Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-11T12:35:08.876Z Has data issue: false hasContentIssue false

Chapter 6 - Probability, Belief, and the Richness of Cognition

from Models of Optimal Beliefs

Published online by Cambridge University Press:  03 November 2022

Julien Musolino
Affiliation:
Rutgers University, New Jersey
Joseph Sommer
Affiliation:
Rutgers University, New Jersey
Pernille Hemmer
Affiliation:
Rutgers University, New Jersey
Get access

Summary

Belief is often formalized using tools of probability theory. However, probability theory often focuses on simple examples – like coin flips or basic parametric distributions – and these do not describe much about actual human thinking. I highlight some basic examples of the complexity and richness of human mental representations and review some work which attempts to marry plausible types of representations with probabilistic models of belief, one of the most exciting current directions in psychology and machine learning.

Type
Chapter
Information
The Cognitive Science of Belief
A Multidisciplinary Approach
, pp. 135 - 150
Publisher: Cambridge University Press
Print publication year: 2022

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barsalou, L. W. (1983) Ad hoc categories. Memory & Cognition, 11(3), 211227.CrossRefGoogle ScholarPubMed
Bigelow, E. J. & Piantadosi, S. T. (2016a) Inferring priors in compositional cognitive models. In Proceedings of the 38th Cognitive Science Society.Google Scholar
Bigelow, E. J. & Piantadosi, S. T. (2016b) A large dataset of generalization patterns in the number game. Journal of Open Psychology Data, 4(1), e4e4.Google Scholar
Boole, G. (1854) An investigation of the laws of thought: on which are founded the mathematical theories of logic and probabilities. Walton and Maberly.Google Scholar
Burris, S. (2000) The laws of Boole’s thought. Preprint.Google Scholar
Chater, N. & Vitányi, P. (2007) Ideal learning of natural language: positive results about learning from positive evidence. Journal of Mathematical Psychology, 51(3), 135163.CrossRefGoogle Scholar
Denison, S. & Xu, F. (2014) The origins of probabilistic inference in human infants. Cognition, 130(3), 335347.Google Scholar
Depeweg, S., Rothkopf, C. A., & Jäkel, F. (2018) Solving bongard problems with a visual language and pragmatic reasoning. arXiv preprint arXiv:1804.04452.Google Scholar
Eckert, J., Call, J., Hermes, J., Herrmann, E., & Rakoczy, H. (2018) Intuitive statistical inferences in chimpanzees and humans follow Weber’s law. Cognition, 180, 99107.Google Scholar
Fodor, J. (1975) The language of thought. Harvard University Press.Google Scholar
Fodor, J. & Pylyshyn, Z. (1988) Connectionism and cognitive architecture: a critical analysis. Cognition, 28, 371.Google Scholar
Gershman, S. J. (2017) On the blessing of abstraction. SAGE.Google Scholar
Gigerenzer, G. & Selten, R. (2002) Bounded rationality: the adaptive toolbox. MIT Press.CrossRefGoogle Scholar
Goodman, N. D., Frank, M. C., Griffiths, T. L., Tenenbaum, J. B., Battaglia, P. W., & Hamrick, J. B. (2015) Relevant and robust: a response to Marcus and Davis (2013). Psychological Science, 26(4), 539541.CrossRefGoogle ScholarPubMed
Goodman, N. D., Tenenbaum, J., Feldman, J., & Griffiths, T. (2008) A rational analysis of rule-based concept learning. Cognitive Science, 32(1), 108154.Google Scholar
Goodman, N. D., Tenenbaum, J. B., & Gerstenberg, T. (2015) Concepts in a probabilistic language of thought. In Margolis, E & Laurence, S (Eds.), The conceptual mind: new directions in the study of concepts. MIT Press.Google Scholar
Goodman, N. D., Ullman, T. D., & Tenenbaum, J. B. (2011) Learning a theory of causality. Psychological Review, 118(1), 110119.Google Scholar
