The discovery and comparison of symbolic magnitudes

Cognitive Psychology

Volumn 71, Issue , 2014, Pages 27-54

  Chen, Dawn ^a   Lu, Hongjing ^a   Holyoak, Keith J ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Magnitude comparisons; Markedness; Reference points; Semantic congruity; Symbolic distance

Indexed keywords

ANIMAL; ATTENTION; BAYES THEOREM; CONCEPT FORMATION; DECISION MAKING; HUMAN; LONG TERM MEMORY; SYMBOLISM;

ANIMALS; ATTENTION; BAYES THEOREM; CONCEPT FORMATION; HUMANS; JUDGMENT; MEMORY, LONG-TERM; SYMBOLISM;

EID: 84893899470     PISSN: 00100285     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cogpsych.2014.01.002     Document Type: Article

References (108)

1. Andrews G., Halford G.S. Children's ability to make transitive inferences: The importance of premise integration and structural complexity. Cognitive Development 1998, 13(4):479-513.
2. Audley R.J., Wallis C.P. Response instructions and the speed of relative judgments: I. Some experiments on brightness discrimination. British Journal of Psychology 1964, 55:59-73.
3. Banks W.P., Clark H.H., Lucy P. The locus of the semantic congruity effect in comparative judgments. Journal of Experimental Psychology: Human Perception and Performance 1975, 104:35-47.
4. Banks W.P., Flora J. Semantic and perceptual processes in symbolic comparisons. Journal of Experimental Psychology: Human Perception and Performance 1977, 3:278-290.
5. Banks W.P., Fujii M., Kayra-Stuart F. Semantic congruity effects in comparative judgments of magnitudes of digits. Journal of Experimental Psychology: Human Perception and Performance 1976, 2:435-447.
6. Banks W.P., White H. Single ordering as a process limitation. Journal of Verbal learning and Verbal Behavior 1982, 21:39-54.
7. Banks W.P., White H., Sturgill W., Mermelstein R. Semantic congruity and expectancy in symbolic judgments. Journal of Experimental Psychology: Human Perception and Performance 1983, 9:560-582.
8. Barner D., Snedeker J. Compositionality and statistics in adjective acquisition: 4-year-olds interpret tall and short based on the size distributions of novel referents. Child Development 2008, 79:594-608.
9. Birnbaum M.H., Jou J.W. A theory of comparative response times and "difference" judgments. Cognitive Psychology 1990, 22:184-210.
10. Bloom P. How children learn the meanings of words 2000, MIT Press, Cambridge, MA.
11. Bower G.H. Adaptation-level coding of stimuli and serial position effects. Adaptation-level theory 1971, 175-201. Academic Press, New York. M.H. Appley (Ed.).
12. Cantlon J., Brannon E.M. Semantic congruity affects numerical judgments similarly in monkeys and humans. Proceedings of the National Academy of Sciences, USA 2005, 102:16507-16511.
13. Cantlon J., Brannon E.M., Carter E., Pelphrey K. Functional imaging of numerical processing in adults and 4-yr-old children. PLoS Biology 2006, 4(e125):1-11.
14. Cantlon J.F., Platt M., Brannon E.M. Beyond the number domain. Trends in Cognitive Sciences 2009, 13:83-91.
15. Čech C.G., Shoben E.J. Context effects in symbolic magnitude comparisons. Journal of Experimental Psychology: Learning, Memory, and Cognition 1985, 11:299-315.
16. Čech C., Shoben E., Love M. Multiple congruity effects in judgments ofmagnitude. Journal of Experimental Psychology Learning, Memory, and Cognition 1990, 16:1142-1152.
17. Chen D., Lu H., Holyoak K.J. Generative inferences based on a discriminative Bayesian model of relation learning. Proceedings of the 35th annual conference of the Cognitive Science Society 2013, 2018-2033. Cognitive Science Society, Austin, TX. M. Knauf, M. Pauven, N. Sebanz, I. Wachsmuth (Eds.).
18. Clark H.H. Linguistic processes in deductive reasoning. Psychological Review 1969, 1969(76):387-404.
19. Clark H.H., Carpenter P.A., Just M.A. On the meeting of semantics and perception. Visual information processing 1973, 311-381. Academic Press, New York. W.G. Chase (Ed.).
20. Cromer J.A., Roy J.E., Miller E.K. Representation of multiple, independent categories in the primate prefrontal cortex. Neuron 2010, 66:796-807.
21. Davis H. Transitive inference in rats (Rattus norvegicus). Journal of Comparative Psychology 1992, 106:342-349.
22. De Deyne S., Verheyen S., Ameel E., Vanpaemel W., Dry M., Voorspoels W., et al. Exemplar by feature applicability matrices and other Dutch normative data for semantic concepts. Behavior Research Methods 2008, 40(4):1030-1048.
