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Unifying Logical and Probabilistic Reasoning

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Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3571))

Abstract

Most formal techniques of automated reasoning are either rooted in logic or in probability theory. These areas have a long tradition in science, particularly among philosophers and mathematicians. More recently, computer scientists have discovered logic and probability theory to be the two key techniques for building intelligent systems which rely on reasoning as a central component. Despite numerous attempts to link logical and probabilistic reasoning, a satisfiable unified theory of reasoning is still missing. This paper analyses the connection between logical and probabilistic reasoning, it discusses their respective similarities and differences, and proposes a new unified theory of reasoning in which both logic and probability theory are contained as special cases.

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References

  1. Adams, E.W.: A Primer of Probability Logic. CSLI Publications, Stanfort (1998)

    Google Scholar 

  2. Cohen, L.J.: The Probable and the Provable. Clarendon Press, Oxford (1977)

    Google Scholar 

  3. Dempster, A.P.: A generalization of Bayesian inference. Journal of the Royal Statistical Society 30, 205–247 (1968)

    MathSciNet  Google Scholar 

  4. Fagin, R., Halpern, J.Y.: Uncertainty, belief, and probability. Computational Intelligence 7(3), 160–173 (1991)

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  6. Gärdenfors, P.: Probabilistic reasoning and evidentiary value. In: Gärdenfors, P., Hansson, B., Sahlin, N.E. (eds.) Evidentiary Value: Philosophical, Judicial and Psychological Aspects of a Theory, C. W. K. Gleerups, Lund, Sweden, pp. 44–57 (1983)

    Google Scholar 

  7. Haenni, R.: Using probabilistic argumentation for key validation in public-key cryptography. International Journal of Approximate Reasoning 38(3), 355–376 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  8. Haenni, R., Anrig, B., Kohlas, J., Lehmann, N.: A survey on probabilistic argumentation. In: ECSQARU 2001, 6th European Conference on Symbolic and Quantitative Approaches to Reasoning under Uncertainty, Workshop on Adventures in Argumentation, Toulouse, France (2001)

    Google Scholar 

  9. Haenni, R., Kohlas, J., Lehmann, N.: Probabilistic argumentation systems. In: Kohlas, J., Moral, S. (eds.) Handbook of Defeasible Reasoning and Uncertainty Management Systems, Algorithms for Uncertainty and Defeasible Reasoning, vol. 5, pp. 221–288. Kluwer, Dordrecht (2000)

    Google Scholar 

  10. Haenni, R., Lehmann, N.: Probabilistic argumentation systems: a new perspective on Dempster-Shafer theory. International Journal of Intelligent Systems (Special Issue: the Dempster-Shafer Theory of Evidence) 18(1), 93–106 (2003)

    MATH  Google Scholar 

  11. Hailperin, T.: Probability logic. Notre Dame Journal of Formal Logic 25(3), 198–212 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  12. Hailperin, T.: Sentential Probability Logic: Origins, Development, Current Status, and Technical Applications. Lehigh University Press (1996)

    Google Scholar 

  13. Halpern, J.Y.: An analysis of first-order logics of probability. Artificial Intelligence 46, 311–350 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  14. Hill, M.J., Paris, J.B., Wilmers, G.M.: Some observations on induction in predicate probabilistic reasoning. Journal of Philosophical Logic 31, 43–75 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  15. Howson, C.: Probability and logic. Journal of Applied Logic 1(3–4), 151–165 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  16. Kohlas, J.: Probabilistic argumentation systems: A new way to combine logic with probability. Journal of Applied Logic 1(3–4), 225–253 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  17. Kohlas, J., Monney, P.A.: A Mathematical Theory of Hints. An Approach to the Dempster-Shafer Theory of Evidence. Lecture Notes in Economics and Mathematical Systems, vol. 425. Springer, Heidelberg (1995)

    MATH  Google Scholar 

  18. Kohlas, J., Monney, P.A.: Statistical information and assumption-based inference: Continuous models. Technical Report 04–08, Department of Informatics, University of Fribourg (2004)

