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14 - Analogy and Similarity

from Part III - Computational Modeling of Basic Cognitive Functionalities

Published online by Cambridge University Press:  21 April 2023

By
John E. Hummel  and
Leonidas A. A. Doumas
Edited by
Ron Sun
Ron Sun
Affiliation:
Rensselaer Polytechnic Institute, New York
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Summary

Analogy is a core cognitive capacity encompassing basic similarity (“this is like that”), relational similarity (proportional analogies of the form A:B::C:x), and complex system mappings, in which the elements of one situation are structurally aligned with the elements of another. The latter permits complex inferences from a known source situation to a less familiar target situation. Because of its centrality in human thinking, analogy has been the subject of numerous computational modeling efforts. Models of similarity come from multiple traditions in cognitive science, including associationist approaches (such as connectionist models), “traditional” symbolic approaches (such as graph matching and production systems), and hybrid symbolic/connectionist approaches. This chapter reviews and evaluates several models from these various approaches in terms of their ability to simulate basic similarity, relational similarity, and system mapping.

Keywords

analogysimilarityrelationssymbolicassociationistmodels
Type
Chapter
Information
The Cambridge Handbook of Computational Cognitive Sciences , pp. 451 - 473
Publisher: Cambridge University Press
Print publication year: 2023

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References

Bowdle, B. F., & Gentner, D. (2005). The career of metaphor. Psychological Review, 112, 193–216.Google Scholar
Bowers, J. S. (2017). Parallel distributed processing theory in the age of deep networks. Trends in Cognitive Sciences, 21(12), 950–961.CrossRefGoogle ScholarPubMed
Chen, D., Peterson, J. C., & Griffiths, T. L. (2017). Evaluating vector-space models of analogy. In Proceedings of the 39th Annual Conference of the Cognitive Science Society.Google Scholar
Cunningham, J., & Shepard, R. (1974). Monotone mapping of similarities into a general metric space. Journal of Mathematical Psychology, 11, 335–363.Google Scholar
Doumas, L. A., & Hummel, J. E. (2005). Approaches to modeling human mental representations: what works, what doesn’t and why. In K. J. Holyoak, , & Morrison, R. G. (Eds.), The Cambridge Handbook of Thinking and Reasoning (pp. 73–94). Cambridge: Cambridge University Press.Google Scholar
Doumas, L. A. A., Hummel, J. E., & Sandhofer, C. M. (2008). A theory of the discovery and predication of relational concepts. Psychological Review, 115(1), 1–43.Google Scholar
Doumas, L. A. A., Puebla, G., Martin, A. E., & Hummel, J. E. (2022). A theory of relation learning and cross-domain generalization. Psychological Review (advance online publication). https://doi.org/10.1037/rev0000346Google Scholar
Ehresman, D., & Wessel, D. L. (1978). Report: Perception of Timbral Analogies. Paris: Centre Georges Pompidou.Google Scholar
Falkenhainer, B., Forbus, K. D., & Gentner, D. (1989). The structure-mapping engine: algorithm and examples. Artificial Intelligence, 41, 1–63.Google Scholar
Forbus, K. D., Gentner, D., & Law, K. (1995). MAC/FAC: a model of similarity-based retrieval. Cognitive Science, 19, 141–205.Google Scholar
Forbus, K. D., & Hinrichs, T. R. (2017). Analogy and qualitative representations in the companion cognitive architecture. AI Magazine, 2017, 34–42.Google Scholar
Gentner, D. (1983). Structure-mapping: a theoretical framework for analogy. Cognitive Science, 7, 155–170.Google Scholar
Gentner, D. (2003). Why we’re so smart. In Gentner, D. & Goldin-Meadow, S. (Eds.), Language in Mind: Advances in the Study of Language and Thought (pp. 195–235). Cambridge, MA: MIT Press.CrossRefGoogle Scholar
Gick, M. L., & Holyoak, K. J. (1980). Analogical problem solving. Cognitive Psychology, 12, 306–355.Google Scholar
Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. Cognitive Psychology, 15, 1–38.CrossRefGoogle Scholar
Halford, G. S. (1992). Analogical reasoning and conceptual complexity in cognitive development. Human Development, 35, 193–217.Google Scholar
Halford, G. S., Wilson, W. H., & Phillips, S. (1998). Processing capacity defined by relational complexity: implications for comparative, developmental, and cognitive psychology. Brain and Behavioral Sciences, 21, 803–864.Google Scholar
Hill, F., Santoro, A., Barrett, D. G., Morcos, A. S., & Lillicrap, T. (2019). Learning to make analogies by contrasting abstract relational structure. arXiv:1902.00120Google Scholar
Hofstadter, D. R., & Mitchell, M. (1994). An overview of the Copycat project. In Holyoak, K. J. & Barnden, J. A. (Eds.), Advances in Connectionist and Neural Computation Theory, Vol. 2: Analogical Connections (pp. 31–112). Norwood, NJ: Erlbaum.Google Scholar
Hofstadter, D., & Sander, E. (2013). Surfaces and Essences: Analogy as the Fuel and Fire of Thinking. New York, NY: Basic Books.Google Scholar
Holland, J. H., Holyoak, K. J., Nisbett, R. E., & Thagard, P. R. (1986). Induction: Processes of Inference, Learning, and Discovery. Cambridge, MA. MIT Press.Google Scholar
Holyoak, K. J. (2019). The Spider’s Thread: Metaphor in Mind, Brain and Poetry. Cambridge, MA: MIT Press.Google Scholar
Holyoak, K. J., & Thagard, P. (1989). Analogical mapping by constraint satisfaction. Cognitive Science, 13, 295–355.CrossRefGoogle Scholar
Holyoak, K. J., & Thagard, P. (1995). Mental Leaps: Analogy in Creative Thought. Cambridge, MA: MIT Press.Google Scholar
Hu, S., Ma, Y., Liu, X., Wei, Y., & Bai, S. (2020). Hierarchical rule induction network for abstract visual reasoning. arXiv:2002.06838.Google Scholar
Hummel, J. E. (2010). Symbolic vs. associative learning. Cognitive Science, 34, 958–965.Google Scholar
Hummel, J. E. (2011). Getting symbols out of a neural architecture. Connection Science, 23, 109–118.Google Scholar
Hummel, J. E., & Biederman, I. (1992). Dynamic binding in a neural network for shape recognition. Psychological Review, 99, 480–517.CrossRefGoogle Scholar
Hummel, J. E., & Holyoak, K. J. (1992). Indirect analogical mapping. In Proceedings of the 14th Annual Conference of the Cognitive Science Society (pp. 516–521). Hillsdale, NJ: Erlbaum.Google Scholar
Hummel, J. E., & Holyoak, K. J. (1997). Distributed representations of structure: a theory of analogical access and mapping. Psychological Review, 104, 427–466.Google Scholar
Hummel, J. E., & Holyoak, K. J. (2003). A symbolic-connectionist theory of relational inference and generalization. Psychological Review, 110, 220–264.CrossRefGoogle ScholarPubMed
Hummel, J. E., Landy, D. H., & Devnich, D. (2008). Toward a process model of explanation with implications for the type-token problem. In Naturally Inspired AI: Papers from the AAAI Fall Symposium. Technical Report FS-08-06, 79-86.Google Scholar
Hummel, J. E., Licato, J., & Bringsjord, S. (2014). Analogy, explanation, and proof. Frontiers in Human Neuroscience (online). http://journal.frontiersin.org/Journal/10.3389/fnhum.2014.00867/abstractGoogle Scholar
Jung, W., & Hummel, J. E., (2015a). Making probabilistic relational categories learnable. Cognitive Science, 39, 1259–1291. https://doi.org/10.1111/cogs.12199Google Scholar
Jung, W., & Hummel, J. E. (2015b). Revisiting Wittgenstein’s puzzle: hierarchical encoding and comparison facilitate learning of probabilistic relational categories. Frontiers in Psychology, 6, 110. https://doi.org/10.3389/fpsyg.2015.00110Google Scholar
Kittur, A., Hummel, J. E., & Holyoak, K. J. (2004). Feature- vs. relation-defined categories: probab(alistical)ly not the same. In Proceedings of the 26th Annual Conference of the Cognitive Science Society (pp. 696–701).Google Scholar
Kittur, A., Hummel, J. E., & Holyoak, K. J. (2006). Ideals aren’t always typical: dissociating goodness-of-exemplar from typicality judgments. In Proceedings of the 28th Annual Conference of the Cognitive Science Society.Google Scholar
Knowlton, B. J., Morrison, R. G., Hummel, J. E., & Holyoak, K. J. (2012). A neurocomputational system for relational reasoning. Trends in Cognitive Sciences, 17, 373–381.Google Scholar
Kogut, P., Gordon, J., Morgenthaler, D., et al. (2011). Recognizing geospatial patterns with biologically-inspired relational reasoning. In Second International Conference on Biologically Inspired Cognitive Architectures (BICA 2011).Google Scholar
Kubose, T. T., Holyoak, K. J., & Hummel, J. E. (2002). The role of textual coherence in incremental analogical mapping. Journal of Memory and Language, 47, 407–435.Google Scholar
Lakoff, G. (1987). Women, Fire and Dangerous Things: What Categories Reveal About the Mind. Chicago, IL: University of Chicago Press.Google Scholar
Lakoff, G., & Johnson, M. (1980). Metaphors We Live By. Chicago, IL: University of Chicago Press.Google Scholar
Leech, R., Mareschal, D., & Cooper, R.P. (2008). Analogy as relational priming: a developmental and computational perspective on the origins of a complex cognitive skill. Behavioral and Brain Sciences, 31(4), 378–414.CrossRefGoogle ScholarPubMed
Licato, J., Bringsjord, S., & Hummel, J. E. (2012). Exploring the role of analogico-deductive reasoning in the balance-beam task. In Rethinking Cognitive Development: Proceedings of the 42nd Annual Meeting of the Jean Piaget Society.Google Scholar
Lin, T. -J., Anderson, R. C., Hummel, J. E., et al. (2012). Children’s use of analogy during Collaborative Reasoning. Child Development, 83, 1429–1443.Google Scholar
Lovett, A., & Forbus, K. (2017). Modeling visual problem solving as analogical reasoning. Psychological Review, 124(1), 60–90.Google Scholar
Lu, H., Chen, D., & Holyoak, K. J., (2012). Bayesian analogy with relational transformations. Psychological Review, 119, 617–648.Google Scholar
Malhotra, G., Evans, B., & Bowers, J. (2020). Hiding a plane behind a pixel: shape-bias in CNNs and the benefit of building in biological constraints. Vision Research, 174, 57–78.Google Scholar
Marcus, G. F. (1998). Rethinking eliminative connectionism. Cognitive Psychology, 37(3), 243–282.CrossRefGoogle ScholarPubMed
Marr, D. (1982). Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. New York, NY: W.H. Freeman.Google Scholar
McClelland, J. L., & Rogers, T. T. (2003). The parallel distributed processing approach to semantic cognition. Nature Reviews Neuroscience, 4(4), 310–322.Google Scholar
Mikolov, T., Sutskever, I., Chen, K., Corrado, G. S., & Dean, J. (2013). Distributed representations of words and phrases and their compositionality. In Jordan, M. I., LeCun, Y., & Solla, S. A. (Eds.), Advances in Neural Information Processing Systems (pp. 3111–3119). Cambridge, MA: MIT Press.Google Scholar
Morrison, R. G., Doumas, L. A., & Richland, L. E. (2011). A computational account of children’s analogical reasoning: balancing inhibitory control in working memory and relational representation. Developmental Science, 14(3), 516–529.Google Scholar
Morrison, R. G., Krawczyk, D. C., Holyoak, K. J., et al. (2004). A neurocomputational model of analogical reasoning and its breakdown in frontotemporal lobar degeneration. Journal of Cognitive Neuroscience, 16, 260–271.Google Scholar
Penn, D. C., Holyoak, K. J., & Povinelli, D. J. (2008). Darwin’s mistake: explaining the discontinuity between human and nonhuman minds. Behavioral and Brain Sciences, 31(2), 109–130.Google Scholar
Pennington, J., Socher, R., & Manning, C. D. (2014). Glove: global vectors for word representation. Empirical Methods in Natural Language Processing, 14, 1532–1543.Google Scholar
Peyre, J., Laptev, I., Schmid, C., & Sivic, J. (2019). Detecting unseen visual relations using analogies. In Proceedings of the IEEE International Conference on Computer Vision (pp. 1981–1990).Google Scholar
Rabagliati, H., Doumas, L. A., & Bemis, D. K. (2017). Representing composed meanings through temporal binding. Cognition, 162, 61–72.Google Scholar
Rabovsky, M., Hansen, S. S., & McClelland, J. L. (2018). Modelling the N400 brain potential as change in a probabilistic representation of meaning. Nature Human Behavior, 2(9), 693–705.Google Scholar
Ross, B. (1987). This is like that: the use of earlier problems and the separation of similarity effects. Journal of Experimental Psychology: Learning, Memory, and Cognition, 13, 629–639.Google Scholar
Rumelhart, D. E., & Abrahamson, A. A. (1973). A model for analogical reasoning. Cognitive Psychology, 5(1), 1–28.CrossRefGoogle Scholar
Sandhofer, C. M., & Doumas, L. A. (2008). Order of presentation effects in learning color categories. Journal of Cognition and Development, 9(2), 194–221.Google Scholar
Santoro, A., Raposo, D., Barrett, D. G., et al. (2017). A simple neural network module for relational reasoning. In Jordan, M. I., LeCun, Y., & Solla, S. A. (Eds.), Advances in Neural Information Processing Systems (pp. 4967–4976). Cambridge, MA: MIT Press.Google Scholar
Son, J. Y., Doumas, L. A., & Goldstone, R. L. (2010). When do words promote analogical transfer? The Journal of Problem Solving, 3(1), 4.Google Scholar
St. John, M. F. (1992). The Story Gestalt: a model of knowledge-intensive processes in text comprehension. Cognitive Science, 16, 271–302.Google Scholar
St. John, M. F., & McClelland, J. L. (1990). Learning and applying contextual constraints in sentence comprehension. Artificial Intelligence, 46, 217–257.Google Scholar
Taylor, E. G., & Hummel, J. E. (2009). Finding similarity in a model of relational reasoning. Cognitive Systems Research, 10, 229–239.Google Scholar
Tversky, A. (1977). Features of similarity. Psychological Review, 84, 327–352.Google Scholar
Viskontas, I., Morrison, R., Holyoak, K. J., Hummel, J. E., & Knowlton, B. J. (2004). Relational integration, inhibition, and analogical reasoning in older adults. Psychology and Aging, 19, 581–591.Google Scholar
Zhou, L., Cui, P., Yang, S., Zhu, W., & Tian, Q. (2019). Learning to learn image classifiers with visual analogy. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (pp. 11497–11506).Google Scholar

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