Skip to main content Accessibility help
×
Hostname: page-component-7bb8b95d7b-w7rtg Total loading time: 0 Render date: 2024-10-06T07:51:19.777Z Has data issue: false hasContentIssue false

15 - Mental Models and Algorithms of Deduction

from Part III - Computational Modeling of Basic Cognitive Functionalities

Published online by Cambridge University Press:  21 April 2023

Ron Sun
Affiliation:
Rensselaer Polytechnic Institute, New York
Get access

Summary

This chapter begins with an outline of logic and of the attempts to use it as a theory of human deduction. The fatal impediments to this approach led to the model theory in which models based on the meanings of premises yield deductive conclusions. And the chapter describes in detail the implementation of this theory’s account of deductions based on sentential connectives such as “if,” and how this simulation led to the discovery of systematic but compelling fallacies.The chapter outlines how algorithms based on models simulate deductions of the spatial relations among objects. And it points out the problems that need to be solved to extend accounts of elementary inferences from quantified assertions to deal with multiply-quantified relations. One alternative to the model theory is the idea that human deduction relies on probabilities. This approach concerns only which inferences people make, not the underlying mental processes by which they are made. The model theory fills the gap, because it applies to the deductions of probabilities, both those based on frequencies or proportions, and those based on evidence pertinent to unique events. The chapter ends with an account of why theories of human deduction need to be simulated in computer programs.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2023

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

Barrouillet, P., & Lecas, J. F. (1999). Mental models in conditional reasoning and working memory. Thinking & Reasoning, 5, 289302.Google Scholar
Beth, E. W., & Piaget, J. (1966). Mathematical Epistemology and Psychology. Dordrecht: Reidel.Google Scholar
Boole, G. (1854). An Investigation of the Laws of Thought. London: Macmillan.Google Scholar
Braine, M. D. S. (1978). On the relation between the natural logic of reasoning and standard logic. Psychological Review, 85, 121.CrossRefGoogle Scholar
Bucciarelli, M., & Johnson-Laird, P. N. (1999). Strategies in syllogistic reasoning. Cognitive Science, 23, 247303.Google Scholar
Byrne, R. M. J. (2005). The Rational Imagination: How People Create Alternatives to Reality. Cambridge, MA: MIT Press.Google Scholar
Byrne, R. M. J., & Johnson-Laird, P. N. (1989). Spatial reasoning. Journal of Memory and Language, 28, 564575.Google Scholar
Byrne, R. M. J., & Johnson-Laird, P. N. (2019). If and or: real and counterfactual possibilities in their truth and probability. Journal of Experimental Psychology: Learning, Memory, and Cognition, 46, 760780.Google Scholar
Carey, S. (2009). The Origin of Concepts. New York, NY: Oxford University Press.CrossRefGoogle Scholar
Cherubini, P., & Johnson-Laird, P. N. (2004). Does everyone love everyone? The psychology of iterative reasoning. Thinking & Reasoning, 10, 3153.Google Scholar
Cook, S. A. (1971). The complexity of theorem proving procedures. Proceedings of the Third Annual Association of Computing Machinery Symposium on the Theory of Computing, 3, 151158.Google Scholar
Goodwin, G. P. (2014). Is the basic conditional probabilistic? Journal of Experimental Psychology: General, 143, 12141241.Google Scholar
Hempel, C. G. (1945). Studies in the logic of confirmation, Parts I and II. Mind, 54, 126, 97–121. http://dx.doi.org/10.1093/mind/LIV.213.1Google Scholar
Hinterecker, T., Knauff, M., & Johnson-Laird, P. N. (2016). Modality, probability, and mental models. Journal of Experimental Psychology: Learning, Memory, and Cognition, 42, 16061620.Google ScholarPubMed
Hughes, G. E., & Cresswell, M. J. (1996). A New Introduction to Modal Logic. London: Routledge.Google Scholar
Jeffrey, R. (1981). Formal Logic: Its Scope and Limits (2nd ed.). New York, NY: McGraw-Hill.Google Scholar
Johnson-Laird, P. N. (1975). Models of deduction. In Falmagne, R. (Ed.), Reasoning: Representation and Process (pp. 754). Springdale, NJ: Erlbaum.Google Scholar
Johnson-Laird, P. N. (1983). Mental Models. Cambridge: Cambridge University Press.Google Scholar
Johnson-Laird, P. N. (2006). How We Reason. New York, NY: Oxford University Press.Google Scholar
Johnson-Laird, P. N., Girotto, V., & Legrenzi, P. (2004). Reasoning from inconsistency to consistency. Psychological Review, 111, 640661.Google Scholar
Johnson-Laird, P. N., Legrenzi, P., Girotto, P., & Legrenzi, M. (2000). Illusions in reasoning about consistency. Science, 288, 531532.Google Scholar
Johnson-Laird, P. N., Legrenzi, P., Girotto, V., Legrenzi, M., & Caverni, J-P. (1999). Naive probability: a mental model theory of extensional reasoning. Psychological Review, 106, 6288.Google Scholar
Johnson-Laird, P. N., & Ragni, M. (2019). Possibilities as the foundation of reasoning. Cognition, 193, 130950.Google Scholar
Johnson-Laird, P. N., & Wason, P. C. (1970a). A theoretical analysis of insight into a reasoning task. Cognitive Psychology, 1, 134148. http://dx.doi.org/10.1016/0010-0285(70)90009-5Google Scholar
Johnson-Laird, P. N., & Wason, P. C. (1970b). Insight into a logical relation. Quarterly Journal of Experimental Psychology, 22, 4961. http://dx.doi.org/10.1080/14640747008401901Google Scholar
Kelly, L., Khemlani, S., & Johnson-Laird, P.N. (2020). Reasoning about durations. Journal of Cognitive Neuroscience, 32 (11), 2103–2116.Google Scholar
Khemlani, S. (2021). Psychological theories of syllogistic reasoning. In Knauff, M. & Spohn, W. (Eds.), Handbook of Rationality. Cambridge, MA: MIT Press.Google Scholar
Khemlani, S. S., Byrne, R. M. J., & Johnson-Laird, P. N. (2018). Facts and possibilities: a model-based theory of sentential reasoning. Cognitive Science, 2018, 1–38. https://doi.org/10.1111/cogs.12634Google Scholar
Khemlani, S., & Johnson-Laird, P. N. (2012). Theories of the syllogism: a meta-analysis. Psychological Bulletin, 138, 427457.CrossRefGoogle ScholarPubMed
Khemlani, S., & Johnson-Laird, P. N. (2013). Cognitive changes from explanations. Journal of Cognitive Psychology, 25, 139146.Google Scholar
Khemlani, S., & Johnson-Laird, P. N. (2017). Illusions in reasoning. Minds and Machines, 27, 1135.Google Scholar
Khemlani, S., & Johnson-Laird, P. N. (2022). Reasoning about properties: a computational theory. Psychological Review (advance online publication). https://doi.org/10.1037/rev0000240Google Scholar
Khemlani, S., Lotstein, M., & Johnson-Laird, P. N. (2015). Naive probability: model-based estimates of unique events. Cognitive Science, 39, 12161258.Google Scholar
Khemlani, S., Mackiewicz, R., Bucciarelli, M., & Johnson-Laird, P. N. (2013). Kinematic mental simulations in abduction and deduction. Proceedings of the National Academy of Sciences, 110 (42), 1676616771. www.pnas.org/cgi/doi/10.1073/pnas.1316275110Google Scholar
Knauff, M. (2013). Space to Reason. Cambridge, MA: MIT Press.Google Scholar
Miller, G. A., & Johnson-Laird, P. N. (1976). Language and Perception. Cambridge, MA: Harvard University Press.Google Scholar
Newell, A. (1973). You can’t play 20 questions with nature and win. In Chase, W. G., (Ed.), Visual Information Processing. New York, NY: Academic Press.Google Scholar
Oaksford, M., & Chater N., (1996). Rational explanation of the selection task. Psychological Review, 103, 381391.Google Scholar
Oaksford, M., & Chater, N. (2020). New paradigms in the psychology of reasoning. Annual Review of Psychology, 71, 12.1–12.26. https://doi.org/10.1146/annurev-psych-010419-%20051132Google Scholar
Osherson, D. N. (1974–1976). Logical Abilities in Children (vols. 1–4). Hillsdale, NJ: Erlbaum.Google Scholar
Popper, K. R. (1959). The Logic of Scientific Discovery. New York, NY: Basic Books.Google Scholar
Ragni, M., Dames, H., & Johnson-Laird, P. N. (2019). A meta-analysis of conditional reasoning. In preparation.Google Scholar
Ragni, M., & Knauff, M. (2013). A theory and a computational model of spatial reasoning with preferred mental modelsPsychological Review120, 561588.Google Scholar
Ragni, M., Kola, I., & Johnson-Laird, P. N. (2018). On selecting evidence to test hypotheses. Psychological Bulletin, 144, 779796. http://dx.doi.org/10.1037/bul0000146Google Scholar
Ramsey, F. R. (1990). F. R. Ramsey, Philosophical Papers. In Mellor, D. H., (Ed.). Cambridge: Cambridge University Press.Google Scholar
Rips, L. J. (1994). The Psychology of Proof. Cambridge, MA: MIT Press.Google Scholar
Schaeken, W., Johnson-Laird, P. N., & d’Ydewalle, G. (1996). Mental models and temporal reasoning. Cognition, 60, 205234.Google Scholar
Stenning, K., & Van Lambalgen, M. (2012). Human Reasoning and Cognitive Science. Cambridge, MA: MIT Press.Google Scholar
Sun, R. (2016). Anatomy of the Mind: Exploring Psychological Mechanisms and Processes with the Clarion Cognitive Architecture. New York, NY: Oxford University Press.CrossRefGoogle Scholar
Tversky, B. (1993). Cognitive maps, cognitive collages, and spatial mental models. In Frank, A. U. & Campari, I. (Eds.), Spatial Information Theory: A Theoretical Basis for GIS, Proceedings COSIT ’93. Lecture Notes in Computer Science, 716, pp. 1424. Berlin: Springer. https://doi.org/10.1007/3-540-57207-4_2Google Scholar
Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychological Review, 90 (4), 293315.Google Scholar
Wason, P. C. (1968). Reasoning about a rule. The Quarterly Journal of Experimental Psychology, 20, 273281.Google Scholar
Wason, P. C. (1969). Regression in reasoning? British Journal of Psychology, 60, 471480.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
×