Abstract
A new criterion is introduced for judging the suitability of various “fuzzy logics” for practical uncertain reasoning in a probabilistic world and the relationship of this criterion to several established criteria, and its consequences for truth functional belief, are investigated.
Similar content being viewed by others
References
Bennett, A.D.C., 1995, Master' Thesis, Manchester University, U.K.
Dubois, D. and Prade, H., 1988, “An introduction to possibilistic and fuzzy logics,” pp. 287-326 in Non-Standard Logics for Automated Reasoning, P. Smets, E.H. Mamdani, D. Dubois, and H. Prade, eds., New York: Academic Press.
Fine, T.L., 1973, Theories of Probability, New York: Academic Press.
Good, I.J., 1965, The Estimation of Probabilities, Cambridge, MA: M.I.T. Press.
Hopcroft, J.E. and Ullman, J.D., 1979, Introduction to Automata Theory, Languages and Computation, Reading, MA: Addison-Wesley.
Jeffrey, H., 1948, Theory of Probability, Oxford: Oxford University Press.
Kozlenko, V.Ya., Kreinovich, V.Ya., and Mirimanishvili, M.G., 1988, “The optimal method of describing the agent information,” Applied Problems in System Analysis, Proceedings Georgian Polytechnic Institute 8, 64-67.
Kreinovich, V.Ya. and Lokshin, A.M., 1990, “On the foundations of fuzzy formalism: Explaining formulas for union, intersection, negation, normalization and modifiers,” Technical Report UTEP-CS-90-28, El Paso Computer Science Department, University of Texas.
Kruse, R., Gebhardt, J., and Klawonn, F., 1994 Foundation of Fuzzy Systems, New York: John Wiley & Sons.
Lawry, J., 1994, “Natural distributions in inexact reasoning,” Doctoral Thesis, Manchester University, Manchester, U.K.
Lawry, J. and Wilmers, G.M., 1994, “An axiomatic approach to systems of prior distributions in inexact reasoning,” pp. 81-89 in Knowledge Representation and Reasoning under Uncertainty, M. Masuch and L. Polos, eds., Lecture Notes in Computer Science, Vol. 808, Berlin: Springer-Verlag.
Li, M. and Vitányi, P., 1993, An Introduction to Kolmogorov Complexity and Its Applications, Berlin: Springer-Verlag.
Ling, C.H., 1965, “Representation of associative functions,” Publ. Math. Debrecen 12, 182-212.
Paris, J.B., 1994, The Uncertain Reasoner's Companion-A Mathematical Perspective, Cambridge: Cambridge University Press.
Paris, J.B. and Vencovská, A., 1992, “A method of updating that justifies minimum cross entropy,” International Journal of Approximate Reasoning 7(1), 1-18.
Paris, J.B., Vencovská, A., and Wilmers, G.M, 1991, “A note on objective inductive inference,” pp. 407-412 in Proceedings of the 1st World Conference on Fundamentals of AI, Paris, M. de Glas and D. Gabbay, eds., Paris: Angkor.
Paris, J.B., Vencovská, A., and Wilmers, G.M., 1994, “A natural prior probability distribution derived from the propositional calculus,” Annals of Pure and Applied Logic 70, 243-285.
Pearl, J., 1988, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, San Mateo, CA: Morgan Kaufmann.
Solomonoff, R.J., 1978, “Complexity based induction systems: Comparison and convergence theorems,” IEEE Transactions on Information Theory IT-24(4), 422-432.
Trillas, E., 1979, “Sobre functiones de negacion en la teoria de conjunctos difusos,” Stochastica 3(1), 47-59.
Wilmers, G.M., Paris, J.B., and Vencovská, A., 1994, “A note on probability versus truthfunctionality,” pp. 283-298 in Proceedings of WUPES 1994 Conference, Třešt, Czech Republic, R. Jirovšek and I. Kramosil, eds., Prague: University of Economics.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bennett, A., Paris, J. & Vencovská, A. A New Criterion for Comparing Fuzzy Logics for Uncertain Reasoning. Journal of Logic, Language and Information 9, 31–63 (2000). https://doi.org/10.1023/A:1008353725927
Issue Date:
DOI: https://doi.org/10.1023/A:1008353725927