Skip to main content
SpringerLink
Log in

Probabilistic Reasoning as a General Unifying Tool

  • Conference paper
  • First Online:
Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2001)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2143))

Abstract

Our starting point is the approach to probabilistic logic through coherence; but we give up de Finetti’s idea of a conditional event EH being a 3-valued entity, with the third value being just an undetermined common value for all ordered pairs (E, H). We let instead the “third” value of EH suitably depend on the given pair. In this way we get, through a direct assignment of conditional probability, a general theory of probabilistic reasoning able to encompass other approaches to uncertain reasoning, such as fuzziness and default reasoning. We are also able to put forward a meaningful concept of conditional independence, which avoids many of the usual inconsistencies related to logical dependence. We give an example in which we put together different kinds of information and show how coherent conditional probability can act as a unifying tool.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Capotorti, A., Vantaggi, B.:Locally Strong Coherence in Inference Processes. Annals of Mathematics and Artificial Intelligence (2001), to appear

    Google Scholar 

  2. Coletti, G., Gilio, A., Scozzafava, R.: Conditional Events with Vague Information in Expert Systems. In: Lecture Notes in Computer Sciences, n. 521, Springer-Verlag, Berlin (1991) 106–114

    Google Scholar 

  3. Coletti, C, Scozzafava, R.: Characterization of Coherent Conditional Probabilities as a Tool for their Assessment and Extension. International Journal of Uncertainty, Fuzziness and Knowledge-Based System 4 (1996) 103–127

    Article  MathSciNet  Google Scholar 

  4. Coletti, C, Scozzafava, R.: Zero Probabilities in Stochastical Independence. In: Information, Uncertainty, Fusion, Kluwer, Dordrecht (2000) 185–196. (Selected papers from IPMU’ 98, Paris)

    Google Scholar 

  5. Coletti, C, Scozzafava, R.: Conditioning and Inference in Intelligent Systems. Soft Computing 3 (1999) 118–130

    Google Scholar 

  6. Coletti, C, Scozzafava, R.: Conditional Subjective Probability and Fuzzy Theory. In: Proc. 18th Int. Conf. of NAFIPS, New York (1999) 77–80

    Google Scholar 

  7. Coletti, C, Scozzafava, R.: The Role of Coherence in Eliciting and Handling Imprecise Probabilities and its Application to Medical Diagnosis. Information Sciences 130 (2000)41–65

    Article  MATH  MathSciNet  Google Scholar 

  8. Coletti, C, Scozzafava, R.: Fuzzy Sets as Conditional Probabilities: which Meaningful Operations can be Defined? In: Proc. 20th Int. Conf. of NAFIPS, Vancouver, Canada, (2001), to appear

    Google Scholar 

  9. Coletti, C, Scozzafava, R., Vantaggi, B.: The Role of Coherent Conditional Probability in Inferential Reasoning, in preparation

    Google Scholar 

  10. Dawid, A.P.: Conditional Independence in Statistical Theory. Journal of Royal Statistical Society B 41 (1979) 15–31

    Google Scholar 

  11. de Finetti, B. Sullímpostazione assiomatica del calcolo delie probabilitá. Annali Univ. Trieste 19 (1949) 3–55. (Engl. transi.: Ch.5 in: Probability, Induction, Statistics, Wiley, London, 1972)

    Google Scholar 

  12. Dubins, L.E.: Finitely Additive Conditional Probabilities, Conglomerability and Disintegration. Annals of Probability 3 (1975) 89–99

    Article  MATH  MathSciNet  Google Scholar 

  13. Frisch, A.M., Haddawy, P.: Anytime Deduction for Probabilistic Logic. Artificial Intelligence 69, 1–2 (1993) 93–122

    MathSciNet  Google Scholar 

  14. Gilio, A.: Conditional events and subjective probability in management of uncertainty. In: Uncertainty in Intelligent Systems, Elsevier, Amsterdam (1993) 109–120

    Google Scholar 

  15. Gilio, A., Scozzafava, R.: Le probabilitá condizionate coerenti nei sistemi esperti. In: Ricerca Operativa e Intelligenza Artificiale, A.I.R.O., IBM Pisa (1988) 317–330

    Google Scholar 

  16. Goldszmidt, M., Pearl, J.: Qualitative probability for default reasoning, belief revision and causal modeling. Artificial Intelligence 84 (1996) 57–112

