Conditioning a state by a Łukasiewicz event: A probabilistic approach to Ulam games

Theoretical Computer Science

Volumn 230, Issue 1-2, 2000, Pages 149-166

  Gerla, Brunella ^a  

^a UNIVERSITY OF SALERNO   (Italy)

Author keywords

Conditioning under uncertainty; Dempster composition rule; MV algebras; States and conditional states; Ulam game

Indexed keywords

EID: 0006975206     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(98)00349-1     Document Type: Article

References (16)

1. E.R. Berlekamp, Block coding for the binary symmetric channel with feedback, in: H.B. Mann (Ed.), Error-correcting Codes, Wiley, New York, 1968, pp. 330-335.
2. D. Butnariu, E.P. Klement, Triangular norm based measures and game with fuzzy coalitions, Kluwer Academic Publishers, Dordrecht, 1995.
3. C.C. Chang, Algebraic analysis of many-valued logics, Trans. Amer. Math. Soc. 88 (1958) 467-490.
4. C.C. Chang, A new proof of the completeness of the Łukasiewicz axioms, Trans. Amer. Math. Soc. 93 (1959) 74-80.
5. R. Cignoli, I.M.L. D'Ottaviano, D. Mundici, Algebras of Łukasiewicz logics, in: Collection CLE, vol. 12, Center of Logic, Epistemology and History of Science, State University of Campinas, UNICAMP, SP, Brazil, 2nd ed., 1995 (in Portuguese). Expanded edition in English, in preparation.
6. A. Di Nola, G. Georgescu, A. Lettieri, Extending probabilities to states of MV-algebras, Collegium Logicum, Annals of the Kurt Gödel Society, Springer, Berlin, Wien, to appear.
7. A. Di Nola, G. Georgescu, A. Lettieri, Conditional states in finite valued logic, in: D. Dubois, H. Prade, E.P. Klement (Eds.), Fuzzy sets, Logics and Reasoning about Knowledge, Proc. of a Seminar held in Linz in 1996, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998, to appear.
8. D. Mundici, Logic of infinite quantum systems. Internat. J. Theoret. Phys. 32 (1993) 1941-1955.
9. D. Mundici, Averaging the truth value in Łukasiewicz sentential logic (Special issue in honor of Helena Rasiowa), Studia Logica 55 (1995) 113-127.
10. D. Mundici, A. Trombetta, Optimal comparison strategies in Ulam's searching game with two errors, Theoret. Comput. Sci. 182 (1997) 217-232.
11. A. Rényi, Foundations of Probability, Holden-Day, San Francisco, CA, 1970.
12. G. Shafer, A Mathematical Theory of Evidence, Princeton University Press, Princeton, NJ, 1976.
13. A. Tarski, J. Łukasiewicz, Investigations into the sentential calculus, in: Logic, Semantics, Metamathematics, Oxford University Press, Oxford, 1956, pp. 38-59. Reprinted by Hackett Publishing Company, Indianapolis, 1983.
14. S.M. Ulam, Adventures of a Mathematician, Scribner's, New York, 1976.
15. S. Weber, Conditioning on MV-algebras and additive measures-II, in: D. Dubois, H. Prade, E.P. Klement (Eds.), Fuzzy sets, Logics and Reasoning about Knowledge, Proc. Seminar held in Linz in 1996, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998, to appear.
16. L. Zadeh, Probability measures of fuzzy events, J. Math. Anal. Appl. 23 (1968) 421-427.