Advertisement

Inference Processes for Quantified Predicate Knowledge

  • J. B. Paris
  • S. R. Rad
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5110)

Abstract

We describe a method for extending an inference process for propositional probability logic to predicate probability logic in the case where the language in purely unary and show that the method is well defined for the Minimum Distance and CM  ∞  inference processes.

Keywords

Uncertain reasoning probability logic inference processes Renyi Entropies 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bacchus, F., Grove, A.J., Halpern, J.Y., Koller, D.: Generating new beliefs from old. In: Proceedings of the Tenth Annual Conference on Uncertainty in Artificial Intelligence (UAI 1994), pp. 37–45 (1994)Google Scholar
  2. 2.
    Bacchus, F., Grove, A.J., Halpern, J.Y., Koller, D.: From statistical knowledge to degrees of belief. Artificial Intelligence 87, 75–143 (1996)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Barnett, O.W., Paris, J.B.: Maximum Entropy inference with qualified knowledge. Logic Journal of the IGPL 16(1), 85–98 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Carnap, R.: A basic system of inductive logic. In: Jeffrey, R.C. (ed.) Studies in Inductive Logic and Probability, vol. II, pp. 7–155. University of California Press (1980)Google Scholar
  5. 5.
    Chang, C.C., Keisler, H.J.: Model Theory. Studies in Logic and the Foundations of Mathematics, vol. 73. North Holland, Amsterdam (1973)zbMATHGoogle Scholar
  6. 6.
    Dimitracopoulos, C., Paris, J.B., Vencovská, A., Wilmers, G.M.: A multivariate probability distribution based on the propositional calculus, Manchester Centre for Pure Mathematics, University of Manchester, UK, preprint number 1999/6, http://www.maths.manchester.ac.uk/~jeff/
  7. 7.
    Fitelson, B.: Inductive Logic, http://fitelson.org/il.pdf
  8. 8.
    Hodges, W.: Model Theory. Cambridge University Press, Cambridge (1993)zbMATHGoogle Scholar
  9. 9.
    Grove, A.J., Halpern, J.Y., Koller, D.: Random Worlds and Maximum Entropy. Journal of Artificial Intelligence Research 2, 33–88 (1994)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Grove, A.J., Halpern, J.Y., Koller, D.: Asymptotic conditional probabilities: the unary case. SIAM J. of Computing 25(1), 1–51 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Grove, A.J., Halpern, J.Y., Koller, D.: Asymptotic conditional probabilities: the non-unary case. J. Symbolic Logic 61(1), 250–276 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Hintikka, J., Niiniluoto, I.: An axiomatic foundation for the logic of inductive generalization. In: Jeffrey, R.C. (ed.) Studies in Inductive Logic and Probability, vol. II, pp. 158–181. University of California Press, Berkeley, Los Angeles (1980)Google Scholar
  13. 13.
    Johnson, W.E.: Probability: The deductive and inductive problems. Mind 41(164), 409–423 (1932)CrossRefGoogle Scholar
  14. 14.
    Kuipers, T.A.F.: A survey of inductive systems. In: Jeffrey, R.C. (ed.) Studies in Inductive Logic and Probability, vol. II, pp. 183–192. University of California Press, Berkeley, Los Angeles (1980)Google Scholar
  15. 15.
    Kuipers, T.A.F.: On the generalization of the continuum of inductive methods to universal hypotheses. Synthese 37, 255–284 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Paris, J.B.: A short course on Inductive Logic. In: JAIST 2007 (2007), http://www.maths.manchester.ac.uk/~jeff
  17. 17.
    Paris, J.B.: The Uncertain Reasoner’s Companion. Cambridge University Press, Cambridge (1994)zbMATHGoogle Scholar
  18. 18.
    Paris, J.B.: On the distribution of probability functions in the natural world. In: Hendricks, V.F., Pedersen, S.A., Jøgensen, K.F. (eds.) Probability Theory: Philosophy, Recent History and Relations to Science. Synthese Library, vol. 297, pp. 125–145 (2001)Google Scholar
  19. 19.
    Paris, J.B.: Vencovská, On the applicability of maximum entropy to inexact reasoning. International Journal of Approximate Reasoning 3(1), 1–34 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Paris, J.B., Vencovská: A note on the inevitability of maximum entropy. International Journal of Approximate Reasoning 4(3), 183–224 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Paris, J.B., Vencovská: In defense of the maximum entropy inference process. International Journal of Approximate Reasoning 17(1), 77–103 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Paris, J.B., Vencovská, A.: Common sense and stochastic independence. In: Corfield, D., Williamson, J. (eds.) Foundations of Bayesianism, pp. 203–240. Kluwer Academic Press, Dordrecht (2001)Google Scholar
  23. 23.
    Rad, S.R.: PhD Thesis, Manchester University, Manchester, UK (to appear)Google Scholar
  24. 24.

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • J. B. Paris
    • 1
  • S. R. Rad
    • 1
  1. 1.School of MathematicsUniversity of ManchesterManchesterUK

Personalised recommendations