    Google Scholar 

  19. Kohlas, J., Monney, P.A.: Statistical information and assumption-based inference: Discrete models. Technical Report 04–07, Department of Informatics, University of Fribourg (2004)

    Google Scholar 

  20. Kolmogorov, A.N.: Foundations of the Theory of Probability. Chelsea Publishing Company, New York (1950)

    Google Scholar 

  21. Kyburg, H.E.: Higher order probabilities and intervals. International Journal of Approximate Reasoning 2, 195–209 (1988)

    Article  MathSciNet  Google Scholar 

  22. Kyburg, H.E.: Interval-valued probabilities. In: Cooman, G.d., Walley, P. (eds.) The Imprecise Probabilities Project, IPP Home Page (1998), available at http://ippserv.rug.ac.be

  23. Nilsson, N.J.: Probabilistic logic. Artificial Intelligence 28(1), 71–87 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  24. Pearl, J.: Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann, San Mateo (1988)

    Google Scholar 

  25. Peirce, C.S.: The probability of induction. Popular Science Monthly 12, 705–718 (1878)

    Google Scholar 

  26. Ruspini, E., Lowrance, J.: Th. Strat. Understanding evidential reasoning. International Journal of Approximate Reasoning 6(3), 401–424 (1992)

    Article  MATH  Google Scholar 

  27. Ruspini, E.H.: The logical foundations of evidential reasoning. Technical Report 408, AI Center, SRI International, Menlo Park, CA (1986)

    Google Scholar 

  28. Russell, S., Norvig, P.: Artificial Intelligence: A Modern Approach, 2nd edn. Prentice-Hall, Englewood Cliffs (2003)

    Google Scholar 

  29. Shafer, G.: The Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)

    Google Scholar 

  30. Smets, P.: Probability of provability and belief functions. Journal de la Logique et Analyse 133, 177–195 (1991)

    MathSciNet  Google Scholar 

  31. Smets, P., Kennes, R.: The transferable belief model. Artificial Intelligence 66, 191–234 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  32. Tessem, B.: Interval probability propagation. International Journal of Approximate Reasoning 7, 95–120 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  33. Walley, P.: Statistical Reasoning with Imprecise Probabilities. In: Monographs on Statistics and Applied Probability, vol. 42. Chapman and Hall, London (1991)

    Google Scholar 

  34. Walley, P.: Towards a unified theory of imprecise probability. International Journal of Approximate Reasoning 24(2–3), 125–148 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  35. Weichselberger, K.: The theory of interval-probability as a unifying concept for uncertainty. International Journal of Approximate Reasoning 24(2–3), 149–170 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  36. Williamson, J.: Probability logic. In: Gabbay, D., Johnson, R., Ohlbach, H.J., Woods, J. (eds.) Handbook of the Logic of Argument and Inference: the Turn Toward the Practical, pp. 397–424. Elsevier, Amsterdam (2002)

    Chapter  Google Scholar 

  37. Williamson, J.: Bayesian Nets and Causality: Philosophical and Computational Foundations. Oxford University Press, Oxford (2005)

    MATH  Google Scholar 

  38. Yager, R.R., Kreinovich, V.: Decision making under interval probabilities. International Journal of Approximate Reasoning 22, 195–215 (1999)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Computer Science and Apllied Mathemathics, University of Berne, CH-3012, Berne, Switzerland

    Rolf Haenni

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  1. Rolf Haenni
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Editor information

Editors and Affiliations

  1. IIIA - CSIC, 08193, Bellaterra, Spain

    Lluís Godo

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© 2005 Springer-Verlag Berlin Heidelberg

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Haenni, R. (2005). Unifying Logical and Probabilistic Reasoning. In: Godo, L. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2005. Lecture Notes in Computer Science(), vol 3571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11518655_66

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  • DOI: https://doi.org/10.1007/11518655_66

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-27326-4

  • Online ISBN: 978-3-540-31888-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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