23. Dehaene S. The varieties of numerical abilities. Cognition 1992, 44:1-42.
24. Dehaene S., Bossini S., Giraux P. The mental representation of parity and number magnitude. Journal of Experimental Psychology: General 1993, 122:371-396.
25. Dehaene S., Changeux J.-P. Development of elementary numerical abilities: A neuronal model. Journal of Cognitive Neuroscience 1993, 5:390-407.
26. DeSoto C.B. The predilection for single orderings. Journal of Abnormal and Social Psychology 1961, 62:16-23.
27. Diester I., Nieder A. Semantic associations between signs and numerical categories in the prefrontal cortex. PLoS Biology 2007, 5:e294.
28. Diester I., Nieder Q. Numerical values leave a semantic imprint on associated signs in monkeys. Journal of Cognitive Neuroscience 2010, 22:174-183.
29. Dosher B.A., Lu Z.-L. Noise exclusion in spatial attention. Psychological Science 2000, 11:139-146.
30. Doumas L.A.A., Hummel J.E., Sandhofer C.M. A theory of the discovery and predication of relational concepts. Psychological Review 2008, 115:1-43.
31. Freedman D.J., Riesenhuber M., Poggio T., Miller E.K. Categorical representation of visual stimuli in the primate prefrontal cortex. Science 2001, 291:312-316.
32. Goldstone R.L. The role of similarity in categorization: Providing a groundwork. Cognition 1994, 52:125-157.
33. Griffiths T.L., Steyvers M., Tenenbaum J.B. Topics in semantic representation. Psychological Review 2007, 114:211-244.
34. Halford G.S. Can young children integrate premises in transitivity and serial order tasks?. Cognitive Psychology 1984, 16:65-93.
35. Halford G.S. Children's understanding: The development of mental models 1993, Erlbaum, Hillsdale, NJ.
36. Halford G.S., Wilson W.H., Phillips S. Processing capacity defined by relational complexity: Implications for comparative, developmental and cognitive psychology. Behavioral Brain Sciences 1998, 21(6):803-831.
37. Halford G.S., Wilson W.H., Phillips S. Relational knowledge: The foundation of higher cognition. Trends in Cognitive Sciences 2010, 14(11):497-505.
38. Hoedemaker, R. S., & Gordon, P. C. (2013). Embodied language comprehension: Encoding-based and goal-driven processes. Journal of Experimental Psychology: General. doi:10.1037/a0032348.
39. Holyoak K.J. The form of analog size information in memory. Cognitive Psychology 1977, 9:31-51.
40. Holyoak K.J. Comparative judgments with numerical reference points. Cognitive Psychology 1978, 10:203-243.
41. Holyoak K.J., Dumais S.T., Moyer R.S. Semantic association effects in a mental comparison task. Memory & Cognition 1979, 7:303-313.
42. Holyoak K.J., Mah W.A. Semantic congruity in symbolic comparisons: Evidence against an expectancy hypothesis. Memory & Cognition 1981, 9:197-204.
43. Holyoak K.J., Mah W.A. Cognitive reference points in judgments of symbolic magnitude. Cognitive Psychology 1982, 14:328-352.
44. Holyoak K.J., Patterson K.K. A positional discriminability model of linear order judgments. Journal of Experimental Psychology: Human Perception and Performance 1981, 7:1283-1302.
45. Holyoak K.J., Walker J.H. Subjective magnitude information in semantic orderings. Journal of Verbal Learning and Verbal Behavior 1976, 15:287-299.
46. Howard R. The semantic congruity effect: Some tests of the expectancy hypothesis. Acta Psychologica 1983, 53:205-216.
47. Jamieson D.G., Petrusic W. Relational judgments with remembered stimuli. Perception & Psychophysics 1975, 18:373-378.
48. Jones S.M., Cantlon J.F., Merritt D.J., Brannon E.M. Context affects the numerical semantic congruity effect in rhesus monkeys (Macaca mulatta). Behavioral Processes 2010, 83:191-196.
49. Kemp C., Tenenbaum J.B. The discovery of structural form. Proceedings of the National Academy of Sciences, USA 2008, 105(31):10687-10692.
50. Kemp C., Tenenbaum J.B. Structured statistical models of inductive reasoning. Psychological Review 2009, 116(1):20-58.
51. Lawrence D.H., DeRivera J. Evidence for relational transposition. Journal of Comparative and Physiological Psychology 1954, 47:465-471.
52. Link S.W. Modeling imageless thought: The relative judgment theory of numerical comparisons. Journal of Mathematical Psychology 1990, 34:2-41.
