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Fuzzy processing in transitivity development

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Abstract

We review the literature on the development of transitive reasoning, and note three historical stages. Stage 1 was dominated by the Piagetian idea that transitive inference is logical reasoning in which relationships between adjacent terms figure as premises. Stage 2 was dominated by the information-processing view that memory for relationships between adjacent terms is determinative in transitivity performance. Stage 3 has produced data that are inconsistent with both the logic and memery positions, leading to a new theory that is designed to account for such findings, fuzzy-trace theory. The basic assumption of fuzzytrace theory is that reasoners rely on global patterns, or gist. We describe the tenets of fuzzytrace theory, and explore its implications for different theoretical conceptions of logical competence, concluding that young children possess transitivity competence. We discuss the connection between transitivity competence (cognition) and intransitive preferences (metacognition).

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References

  1. M.J. Adams, Logical competence and transitive inference in young children, J. Exp. Child Psychol. 25(1978)477–489.

    Google Scholar 

  2. C. Argyris, Problems in producing usable knowledge for implementing liberating alternatives, in:Decision Making: Descriptive, Normative, and Prescriptive Interactions, ed. D.E. Bell, H. Raiffa and A. Tversky (Cambridge University Press, Cambridge, 1988).

    Google Scholar 

  3. D.F. Bjorklund,Children's Thinking: Developmental Function and Individual Differences (Brooks Cole, Pacific Grove, CA, 1989).

    Google Scholar 

  4. G.H. Bower, Adaption-level coding of stimuli and serial position effects, in:Adaption-Level Theory, ed. M.H. Appley (Academic Press, New York, 1971).

    Google Scholar 

  5. M.D.S. Braine, The ontogeny of certain logical operations: Piaget's formulation examined by nonverbal methods, Psychological Monographs 73 (5, Whole No. 475) (1959).

  6. C.J. Brainerd, Judgments and explanations as criteria for the presence of cognitive structures, Psychol. Bull. 79(1973)172–179.

    Google Scholar 

  7. C.J. Brainerd, Order of acquisition of transitivity, conservation, and class inclusion of length and weight, Develop. Psychol. 8(1973)105–116.

    Google Scholar 

  8. C.J. Brainerd, Response criteria in concept development research, Child Develop. 48(1977)360–366.

    Google Scholar 

  9. C.J. Brainerd,Piaget's Theory of Intelligence (Prentice-Hall, Englewood Cliffs, NJ, 1978).

    Google Scholar 

  10. C.J. Brainerd, Do children have to remember to reason?, in:Developmental Psychology, ed. C.J. Brainerd and V.F. Reyna (North-Holland, Amsterdam, 1985).

    Google Scholar 

  11. C.J. Brainerd and J. Kingma, Do children have to remember to reason? A fuzzy-trace theory of transitivity development, Develop. Rev. 4(1984)311–377.

    Google Scholar 

  12. C.J. Brainerd and J. Kingma, On the independence of short-term memory and working memory in cognitive development, Cognitive Psychol. 17(1985)210–247.

    Google Scholar 

  13. C.J. Brainerd and V.F. Reyna, Gist is the grist. Fuzzy-trace theory and the new intuitionism, Develop. Rev. (in press).

  14. L. Breslow, Re-evaluation of the literature on the development of transitive inference, Psychol. Bull. 89(1981)325–351.

    Google Scholar 

  15. P.E. Bryant, What the young child has to learn about logic, in:Constraints on Learning, ed. R.A. Hinde and J. Stevenson-Hinde (Academic Press, New York, 1973).

    Google Scholar 

  16. P.E. Bryant and T. Trabasso, Transitive inference and memory in young children, Nature (London) 232(1971)456–458.

    Google Scholar 

  17. S.J. Ceci, D.F. Ross and M.P. Toglia, Suggestibility of children's memory: Psycholegal implications, J. Exp. Psychol.: General 116(1987)38–49.

    Google Scholar 

  18. M. Chalmers and B. McGonigle, Are children any more logical than monkeys on the five-term series problem?, J. Exp. Child Psychol. 37(1984)355–377.

    Google Scholar 

  19. M. Chapman, Cognitive competence and verbal explanations in studies of children's reasoning, Paper presented at the Meeting of the Society for Research in Child Development, Kansas City, MO (1989).

  20. M. Chapman and U. Lindenberger, Functions, operations, and decalage in the development of transitivity, Develop. Psychol. 24(1988)542–551.

    Google Scholar 

  21. H. Clark and E. Clark,Psychology and Language (Harcourt Brace Jovanovich, New York, 1977).

    Google Scholar 

  22. P.A. Cowan, A developmental study of logical transformations, Dissertation Abstracts International 25(1964)2027–2028 (University Microfilms no. 64-3723).

    Google Scholar 

  23. B. De Boysson-Bardies and K. O'Regan, What children do in spite of adults' hypotheses, Nature 246(1973)531–534.

    Google Scholar 

  24. W.K. Estes, Is human memory obsolete?, Amer. Sci. 68(1980)62–69.

    Google Scholar 

  25. J.H. Flavell,Cognitive Development (Prentice-Hall, Englewood Cliffs, NJ, 1977).

    Google Scholar 

  26. J. Glick and S. Wapner, Development of transitivity: Some findings and problems of analysis, Child Develop. 39(1968)621–633.