Griffiths, T. L., Lieder, F., & Goodman, N. D. (2015) Rational use of cognitive resources: levels of analysis between the computational and the algorithmic. Topics in Cognitive Science, 7(2), 217229.Google Scholar
Heinze-Deml, C., Maathuis, M. H., & Meinshausen, N. (2018) Causal structure learning. Annual Review of Statistics and Its Application, 5(1), 371391.CrossRefGoogle Scholar
Hutter, M. (2005) Universal artificial intelligence: sequential decisions based on algorithmic probability. Springer Science & Business Media.Google Scholar
Jaynes, E. (2003) Probability theory: the logic of science. Cambridge University Press.Google Scholar
Jones, M. & Love, B. C. (2011) Bayesian fundamentalism or enlightenment? On the explanatory status and theoretical contributions of Bayesian models of cognition. Behavioral and Brain Sciences, 34(4), 169231.Google Scholar
Katz, Y. & Springer, M. (2016) Probabilistic adaptation in changing microbial environments. PeerJ, 4, e2716.Google Scholar
Katz, Y., Springer, M., & Fontana, W. (2018) Embodying probabilistic inference in biochemical circuits. arXiv preprint arXiv:1806.10161.Google Scholar
Kemp, C. & Tenenbaum, J. (2008) The discovery of structural form. Proceedings of the National Academy of Sciences, 105(31), 1068710692.Google Scholar
Kemp, C., Tenenbaum, J. B., Niyogi, S., & Griffiths, T. L. (2010) A probabilistic model of theory formation. Cognition, 114(2), 165196.Google Scholar
Kidd, C., Piantadosi, S. T., & Aslin, R. (2012) The Goldilocks effect: human infants allocate attention to visual sequences that are neither too simple nor too complex. PLoS ONE 7(5), e36399.Google Scholar
Kidd, C., Piantadosi, S. T., & Aslin, R. N. (2014) The goldilocks effect in infant auditory attention. Child Development, 85(5), 17951804.CrossRefGoogle ScholarPubMed
Knill, D. (1996) Perception as Bayesian inference. Cambridge University Press.Google Scholar
Kolmogorov, A. (1950) Foundations of the theory of probability. Chelsea Publishing Company.Google Scholar
Lake, B. M., Salakhutdinov, R., & Tenenbaum, J. B. (2015). Human-level concept learning through probabilistic program induction. Science, 350(6266), 13321338.CrossRefGoogle ScholarPubMed
Marcus, G. F. & Davis, E. (2013) How robust are probabilistic models of higher-level cognition? Psychological science, 24(12), 23512360.Google Scholar
Marcus, G. F. & Davis, E. (2015) Still searching for principles: a response to Goodman et al. (2015). Psychological Science, 26 (4), 542544.CrossRefGoogle Scholar
Musolino, J., d’Agostino, K. L., & Piantadosi, S. T. (2019) Why we should abandon the semantic subset principle. Language Learning and Development, 15(1), 3246.Google Scholar
Nilsson, N. J. (2009). The quest for artificial intelligence. Cambridge University Press.Google Scholar
Overlan, M. C., Jacobs, R. A., & Piantadosi, S. T. (2017) Learning abstract visual concepts via probabilistic program induction in a language of thought. Cognition, 168, 320334.Google Scholar
Piantadosi, S. T. (2011) Learning and the language of thought (Doctoral dissertation, Massachusetts Institute of Technology).Google Scholar
Piantadosi, S. T. & Jacobs, R. (2016) Four problems solved by the probabilistic language of thought. Current Directions in Psychological Science, 25(1), 5459.Google Scholar
Piantadosi, S. T., Kidd, C., & Aslin, R. (2014) Rich analysis and rational models: inferring individual behavior from infant looking data. Developmental Science, 17, 321337.CrossRefGoogle ScholarPubMed
Piantadosi, S. T., Tenenbaum, J., & Goodman, N. (2012) Bootstrapping in a language of thought: a formal model of numerical concept learning. Cognition, 123(2), 199217.CrossRefGoogle Scholar
Piantadosi, S. T., Tenenbaum, J., & Goodman, N. (2016) The logical primitives of thought: Empirical foundations for compositional cognitive models. Psychological Review, 123(4), 392424.CrossRefGoogle ScholarPubMed