53. Lu H., Chen D., Holyoak K.J. Bayesian analogy with relational transformations. Psychological Review 2012, 119:617-648.
54. Luce R.D., Green D.M., Weber D.L. Attention bands in absolute identification. Perception & Psychophysics 1976, 20:49-54.
55. Markovits H., Dumas C. Can pigeons really make transitive inferences?. Journal of Experimental Psychology: Animal Behavior Processes 1992, 18:311-312.
56. Marks D.F. Relative judgment: A phenomenon and a theory. Perception & Psychophysics 1972, 11:156-160.
57. Marr D. Vision: A computational investigation into the human representation and processing of visual information 1982, W. H. Freeman, New York.
58. Marschark M., Paivio A. Semantic congruity and lexical marking in symbolic comparisons: An expectancy hypothesis. Memory & Cognition 1979, 7:175-184.
59. McGonigle B.O., Chalmers M. Are monkeys logical?. Nature 1977, 267:694-696.
60. Merritt D.J., Terrace H.S. Mechanisms of inferential order judgments in humans (Homo sapiens) and rhesus monkeys (Macaca mulatta). Journal of Comparative Psychology 2011, 125:227-238.
61. Miller G.A. The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review 1956, 63:81-97.
62. Morgan C.L. An introduction to comparative psychology 1894, Walter Scott, London.
63. Moyer R.S. Comparing objects in memory: Evidence suggesting an internal psychophysics. Perception & Psychophysics 1973, 13:180-184.
64. Moyer R.S., Bayer R.H. Mental comparison and the symbolic distance effect. Cognitive Psychology 1976, 8:228-246.
65. Moyer R.S., Dumais S.T. Mental comparison. The psychology of learning and motivation 1978, Vol. 12:117-155. Academic Press, New York.
66. Moyer R.S., Landauer T.K. Time required for judgments of numerical inequality. Nature 1967, 215(1519-1):520.
67. Murdock B.B. The distinctiveness of stimuli. Psychological Review 1960, 67:16-31.
68. Nagpal A., Krishnamurthy P. Attribute conflict in consumer decision making: The role of task compatibility. Journal of Consumer Research 2008, 34:696-705.
69. Nieder A., Miller E.K. Coding of cognitive magnitude: Compressed scaling of numerical information in the primate prefrontal cortex. Neuron 2003, 37:149-157.
70. Nosofsky R.M. Shifts of attention in the identification and discrimination of intensity. Perception & Psychophysics 1983, 33:103-112.
71. Opfer J.E., Siegler R.S. Development of quantitative thinking. Oxford handbook of thinking and reasoning 2012, 585-605. Oxford University Press, New York. K.K. Holyoak, R.G. Morrison (Eds.).
72. Parikh, D., & Grauman, K. (2011). Relative attributes. In D. M. Metaxas, L. Quan, & L. J. Van (Eds.), Proceedings of the IEEE international conference on computer vision (pp. 503-510). Barcelona, Spain: IEEE.
73. Partee, B. (1995). Lexical semantics and compositionality. In D. Osherson (General Ed.), & L. Gleitman, & M. Liberman (Eds.), Invitation to cognitive science. Part I: Language (2nd ed., pp. 311-360). Cambridge, MA: MIT Press.
74. Penn D.C., Holyoak K.J., Povinelli D.J. Darwin's mistake: Explaining the discontinuity between human and nonhuman minds. Behavioral and Brain Sciences 2008, 31:109-178.
75. Petrusic W.M. Semantic congruity effects and theories of the comparison process. Journal of Experimental Psychology: Human Perception and Performance 1992, 18:962-986.
76. Petrusic W.M., Baranski J.V. Semantic congruity effects in perceptual comparisons. Perception & Psychophysics 1989, 45:439-452.
77. Phillips S., Halford G.S., Wilson W.H. The processing of associations versus the processing of relations and symbols: A systematic comparison. Proceedings of the seventeenth annual conference of the Cognitive Science Society 1995, 688-691. Erlbaum, Mahwah, NJ. J.D. Moore, J.F. Lehman (Eds.).
78. Piazza M., Izard V., Pinel P., Bihan D., Dehaene S. Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron 2004, 44:547-555.
79. Piazza M., Mechelli A., Price C.J., Butterworth B. Exact and approximate judgements of visual and auditory numerosity: An fMRI study. Brain Research 2006, 1106:177-188.
80. Piazza M., Pinel P., Le Bihan D., Dehaene S. A magnitude code common to numerosities and number symbols in human intraparietal cortex. Neuron 2007, 53:293-305.
81. Pinel P., Piazza M., Bihan D.L., Dehaene S. Distributed and overlapping cerebral representations of number, size, and luminance during comparative judgments. Neuron 2004, 41:1-20.
