Self-Conditional Probabilities and Probabilistic Interpretations of Belief Functions

1. B.F. Chellas, Modal Logic (Cambridge University Press, Cambridge, UK, 1980).

   Google Scholar 

2. A.P. Dempster, Upper and lower probabilities induced by a multiple valued mapping, Ann. Math. Statist. 38 (1967) 325-339.

   Google Scholar 

3. A.P. Dempster, Upper and lower probability inferences based on a sample from a finite univariate population, Biometrika 54 (1967) 515-528.

   Google Scholar 

4. A.P. Dempster, Upper and lower probabilities generated by a random closed interval, Ann. Math. Statist. 39 (1968) 957-966.

   Google Scholar 

5. A.P. Dempster, A generalization of Bayesian inference, J. Roy. Statist. Soc. Ser. B 30 (1968) 205-247.

   Google Scholar 

6. A.P. Dempster, Upper and lower probability inferences for families of hypothesis with monotone density ratios, Ann. Math. Statist. 40 (1969) 953-969.

   Google Scholar 

7. A.P. Dempster, A class of random convex polytopes, Ann. Math. Statist. 43 (1972) 250-272.

   Google Scholar 

8. D.M. Gabbay and P. Smets (eds.), Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol. 1 (Kluwer, Dordrecht, The Netherlands, 1998).

   Google Scholar 

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

   Google Scholar 

10. J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (Morgan Kaufmann, San Mateo, CA, 1988). R. Cooke, P. Smets / Self-conditional probabilities and probabilistic interpretations 285

11. E.H. Ruspini, The logical foundations of evidential reasoning, Technical Report, Technical note 408, SRI International, Menlo Park, CA (1986).

    Google Scholar 

12. E.H. Ruspini, Epistemic logics, probability and the calculus of evidence, in: IJCAI-87, Intern. Joint Conf. on Artificial Intelligence (Morgan Kaufmann, San Mateo, CA, 1987) pp. 924-931.

    Google Scholar 

13. G. Shafer, A Mathematical Theory of Evidence (Princeton Univ. Press, Princeton, NJ, 1976).

    Google Scholar 

14. L.I. Savage, The Foundations of Statistics (Wiley, New York, 1954).

    Google Scholar 

15. P. Smets, Probability of provability and belief functions, Logique Anal. 133 (1991) 177-195.

    Google Scholar 

16. P. Smets, Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem, Internat. J. Approx. Reasoning 9 (1993) 1-35.

    Google Scholar 

17. P. Smets, Probability of deductibility and belief functions, in: Symbolic and Quantitative Approaches to Uncertainty, eds. M. Clarke, R. Kruse and S. Moral (Springer, Berlin, 1993) pp. 332-341.

    Google Scholar 

18. P. Smets, What is Dempster-Shafer' model? in: Advances in the Dempster-Shafer Theory of Evidence, eds. R.R. Yager, J. Kacprzyk and M. Fedrizzi (Wiley, New York, 1994) pp. 5-34.

    Google Scholar 

19. P. Smets, The transferable belief model for quantified belief representation, in: Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol. 1, eds. D.M. Gabbay and P. Smets (Kluwer, Dordrecht, The Netherlands, 1998) pp. 267-301.

    Google Scholar 

20. P. Smets and R. Kennes, The transferable belief model, Artif. Intell. 66 (1994) 191-234.

    Google Scholar 

21. E. Tsiporkova, V. Boeva and B. De Baets, Dempster-Shafer' theory framed in modal logic, Internat. J. Approx. Reasoning, to appear (1999).

22. E. Tsiporkova, B. De Baets and V. Boeva, Dempster' rule of conditioning translated into modal logic, Fuzzy Sets and Systems 102 (1999) 371-383.

    Google Scholar 

23. E. Tsiporkova, B. De Baets and V. Boeva, Evidence theory in multivalued models of modal logic, J. Appl. Non-Classical Logics, to appear (1999).

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