    Google Scholar 

  27. R. Grieve and A.R. Nesdale, Observations on a test of transitive inference in children, Austral. J. Psychol. 31(1979)43–48.

    Google Scholar 

  28. G.S. Halford, Measurement and memory in transitivity: A reply to Grieve and Nesdale, Austral. J. Psychol. 31(1979)49–56.

    Google Scholar 

  29. G.S. Halford and W. Galloway, Children who fail to make transitive inferences can remember comparisons, Austral. J. Psychol. 29(1977)1–5.

    Google Scholar 

  30. P.L. Harris and E. Bassett, Transitive inferences by 4-year-old children?, Develop. Psychol. 11(1975)875–876.

    Google Scholar 

  31. M.S. Humphreys, The derivation of endpoint and distance effects in linear orderings from frequency information, J. Verbal Learning and Verbal Behavior 14(1975)496–505.

    Google Scholar 

  32. J. Huttenlocher and E.T. Higgins, Adjectives, comparatives, and syllogisms, Psychol. Rev. 78(1971)487–504.

    Google Scholar 

  33. B. Inhelder and J. Piaget,The Early Growth of Logic in the Child (Routledge and Kegan Paul, London, 1964).

    Google Scholar 

  34. J. Kingma, De ontwikkeling van quantitatieve en relationale begrippen bij kinderen van 4 tot 12 jaar, Doctoral Dissertation, State University of Groningen, The Netherlands (1981), unpublished.

    Google Scholar 

  35. D. Klahr and J.G. Wallace,Cognitive Development: An Information Processing View (Erlbaum, Hillsdale, NJ, 1976).

    Google Scholar 

  36. J.L. Kolodner and C.K. Riesbeck,Experience, Memory and Reasoning (Erlbaum, Hillsdale, NJ, 1986).

    Google Scholar 

  37. R. Lawson, Representation of individual sentences and holistic ideas, J. Exp. Psychol.: Human Learning and Memory 3(1977)1–9.

    Google Scholar 

  38. L.S. Liben and C.J. Posnansky, Inferences on inference: The effect of age, transitive ability, memory load, and lexical factors, Child Develop. 48(1977)490–497.

    Google Scholar 

  39. A. Lutkus and T. Trabasso, Transitive inferences by preoperational, retarded adolescents, Amer. J. Mental Deficiency 78(1974)599–606.

    Google Scholar 

  40. K.R. MacCrimmon, An experimental study of the decision making behavior of business executives, Doctoral Dissertation, University of California, Los Angeles (1965), unpublished.

    Google Scholar 

  41. B. McGonigle and M. Chalmers, Are monkeys logical?, Nature 267(1977)694–696.

    Google Scholar 

  42. J.P. Murray and J. Youniss, Achievement of inferential transitivity and its relation to serial ordering, Child Develop. 39(1968)1259–1268.

    Google Scholar 

  43. R. Nisbett and L. Ross,Human Inference: Strategies and Shortcomings of Social Judgment (Prentice-Hall, Englewood Cliffs, NJ, 1980).

    Google Scholar 

  44. R. Nisbett and T.D. Wilson, Telling more than we can know: Verbal reports on mental processes, Psychol. Rev. 84(1977)231–259.

    Google Scholar 

  45. J. Perner and D.G. Mansbridge, Developmental differences in encoding length series, Child Develop. 54(1983)710–719.

    Google Scholar 

  46. J. Perner, G. Steiner and C. Stachelin, Mental representation of length and weight series and transitive inferences in young children. J. Exp. Child Psychol. 31(1981)177–192.

    Google Scholar 

  47. J. Piaget,Classes, Rélations, et Nombres: Essai sur le “Groupements” de la Logistique et la Reversibilite de la Pensée (Vrin, Paris, 1942).

    Google Scholar 

  48. J. Piaget,Genetic Epistemology (Columbia University Press, New York 1970).

    Google Scholar 

  49. J. Piaget, B. Inhelder and A. Szeminska,The Child's Conception of Geometry (Routledge and Kegan Paul, London, 1960).

    Google Scholar 

  50. G.R. Potts, Information processing strategies used in the encoding of linear orderings, J. Verbal Learning and Verbal Behavior 11(1972)727–740.

    Google Scholar 

  51. V.F. Reyna, Figure and fantasy in children's language, in:Cognitive Learning and Memory in Children, ed. M. Pressley and C.J. Brainerd (Springer, New York, 1985).

    Google Scholar 

  52. V.F. Reyna, Understanding verbs: Easy extension, hard comprehension, in:Progress in the Psychology of Language, Vol. 3, ed. A. Ellis (Erlbaum, London, 1987).

    Google Scholar 

  53. V.F. Reyna, Reasoning, remembering, and their relationship: Social, cognitive, and developmental issues, in:Development of Long-Term Retention, ed. M.L. Howe, C.J. Brainerd and V.F. Reyna (Springer, New York), in press.