82. Potts G.R. Storing and retrieving information about ordered relationships. Journal of Experimental Psychology 1974, 103:431-439.
83. Rahnev D., Maniscalco B., Graves T., Huang E., de Lange F.P., Lau H. Attention induces conservative subjective biases in visual perception. Nature Neuroscience 2011, 14:1513-1515.
84. Range F., Noë R. Familiarity and dominance relations among female sooty mangabeys in the Taï National Park. American Journal of Primatology 2002, 56:137-153.
85. Ratcliff R. A theory of memory retrieval. Psychological Review 1978, 85:59-108.
86. Ratcliff R., Cherian A., Segraves M. A comparison of macaque behavior and superior colliculus neuronal activity to predictions from models of simple two-choice decisions. Journal of Neurophysiology 2003, 90:1392-1407.
87. Ratcliff R., McKoon G. The diffusion decision model: Theory and data for two-choice decision tasks. Neural Computation 2010, 20:873-922.
88. Ratcliff R., Van Zandt T., McKoon G. Connectionist and diffusion models of reaction time. Psychological Review 1999, 106:261-300.
89. Rescorla R.A., Wagner A.R. A theory of Pavlovian conditioning: Variations in the effectiveness of reinforcement and nonreinforcement. Classical conditioning II: Current research and theory 1972, 64-99. Appleton-Century-Crofts, New York. A.H. Black, W.F. Prokasy (Eds.).
90. Reynolds J.H., Chelazzi R. Attentional modulation of visual processing. Annual Review of Neuroscience 2004, 27:611-647.
91. Ryalls B.O., Winslow E., Smith L.B. A semantic congruity effect in children's acquisition of high and low. Journal of Memory and Language 1998, 39:543-557.
92. Rylass B.O., Smith L.B. Adults' acquisition of novel dimension words: Creating a semantic congruity effect. Journal of General Psychology 2000, 127:279-326.
93. Shafto P., Kemp C., Mansinghka V., Tenenbaum J.B. A probabilistic model of cross-categorization. Cognition 2011, 120:1-25.
94. Shaki S., Leth-Steensen C., Petrusic W.W. Effects of instruction presentation mode in comparative judgment. Memory & Cognition 2006, 34:196-206.
95. Shaki S., Petrusic W.M., Leth-Steensen C. SNARC effects with numerical and non-numerical symbolic comparative judgments: Instructional and cultural dependencies. Journal of Experimental Psychology: Human Perception and Performance 2012, 38:515-530.
96. Shepard R.N., Kilpatric D.W., Cunningham J.P. The internal representation of numbers. Cognitive Psychology 1975, 7:82-138.
97. Shoben E.J., Sailor K.M., Wang M. The role of expectancy in comparative judgments. Memory & Cognition 1989, 17:18-26.
98. Smith L.B., Gasser M., Sandhofer C.M. Learning to talk about the properties of objects: A network model of the development of dimensions. Perceptual learning 1997, Vol. 36:219-255. Academic Press, San Diego, CA. R.L. Goldstone, D.L. Medin, P.G. Schyns (Eds.).
99. Trabasso T., Riley C.A. The construction and use of representations involving linear order. Information processing and cognition: The Loyola symposium 1975, 381-410. Erlbaum, Hillsdale, NJ. R.L. Solso (Ed.).
100. Tribushinina E. Reference points in linguistic construal: Scalar adjectives revisited. Studia Linguistica 2009, 63:233-260.
101. Tversky A., Kahneman D. The framing of decisions and the psychology of choice. Science 1981, 211:453-458.
102. von Fersen L., Wynne C.D.L., Delius J.D., Staddon J.E. Transitive inference in pigeons. Journal of Experimental Psychology: Animal Behavior Processes 1991, 17:334-341.
103. Wallis C.P., Audley R.J. Response instructions and the speed of relative judgments: II. Pitch discrimination. British Journal of Psychology 1964, 55:121-132.
104. Waltz J.A., Knowlton B.J., Holyoak K.J., Boone K.B., Mishkin F.S., de Menezes Santos M., et al. A system for relational reasoning in human prefrontal cortex. Psychological Science 1999, 10(2):119-125.
105. Wickens T.D. Elementary signal detection theory 2002, Oxford University Press, New York.
106. Wong K.-F., Wang X.-J. A recurrent network mechanism of time integration in perceptual decisions. Journal of Neuroscience 2006, 26:1314-1328.
107. Woocher F.D., Glass A.L., Holyoak K.J. Positional discriminability in linear orderings. Memory & Cognition 1978, 6:165-173.
108. Wynne C.D.L. Reinforcement accounts for transitive inference performance. Animal Learning & Behavior 1995, 23:207-217.