Rakoczy, H., Clüver, A., Saucke, L. et al. (2014) Apes are intuitive statisticians. Cognition, 131(1), 6068.Google Scholar
Ramsey, F. P. (1926) Truth and probability. In Readings in formal epistemology (pp. 2145). Springer.Google Scholar
Rothe, A., Lake, B. M., & Gureckis, T. (2017) Question asking as program generation. Advances in Neural Information Processing Systems, 1047–1056.Google Scholar
Rule, J., Tenenbaum, J., & Piantadosi, S. (2020) The child as hacker. Trends in Cognitive Sciences, 24(11), 900915.Google Scholar
Russell, S. & Norvig, P. (2009) Artificial intelligence: a modern approach. Prentice Hall.Google Scholar
Saffran, J., Aslin, R., & Newport, E. (1996) Statistical learning by 8-month-old infants. Science, 274(5294), 19261928.Google Scholar
Saffran, J., Johnson, E. K., Aslin, R. N., & Newport, E. L. (1999) Statistical learning of tone sequences by human infants and adults. Cognition, 70(1), 2752.Google Scholar
Savage, L. J. (1954) The Foundations of Statistics. New York, Wiley.Google Scholar
Shepard, R. N. (1980) Multidimensional scaling, tree-fitting, and clustering. Science, 210(4468), 390398.Google Scholar
Sides, A., Osherson, D., Bonini, N., & Viale, R. (2002) On the reality of the conjunction fallacy. Memory & Cognition, 30(2), 191198.CrossRefGoogle ScholarPubMed
Solomonoff, R. J. (1964a) A formal theory of inductive inference. Part I. Information and Control, 7(1), 122.Google Scholar
Solomonoff, R. J. (1964b) A formal theory of inductive inference. Part II. Information and control, 7(2), 224254.CrossRefGoogle Scholar
Talbott, W. (2016) Bayesian Epistemology. In Zalta, E. N. (Ed.). The stanford encyclopedia of philosophy (Winter 2016 ed.). Metaphysics Research Lab, Stanford University.Google Scholar
Tecwyn, E. C., Denison, S., Messer, E. J., & Buchsbaum, D. (2017) Intuitive probabilistic inference in capuchin monkeys. Animal Cognition, 20(2), 243256.CrossRefGoogle ScholarPubMed
Téglás, E., Vul, E., Girotto, V., Gonzalez, M., Tenenbaum, J. B., & Bonatti, L. L. (2011) Pure Reasoning in 12-Month-Old Infants as Probabilistic Inference. Science, 27(332), 10541059.Google Scholar
Tenenbaum, J. (1999) A Bayesian framework for concept learning (Unpublished doctoral dissertation). Massachusetts Institute of Technology.Google Scholar
Tenenbaum, J. (2000) Rules and similarity in concept learning. Advances in Neural Information Processing Systems, 12, 5965.Google Scholar
Tenenbaum, J., Kemp, C., Griffiths, T., & Goodman, N. (2011) How to grow a mind: statistics, structure, and abstraction. Science, 331(6022), 12791285.Google Scholar
Tijms, H. & Staats, K. (2007) Negative probabilities at work in the m/d/1 queue. Probability in the Engineering and Informational Sciences, 21(1), 6776.CrossRefGoogle Scholar
Tversky, A. & Kahneman, D. (1981) Judgments of and by representativeness (Tech. Rep.). Stanford University, Department of Psychology.Google Scholar
Tversky, A. & Kahneman, D. (1983) Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychological Review, 90(4), 293315.Google Scholar
Ullman, T., Goodman, N., & Tenenbaum, J. (2012) Theory learning as stochastic search in the language of thought. Cognitive Development, 27(4), 455480.Google Scholar
Xu, F. & Denison, S. (2009) Statistical inference and sensitivity to sampling in 11-month-old infants. Cognition, 112(1), 97104.CrossRefGoogle ScholarPubMed
Xu, F. & Garcia, V. (2008) Intuitive statistics by 8-month-old infants. Proceedings of the National Academy of Sciences, 105(13), 50125015.Google Scholar
Zednik, C. & Jäkel, F. (2016) Bayesian reverse-engineering considered as a research strategy for cognitive science. Synthese, 193(12), 39513985.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×