  54. V.F. Reyna and C.J. Brainerd, Piaget under scrutiny, Science 241(1988)733.

    Google Scholar 

  55. V.F. Reyna, C.J. Brainerd and T. Connolly, Just the bottom line, please: A fuzzy-trace theory of framing effects in choice (1989), submitted for publication.

  56. C.A. Riley, The representation of comparative relations and the transitive inference task, J. Exp. Child Psychol. 22(1976)1–22.

    Google Scholar 

  57. C.A. Riley and T. Trabasso, Comparatives, logical structures, and encoding in a transitive inference task, J. Exp. Child Psychol. 17(1974)187–302.

    Google Scholar 

  58. M.L. Roodin and G.E. Gruen, The role of memory in making transitive judgments, J. Exp. Child Psychol. 10(1970)264–275.

    Google Scholar 

  59. J. Russell, Children's memory for premises in a transitive measurement task assessed by elicited and spontaneous justifications, J. Exp. Child Psychol. 31(1981)300–309.

    Google Scholar 

  60. R. Schank,Dynamic Memory (Cambridge University Press, New York, 1982).

    Google Scholar 

  61. H.A. Simon, Rationality as process and product of thought, in:Decision Making: Descriptive, Normative, and Prescriptive Interactions, ed. D.E. Bell, H. Raiffa and A. Tversky (Cambridge University Press, Cambridge, 1988).

    Google Scholar 

  62. P. Slovic and S. Lichtenstein, Preference reversals: A broader perspective, Amer. Econ. Rev. 73(1983)596–605.

    Google Scholar 

  63. J. Smedslund, Apprentissage des notions de la conservation et de la transitivite du poids, Etudes d'Epistémologie Génétique 9(1959)3–13.

    Google Scholar 

  64. J. Smedslund, Development of concrete transitivity of length in children, Child Develop. 34(1963)389–405.

    Google Scholar 

  65. C. Staehelin, Transitive Schlussfolgerungen und das Problem der Representation bei Kindern im alter von 7 bis 8 Jahren, Thesis, University of Basel (1980), unpublished.

  66. R.J. Sternberg, The development of linear syllogistic reasoning, J. Exp. Child Psychol. 29(1980)342–356.

    Google Scholar 

  67. R.J. Sternberg, Representation and process in linear syllogistic reasoning, J. Exp. Psychol.: General 109(1980)119–159.

    Google Scholar 

  68. E. Thayer and C. Collyer, The development of transitive inference: A review of recent approaches, Psychol. Bull. 85(1978)1327–1343.

    Google Scholar 

  69. M.P. Toglia, S.J. Ceci and D.F. Ross, The prestige effect in children's susceptibility to suggestion, Paper presented at the Annual Meeting of the Psychonomic Society, Chicago, IL (1988).

  70. T. Trabasso, Representation, memory, and reasoning: How do we make transitive inference?, in:Minnesota Symposia on Child Psychology, Vol. 9, ed. A.D. Pick (University of Minnesota Press, Minneapolis, 1975).

    Google Scholar 

  71. T. Trabasso, The role of memory as a system in making transitive inferences, in:Perspectives on the Development of Memory and Cognition, ed. R.V. Kail, Jr. and J.W. Hagan (Erlbaum, Hillsdale, NJ, 1977).

    Google Scholar 

  72. T. Trabasso, C.A. Riley and E. Wilson, The representation of linear order and spatial strategies in reasoning: A developmental study, in:Reasoning: Representation and Process in Children and Adults, ed. R.J. Falmagne (Erlbaum, Hillsdale, NJ, 1975).

    Google Scholar 

  73. A. Tversky, Intransitivity of preferences, Psychol. Rev. 76(1969)31–48.

    Google Scholar 

  74. A. Tversky, P. Slovic and D. Kahneman, The causes of preference reversal, Working Paper No. 6, Stanford University, Stanford Center on Conflict and Negotiation, Stanford, CA (1988).

    Google Scholar 

  75. J. von Neumann,The Computer and the Brain (Yale University Press, New Haven, 1958).

    Google Scholar 

  76. L.S. Vygoysky,Mind in Society: The Development of Higher Psychological Processes, ed. M. Cole, V. John-Steiner, S. Scribner and E. Souberman (Harvard University Press, Cambridge, MA, 1978).

    Google Scholar 

  77. J. Youniss and H. Furth, Reasoning and Piaget, Nature 244(1973)314–316.

    Google Scholar 

  78. J. Youniss and J. Murray, Transitive inference with nontransitive solutions controlled, Develop. Psychol. 2(1970)1969–1975.

    Google Scholar 

  79. K.A. Ericsson and H.A. Simon, Verbal reports as data, Psychol. Rev. 87(1980)215–251.

    Google Scholar 

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  1. College of Education, University of Arizona, 85721, Tucson, AZ, USA

    Valerie F. Reyna & Charles J. Brainerd

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  1. Valerie F. Reyna
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Reyna, V.F., Brainerd, C.J. Fuzzy processing in transitivity development. Ann Oper Res 23, 37–63 (1990). https://doi.org/10.1007/BF02204838

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