    Article  MathSciNet  Google Scholar 

  17. Harper, W.L.: Rational Belief Change, Popper Functions and Counterfactuals. In: Harper, Hooker (eds): Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Sciences 1 (1976) 73–115

    Google Scholar 

  18. Holzer, S.: On Coherence and Conditional Prevision. Boll. Un. Mat. Ital. (6)4 (1985) 441–460

    MathSciNet  Google Scholar 

  19. Koopman, B.O.: The Bases of Probability. Bulletin A.M.S. 46 (1940) 763–774

    Article  MATH  MathSciNet  Google Scholar 

  20. Krauss, P.H.: Representation of Conditional Probability Measures on Boolean Algebras. Acta Math. Acad. Scient. Hungar. 19 (1968) 229–241

    Article  MATH  MathSciNet  Google Scholar 

  21. Lauritzen, S.L.: Graphical Models. Clarendon Press, Oxford (1996)

    Google Scholar 

  22. Nilsson, N.J.: Probabilistic Logic. Artificial Intelligence 28 (1986) 71–87

    Article  MATH  MathSciNet  Google Scholar 

  23. Nilsson, N.J.: Probabilistic Logic Revisited. Artificial Intelligence 59 (1993) 39–42

    Article  MathSciNet  Google Scholar 

  24. Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo CA (1988)

    Google Scholar 

  25. Popper, K.R.: The Logic of Scientific Discovery. Routledge, London and New York (1959)

    MATH  Google Scholar 

  26. Regazzini, E.: Finitely Additive Conditional Probabilities. Rend. Sem. Mat. Fis. Milano 55 (1985) 69–89

    Article  MATH  MathSciNet  Google Scholar 

  27. Reiter, R.: A Logic for Default Reasoning. Artificial Intelligence, 13, 1–2 (1980) 81–132

    Article  MATH  MathSciNet  Google Scholar 

  28. Rényi, A.: On Conditional Probability Spaces Generated by a Dimensionally Ordered Set of Measures. Theory of Probability and its Applications 1 (1956) 61–71

    Article  MATH  Google Scholar 

  29. Russel, S.J., Norvig, P.: Artificial Intelligence. A Modern Approach. Pentice-Hall, New Jersey (1995)

    Google Scholar 

  30. Shenoy, P.P.: On Spohn’s Rule for Revision of Beliefs. International Journal of Approximate Reasoning 5 (1991) 149–181

    Article  MATH  MathSciNet  Google Scholar 

  31. Spohn, W.: On the Properties of Conditional Independence. In: Humphreys, P., Suppes, P. (eds): Scientific Philosopher 1: Probability and Probabilistic Causality, Kluwer, Dordrecht (1994) 173–194

    Google Scholar 

  32. Spohn, W.: Ranking Functions, AGM Style. Research Group “Logic in Philosophy” Preprint 28 (1999)

    Google Scholar 

  33. Vantaggi, Conditional Independence and Graphical Models in a Coherent Setting. PhD thesis, Universitá di Perugia, Italy (1999)

    Google Scholar 

  34. Vantaggi, Conditional Independence in a Finite Coherent Setting. Annals of Mathematics and Artificial Intelligence (2001), to appear

    Google Scholar 

  35. Witthaker, J.: Graphical Models in Applied Multivariate Statistics. Wiley & Sons, New York (1990)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Universitá di Perugia, Via Vanvitelli, 1 - 06100, Perugia, Italy

    Giulianella Coletti

  2. Dipartimento Metodi e Modelli Matematici, Universitá “La Sapienza”, Via Scarpa, 16 - 00161, Roma, Italy

    Romano Scozzafava & Barbara Vantaggi

Authors
  1. Giulianella Coletti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Romano Scozzafava
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Barbara Vantaggi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Université Paul Sabatier, IRIT-CNRS, 118 route de Narbonne, 31062, Toulouse Cedex 4, France

    Salem Benferhat  & Philippe Besnard  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Coletti, G., Scozzafava, R., Vantaggi, B. (2001). Probabilistic Reasoning as a General Unifying Tool. In: Benferhat, S., Besnard, P. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2001. Lecture Notes in Computer Science(), vol 2143. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44652-4_12

Download citation

  • DOI: https://doi.org/10.1007/3-540-44652-4_12

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42464-2

  • Online ISBN: 978-3-540-44652-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation