Abstract
How humans reason in general about syllogisms is, despite a century of research and many proposed cognitive theories, still an unanswered question. It is even more difficult, however, to answer how an individual human reasons. The goal of this article is twofold: First, it analyses the predictive quality of existing cognitive theories by providing a standardized (re-) implementation of existing theories. Towards this, theories are algorithmically formalized, including their potential capabilities for adaptation to an individual reasoner. The implementations are modular with regard to the underlying mental operations defined by the cognitive theories. Second, it proposes a novel composite approach based on existing cognitive theories, resulting in a cognitive model for predicting an individual reasoner before s/he draws a conclusion. This approach uses sequences of operations, inherited and combined from different theories, to form its predictions. Among the existing models, our implementations of PHM, mReasoner, and Verbal Models make the most accurate predictions of the conclusions drawn by individual reasoners. The designed composite model, however, is able to significantly surpass those implementations by exploiting synergies between different models. In particular, it successfully combines operations from PHM and Verbal Models. Therefore, the composite approach is a promising tool to model and study syllogistic reasoning and to generate tailored cognitive theories. At the same time it provides a general method that can potentially be applied to predict individual human reasoners in other domains, too.
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References
Begg, I., Denny, J.P.: Empirical reconciliation of atmosphere and conversion interpretations of syllogistic reasoning errors. J. Exp. Psychol. 81(2), 351–354 (1969). https://doi.org/10.1037/h0027770
Bucciarelli, M., Johnson-Laird, P.N.: Strategies in syllogistic reasoning. Cogn. Sci. 23 (3), 247–303 (1999). https://doi.org/10.1207/s15516709cog2303_1
Chapman, L.J., Chapman, J.P.: Atmosphere effect re-examined. J. Exp. Psychol. 58(3), 220–226 (1959). https://doi.org/10.1037/h0041961
Chater, N., Oaksford, M.: The probability heuristics model of syllogistic reasoning. Cogn. Psychol. 38(2), 191–258 (1999). https://doi.org/10.1006/cogp.1998.0696
Erickson, J.R.: A set analysis theory of behavior in formal syllogistic reasoning tasks. In: Solso, R.L. (ed.) Loyola Symposium on Cognition, vol. 2. Lawrence Erlbaum, Hillsdale (1974)
Ford, M.: Two modes of mental representation and problem solution in syllogistic reasoning. Cognition 54(1), 1–71 (1995). https://doi.org/10.1016/0010-0277(94)00625-u
Geurts, B.: Reasoning with quantifiers. Cognition 86(3), 223–251 (2003)
Johnson-Laird, P.N., Khemlani, S.: Toward a unified theory of reasoning. In: Psychology of Learning and Motivation. https://doi.org/10.1016/b978-0-12-407187-2.00001-0, pp 1–42. Elsevier (2013)
Johnson-Laird, P.N., Steedman, M.: The psychology of syllogisms. Cogn. Psychol. 10 (1), 64–99 (1978). https://doi.org/10.1016/0010-0285(78)90019-1
Khemlani, S., Johnson-Laird, P.N.: Theories of the syllogism: a meta-analysis. Psychol. Bull. 138(3), 427–457 (2012). https://doi.org/10.1037/a0026841
Khemlani, S., Johnson-Laird, P.N.: The processes of inference. Argument & Computation 4(1), 4–20 (2013). https://doi.org/10.1080/19462166.2012.674060
Khemlani, S., Johnson-Laird, P.N.: How people differ in syllogistic reasoning. In: Papafragou, A., Grodner, D., Mirman, D., Trueswell, J. (eds.) Proceedings of the 38th Annual Conference of the Cognitive Science Society, Cognitive Science Society, Austin, TX (2016)
Newell, A.: Reasoning, problem solving and decision processes: the problem space as a fundamental category. In: Nickerson, R.S. (ed.) Attention and Performance VIII, pp 693–718. Lawrence Erlbaum Associates, Hillsdale (1980)
Polk, T.A., Newell, A.: Deduction as verbal reasoning. Psychol. Rev. 102(3), 533–566 (1995). https://doi.org/10.1037/0033-295x.102.3.533
Revlis, R.: Two models of syllogistic reasoning: Feature selection and conversion. J. Verbal Learn. Verbal Behav. 14(2), 180–195 (1975). https://doi.org/10.1016/s0022-5371(75)80064-8
Riesterer, N., Brand, D., Ragni, M.: Predictive modeling of individual human cognition: Upper bounds and a new perspective on performance. Top. Cogn. Sci. 12(3), 960–974 (2019). https://doi.org/10.1111/tops.12501
Rips, L.J.: The Psychology of Proof. MIT Press, Cambridge (1994)
Stenning, K., Yule, P.: Image and language in human reasoning: a syllogistic illustration. Cogn. Psychol. 34(2), 109–159 (1997). https://doi.org/10.1006/cogp.1997.0665
Wetherick, N.E., Gilhooly, K.J.: ‘atmosphere’, matching, and logic in syllogistic reasoning. Current Psychology 14(3), 169–178 (1995). https://doi.org/10.1007/bf02686906
Woodworth, R.S., Sells, S.B.: An atmosphere effect in formal syllogistic reasoning. J. Exp. Psychol. 18(4), 451–460 (1935). https://doi.org/10.1037/h0060520
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The authors declare that they have no conflict of interest. The code of all implemented modelsFootnote 1 and the evaluation framework,Footnote 2 which also includes the training and evaluation data have been published.
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The work has been partially supported by DFG research grants to MR: RA1934/4-1 and RA1934/9-1.
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Bischofberger, J., Ragni, M. An adaptive model for human syllogistic reasoning. Ann Math Artif Intell 89, 923–945 (2021). https://doi.org/10.1007/s10472-021-09737-3
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DOI: https://doi.org/10.1007/s10472-021-09737-3