type spaces. Games and economic behavior (2001) 35:31–53.[CrossRef][ISI]

  5. Horvitz E, Jensen F. Generalized qualitative probability: Savage revisited. (1996) Procs. of 12 th Conference on Uncertainty in Artificial Intelligence (UAI-96). 381–388.

  6. Marchioni E, Godo L. A Logic for Reasoning about Coherent Conditional Probability: A Modal Fuzzy Logic Approach. Leite J, Alferes J, eds. (2004) 3229. 9th European Conference Jelia'04, Lecture notes in artificial intelligence (LNCS/LNAI). 213–225.

  7. Meier M. An infinitary probability logic for type spaces. Israel J. of Mathematics, {infty}.

  8. Narens L. On qualitative axiomatizations for probability theory. Journal of Philosophical Logic (1980) Volume 9(Number 2). Springer. 143–151.[ISI]

  9. Nilsson N. Probabilistic logic. Artificial intelligence (1986) 28:71–87.[CrossRef][ISI]

  10. Ognjanovic Z, Raskovic M. A logic with higher order probabilities. Publications de l'sinstitut mathematique, Nouvelle série, tome (1996) 60(74):1–4.

  11. Ognjanovic Z, Raskovic M. Some probability logics with new types of probability operators. J. Logic Computat (1999) Vol 9(No. 2):181–195.[CrossRef]

  12. Ognjanovic Z, Raskovic M. Some first-order probability logics. Theoretical Computer Science (2000) 247(1–2):191–212.[CrossRef][ISI]

  13. Ognjanovic Z, Timotijevic T, Stanojevic A. Database of papers about probability logics. In: Mathematical institute Belgrade (2005) page http://problog.mi.sanu.ac.yu.

  14. Ognjanovic Z, Markovic Z, Raskovic M. Completeness Theorem for a Logic with imprecise and conditional probabilities. Publications de L'Institute Matematique (Beograd) (2005) 78(92):35–49.

  15. Raskovic M. Classical logic with some probability operators. Publications de l'institut mathematique, Nouvelle série, tome (1993) 53(67):1–3.

  16. Raskovic M, Ognjanovic Z. A first order probability logic LPQ. Publications de l'institut mathematique, Nouvelle série, tome (1999) 65(79):1–7.

  17. Leite J, Alferes J. A logic with Conditional Probabilities. (2004) 9th European Conference Jelia'04 Logics in Artificial Intelligence, volume 3229 of Lecture notes in computer science. Springer-Verlag. 226–238.

  18. Scott D. Measurement models and linear inequalities. Journal of Mathematical Psychology (1964) 1:233–247.[CrossRef][ISI]

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

  20. Wellman MP. Some varieties of qualitative probability. (1994) Proceedings of the 5th International Conference on Information Processing and the Management of Uncertainty: Paris.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?



This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Ognjanovic, Z.
Right arrow Articles by Raskovic, M.
Social Bookmarking
 Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?