Possible Semantics for a Common Framework of Probabilistic Logics

  • Rolf Haenni
  • Jan-Willem Romeijn
  • Gregory Wheeler
  • Jon Williamson

Summary

This paper proposes a common framework for various probabilistic logics. It consists of a set of uncertain premises with probabilities attached to them. This raises the question of the strength of a conclusion, but without imposing a particular semantics, no general solution is possible. The paper discusses several possible semantics by looking at it from the perspective of probabilistic argumentation.

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References

  1. 1.
    Adams, E.W.: A Primer of Probability Logic. CSLI Publications, Stanford (1998)MATHGoogle Scholar
  2. 2.
    Anderson, K.A., Hooker, J.N.: A linear programming framework for logics of uncertainty. Decision Support Systems 16(1), 39–53 (1996)CrossRefGoogle Scholar
  3. 3.
    Bergmann, G.: The logic of probability. American Journal of Physics 9, 263–272 (1941)CrossRefGoogle Scholar
  4. 4.
    Carnap, R.: Logical Foundations of Probability. University of Chicago Press (1950)Google Scholar
  5. 5.
    Cozman, F.G.: Credal networks. Artificial Intelligence 120(2), 199–233 (2000)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    de Finetti, B.: The logic of probability. Philosophical Studies 77(1), 181–190 (1995)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Fagin, R., Halpern, J.Y., Megiddo, N.: A logic for reasoning about probabilities. Information and Computation 87(1/2), 78–128 (1990)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Fox, J.: Probability, logic and the cognitive foundations of rational belief. Journal of Applied Logic 1(3–4), 197–224 (2003)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Gaifman, H.: Concerning measures in first order calculi. Israel Journal of Mathematics 2, 1–18 (1964)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Gerla, G.: Inferences in probability logic. Artificial Intelligence 70(1–2), 33–52 (1994)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Haenni, R.: Towards a unifying theory of logical and probabilistic reasoning. In: Cozman, F.B., Nau, R., Seidenfeld, T. (eds.) ISIPTA 2005, 4th International Symposium on Imprecise Probabilities and Their Applications, Pittsburgh, USA, pp. 193–202 (2005)Google Scholar
  12. 12.
    Haenni, R.: Using probabilistic argumentation for key validation in public-key cryptography. International Journal of Approximate Reasoning 38(3), 355–376 (2005)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Haenni, R.: Probabilistic argumentation. Journal of Applied Logic (forthcoming, 2008)Google Scholar
  14. 14.
    Haenni, R., Hartmann, S.: Modeling partially reliable information sources: A general approach based on Dempster-Shafer theory. International Journal of Information Fusion 7(4), 361–379 (2006)CrossRefGoogle Scholar
  15. 15.
    Haenni, R., Kohlas, J., Lehmann, N.: Probabilistic argumentation systems. In: Gabbay, D.M., Smets, P. (eds.) Handbook of Defeasible Reasoning and Uncertainty Management Systems. Algorithms for Uncertainty and Defeasible Reasoning, vol. 5, pp. 221–288. Kluwer Academic Publishers, Dordrecht (2000)Google Scholar
  16. 16.
    Hailperin, T.: Probability logic. Notre Dame Journal of Formal Logic 25(3), 198–212 (1984)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Hailperin, T.: Sentential Probability Logic. Lehigh University Press (1996)Google Scholar
  18. 18.
    Halpern, J.Y.: An analysis of first-order logics of probability. Artificial Intelligence 46, 311–350 (1990)MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Howson, C.: Probability and logic. Journal of Applied Logic 1(3–4), 151–165 (2003)MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Jaynes, E.T.: Probability theory as logic. In: Fougère, P.F. (ed.) 9th Annual Workshop on Maximum Entropy and Bayesian Methods, pp. 1–16 (1990)Google Scholar
  21. 21.
    Kohlas, J.: Probabilistic argumentation systems: A new way to combine logic with probability. Journal of Applied Logic 1(3–4), 225–253 (2003)MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Kyburg, H.E.: Probability and Inductive Logic. Macmillan, New York (1970)Google Scholar
  23. 23.
    Levi, I.: The Enterprise of Knowledge. The MIT Press, Cambridge (1980)Google Scholar
  24. 24.
    Ng, R., Subrahmanian, V.S.: Probabilistic logic programming. Information and Computation 101(2), 150–201 (1992)MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Nilsson, N.J.: Probabilistic logic. Artificial Intelligence 28(1), 71–87 (1986)MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Reichenbach, H.: Wahrscheinlichkeitslogik. Erkenntnis 5, 37–43 (1935)MATHGoogle Scholar
  27. 27.
    Richardson, M., Domingos, P.: Markov logic networks. Machine Learning 62(1–2), 107–136 (2006)CrossRefGoogle Scholar
  28. 28.
    Ruspini, E.H.: The logical foundations of evidential reasoning. Tech. Rep. 408, SRI International, AI Center, Menlo Park, USA (1986)Google Scholar
  29. 29.
    Ruspini, E.H., Lowrance, J., Strat, T.: Understanding evidential reasoning. International Journal of Approximate Reasoning 6(3), 401–424 (1992)MATHCrossRefGoogle Scholar
  30. 30.
    Scott, D., Krauss, P.: Assigning probabilities to logical formulas. In: Hintikka, J., Suppes, P. (eds.) Aspects of Inductive Logic, pp. 219–264. North-Holland, Amsterdam (1966)Google Scholar
  31. 31.
    Williamson, J.: Probability logic. In: Gabbay, D., et al. (eds.) Handbook of the Logic of Argument and Inference: The Turn Toward the Practical, pp. 397–424. Elsevier, Amsterdam (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Rolf Haenni
    • 1
  • Jan-Willem Romeijn
    • 2
  • Gregory Wheeler
    • 3
  • Jon Williamson
    • 4
  1. 1.Engineering and Information TechnologyBern University of Applied SciencesSwitzerland
  2. 2.Faculty of PhilosophyUniversity of GroningenGL GroningenThe Netherlands
  3. 3.Department of Computer ScienceUniversidade Nova de LisboaCaparicaPortugal
  4. 4.SECL, PhilosophyUniversity of KentCanterburyUnited Kingdom

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