Summary
The method of approximate reasoning using a fuzzy logic introduced by Baldwin (1978 a,b,c), is used to model human reasoning in the resolution of two well known paradoxes.
It is shown how classical propositional logic fails to resolve the paradoxes, how multiple valued logic partially succeeds and that a satisfactory resolution is obtained with fuzzy logic.
The problem of precise representation of vague concepts is considered in the light of the results obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baldwin, J.F.: 1978A, ‘A new approach to approximate reasoning using a fuzzy logic’, to appear in Fuzzy Sets and Systems.
Baldwin, J.F.: 1978b, ‘Fuzzy logic and approximate reasoning for mixed input arguments’, University of Bristol, Department of Engineering Mathematics, Research Report EM/FS4.
Baldwin, J.F.: 1978c, “A model for fuzzy reasoning and fuzzy logic’, University of Bristol, Department of Engineering Mathematics, Research Report EM/FS10.
Baldwin, J.F. and Guild, N.C.F.: 1978, ‘Feasible algorithms for approximate reasoning using a fuzzy logic’, University of Bristol, Department of Engineering Mathematics, Research Report EM/FS8.
Baldwin, J.F. and Pilsworth, B.W.: 1978, ‘Axiomatic approach to implication for approximate reasoning using a fuzzy logic’, University of Bristol, Department of Engineering Mathematics, Research Report EM/FS9.
Bellman, R.E.: 1971, ‘Mathematics, systems and society’, F.E.K. Report, Stockholm.
Bellman, R.E. and Giertz, M.: 1973, ‘On the analytical formalism of the theory of fuzzy sets’, Information Sciences 5, 149–156.
Black, M.: 1970, The Margins of Precision, Cornell University Press, Ithaca, New York.
Gaines, B.R.: 1976, ‘Foundations of fuzzy reasoning’, International Journal of Man-Machine Studies 8, 623–668.
Gardner, M.: 1963, ‘Mathematical games’, Scientific American 208, 144–154.
Gougen, J.A.: 1969, ‘The logic of inexact concepts’, Synthese 19, 325–373.
Halmos, P.R.: 1960, Naive Set Theory, Van Nostrand, New York.
Koczy, L.T. and Hajnal, M.: 1975, ‘A new fuzzy calculus and its application as a pattern recognition technique’, Proceedings of the 3rd International Congress on Cybernetics and Systems, Rumania.
Łukasiewicz, J.: 1920, ‘On 3-valued logic’, Ruch Filozoficzny 5, 169–171.
Oden, G.C.: 1977, ‘Integration of fuzzy logical information’, Journal of Experimental Psychology, Human Perception and Performance 3, 565–575.
Rescher, N.: 1969, Many Valued Logic, McGraw Hill, New York.
Russell, B.: 1903, Principles of Mathematics, Volume 1, Cambridge University Press, Cambridge, England.
Russel, B.: 1923, ‘Vagueness’, Australasian Journal of Psychology and Philosophy 1, 84–92.
Zadeh, L.A.: 1965, ‘Fuzzy sets’, Information and Control 8, 338–353.
Zadeh, L.A.: 1973, ‘Outline of a new approach to the analysis of complex systems and decision processes’, IEEE Transactions on Systems, Man and Cybernetics SMC-3, 28-44.
Zadeh, L.A.: 1975a, ‘Calculus of fuzzy restrictions’, in Zadeh, L.A., Fu, K.S., Tanaka, K. and Shimura, M. (eds.), Fuzzy Sets and Their Applications to Cognitive and Decision Processes, Academic Press, New York.
Zadeh, L.A.: 1975b, ‘Fuzzy logic and approximate reasoning’, Synthese 30, 407–428.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Baldwin, J.F., Guild, N.C.F. The resolution of two paradoxes by approximate reasoning using a fuzzy logic. Synthese 44, 397–420 (1980). https://doi.org/10.1007/BF00413469
Issue Date:
DOI: https://doi.org/10.1007/BF00413469