Contributions to foundations of probability calculus on the basis of the modal logical calculus M C ν or M C * ν

A. Montanaro; A. Bressan

Rendiconti del Seminario Matematico della Università di Padova (1981)

  • Volume: 64, page 109-126
  • ISSN: 0041-8994

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Montanaro, A., and Bressan, A.. "Contributions to foundations of probability calculus on the basis of the modal logical calculus $MC^\nu $ or $MC^\nu _\ast $." Rendiconti del Seminario Matematico della Università di Padova 64 (1981): 109-126. <http://eudml.org/doc/107785>.

@article{Montanaro1981,
author = {Montanaro, A., Bressan, A.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {probability function of propositions as a primitive; existence axioms; extensional logic; modal calculi; existence rule; random variables; probability spaces},
language = {eng},
pages = {109-126},
publisher = {Seminario Matematico of the University of Padua},
title = {Contributions to foundations of probability calculus on the basis of the modal logical calculus $MC^\nu $ or $MC^\nu _\ast $},
url = {http://eudml.org/doc/107785},
volume = {64},
year = {1981},
}

TY - JOUR
AU - Montanaro, A.
AU - Bressan, A.
TI - Contributions to foundations of probability calculus on the basis of the modal logical calculus $MC^\nu $ or $MC^\nu _\ast $
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1981
PB - Seminario Matematico of the University of Padua
VL - 64
SP - 109
EP - 126
LA - eng
KW - probability function of propositions as a primitive; existence axioms; extensional logic; modal calculi; existence rule; random variables; probability spaces
UR - http://eudml.org/doc/107785
ER -

References

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  1. [1] A. Bressan, Metodo di assiomatizzazione in senso stretto della Meccanica classica. Applicazione di esso ad alcuni problemi di assiomatizzazione non completamente risolti, Rend. Sem. Mat. Univ. Padova, 32 (1962), pp. 55-212. Zbl0114.14902MR148437
  2. [2] A. Bressan, A General Interpreted Modal Calculus, New Haven and London, Yale University Press, 1972. Zbl0255.02015MR401432
  3. [3] A. Bressan, Generalizations of the modal calculi MCv and MC∞. Their comparison with similar calculi endowed with different semantics. Application to probability theory, being printed in the Proceedings of the workshop on modal logic held in Tübingen in Dec. 1977, Synthese Library Series, Dr. Reidel Publishing Co., Dordrecht (Holland), Boston. 
  4. [4] A. Bressan, Comments on Suppes' Paper: the essential but implicit rule of modal concept in Science, PSA 1973, Proceedings of the Biennal Meeting of the Philosophy of Science Association, edited by K. F. Schaffner and R. S. Cohen (1974), pp. 315-321. Zbl0317.02005
  5. [5] R. Carnap, Introduction to Symbolic Logic and Its Applications, New York, Dover Pubblications, 1958. Zbl0083.00104MR103814
  6. [6] B. De Finetti, Il buon senso e le foglie di fico, Boll. U.M.I., (4), 12 (1975), p. 1. Zbl0331.60001
  7. [7] P. Dore, Introduzione al calcolo delle probabilità, Casa Editrice Prof. Riccardo Pàtron, Bologna, 1962. Zbl0129.29901
  8. [8] H. Freudenthal, The crux of course design in probability, in Educational Studies in Probability, Reidel, Dordrecht (Holland) (1974), p. 261. Zbl0275.60002
  9. [9] I.I. Gihman - A. V. SKOROHOD, Introduction to the Theory of Random Processes, Saunders, Philadelphia, 1969. MR247660
  10. [10] I.I. Gihman - A. V. SKOROHOD, The theory of stochastic processes II, Die Grundlehren der mathematischen Wiss. 218, Springer, Berlin, 1975. Zbl0305.60027MR375463
  11. [11] H. Hermes, Eine Axiomatisierung der allgemeinen Mechanik. Forschungen zur Logik und zur Grundlegung der exakten Wissenschaften, vol. 3, Leipzig, Verlag Von Hirzel, 1938. Zbl0019.09804JFM64.0032.02
  12. [12] H. Hermes, Zur Axiomatisierung der Mechanik, Procedings of the International Symposium on the Axiomatic Method, Berkeley, 1957-58, Amsterdam, North-Holland Publishing Co., 1959, p. 250. MR109451
  13. [13] E. Mendelson, Introduction to Mathematical logic, Von Nostrand, Reinhold, 1964. Zbl0192.01901MR164867
  14. [14] R. Von Mises, Grundlagen der Wahrscheinlichkeitsrechnung, in Math. Zs., vol. V (1919). JFM47.0483.01
  15. [15] H. Reichenbach, The theory of probability. An inquiry into the logical and mathematical foundations of the calculus of probability, University of California Press, Berkeley and Los Angeles, 1949. Zbl0038.28604MR31452
  16. [16] J.B. Rosser, Review of H. Hermes, Journal of Symbolic Logic, 3 (1938), pp. 119-120. 
  17. [17] D. Scott, Assigning probabilities to logical formulas, a p. 218 in « Aspects of induction logic », Ed. Hintikka e Suppes, 1960. Zbl0202.29905

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