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Part of the book series: Studies in Computational Intelligence ((SCI,volume 910))

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Abstract

The function of the mind consists of two different types, namely, System 1 and System 2 (Kahneman in Thinking, fast and slow. Allen Lane, Penguin Books, 2011). The basic function of System 1 (fast thinking) is associative activation.

I advocate a third form of representing information that is based on using geometrical structures rather than symbols or connections among neurons.

—(Gärdenfors 2000, p. 2)

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Notes

  1. 1.

    The Third Law of Cognition: Feeling comes first (Tversky 2019, p. 42).

  2. 2.

    The Seventh Law of Cognition: The mind fills in missing information (Tversky 2019, pp. 78, 244).

  3. 3.

    Dyer (1988) called this “connectoplasm”.

  4. 4.

    Connectionism is a special case of associationism that models associations using artificial neuron networks (Gärdenfors 2000, p. 1).

References

  • Bordes, A., Usunier, N., Garcia-Duran, A., Weston, J., & Yakhnenko, O. (2013). Translating embeddings for modelling multi-relational data. In C. J. C. Burges, L. Bottou, M. Welling, Z. Ghahramani, & K. Q. Weinberger (Eds.), Advances in neural information processing systems (Vol. 26, pp. 2787–2795). Curran Associates, Inc.

    Google Scholar 

  • Byrne, R. W. (1979). Memory for urban geography. Quarterly Journal of Experimental Psychology, 31, 147–154.

    Article  Google Scholar 

  • Dinsmore, J. (1992). Thunder in the gap. In The symbolic and connectionist paradigms: Closing the gap (pp. 1–23). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Dong, T., Wang, Z., Li, J., Bauckhage, C., & Cremers, A. B. (2019a). Triple classification using regions and fine-grained entity typing. In Proceedings of the Thirty-Third AAAI Conference on Artificial Intelligence (AAAI-19), (pp. 77–85), Honolulu, Hawaii, USA, 27 January–1 February 2019.

    Google Scholar 

  • Dong, T., Bauckhage, C., Jin, H., Li, J., Cremers, O. H., Speicher, D., Cremers, A. B., & Zimmermann, J. (2019b). Imposing category trees onto word-embeddings using a geometric construction. In ICLR-19, New Orleans, USA. 6-9 May 2019.

    Google Scholar 

  • Dreyfus, H. L., Dreyfus, S. E., & Athanasiou, T. (1986). Mind over machine: The power of human intuition and expertise in the era of the computer. New York, NY, USA: The Free Press.

    Google Scholar 

  • Dyer, M. G. (1988). The promise and problems of connectionism. Behavioral and Brain Sciences, 1, 32–33.

    Article  Google Scholar 

  • Erk, K. (2009). Supporting inferences in semantic space: Representing words as regions. In IWCS-8’09 (pp. 104–115). Stroudsburg, PA, USA: Association for Computational Linguistics.

    Google Scholar 

  • Faruqui, M., Dodge, J., Jauhar, S. K., Dyer, C., Hovy, E., & Smith, N. A. (2015). Retrofitting word vectors to semantic lexicons. In Proceedings of the 2015 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (pp. 1606–1615). ACL.

    Google Scholar 

  • Feldman, J. (2006). From molecule to metaphor: A neural theory of language. Cambridge, MA: The MIT Press.

    Book  Google Scholar 

  • Fu, R., Guo, J., Qin, B., Che, W., Wang, H., & Liu, T. (2015). Learning semantic hierarchies: A continuous vector space approach. Transactions on Audio, Speech, and Language Processing, 23(3), 461–471.

    Google Scholar 

  • Gärdenfors, P. (2000). Conceptual spaces—The geometry of thought. Cambridge, MA, USA: MIT Press.

    Book  Google Scholar 

  • Grady, J. (1997). Foundations of meaning: Primary metaphors and primary scenes, University Microfilms.

    Google Scholar 

  • Harnad, S. (1990). The symbol grounding problem. Physics D, 42(1–3), 335–346.

    Article  Google Scholar 

  • Harnad, S. (2003). The symbol grounding problem. In Encyclopedia of cognitive science. Nature Publishing Group/Macmillan.

    Google Scholar 

  • Hristov, Y., Penkov, S., Lascarides, A., & Ramamoorthy, S. (2017). Grounding symbols in multi-modal instructions. In Proceedings of the First Workshop on Language Grounding for Robotics (pp. 49–57). Vancouver, Canada: Association for Computational Linguistics.

    Google Scholar 

  • Ji, G., He, S., Xu, L., Liu, K., & Zhao, J. (2015). Knowledge graph embedding via dynamic mapping matrix. In ACL’2015 (pp. 687–696). Beijing: ACL.

    Google Scholar 

  • Kahneman, D. (2011). Thinking, fast and slow. Allen Lane, Penguin Books. Nobel laureate in Economics in 2002.

    Google Scholar 

  • Lakoff, G., & Johnson, M. (1980). Metaphors We live by. Chicago: The University of Chicago Press. Citation is based on the reprinted in 2003.

    Google Scholar 

  • Li, X., Vilnis, L., Zhang, D., Boratko, M., & McCallum, A. (2019). Smoothing the geometry of box embeddings. In International Conference on Learning Representations (ICLR).

    Google Scholar 

  • Lin, Y., Liu, Z., Sun, M., Liu, Y., & Zhu, X. (2015). Learning entity and relation embeddings for knowledge graph completion. In AAAI’15 (pp. 2181–2187). AAAI Press.

    Google Scholar 

  • McNamara, T. P. (1991). Memory’s view of space. The Psychology of Learning and Motivation, 27, 147–186.

    Article  Google Scholar 

  • Quillian, M. (1968). Semantic memory. In M. Minsky (Ed.), Semantic information processing. Cambridge, MA: MIT Press.

    Google Scholar 

  • Regier, T. (1997). The human semantic potential: Spatial language and constrained connectionism. Cambridge, MA: The MIT Press.

    Google Scholar 

  • Steels, L. (2008). The symbol grounding problem has been solved. So what’s next. In Symbols and embodiment: Debates on meaning and cognition (pp. 223–244). New Orleans, USA: Oxford University Press.

    Google Scholar 

  • Stevens, A., & Coupe, P. (1978). Distance estimation from cognitive maps. Cognitive Psychology, 13, 526–550.

    Google Scholar 

  • Sun, R. (2015). Artificial intelligence: Connectionist and symbolic approaches. In D. W. James (Ed.), International encyclopedia of the social and behavioral sciences (2nd ed., pp. 35–40). Oxford: Pergamon/Elsevier.

    Chapter  Google Scholar 

  • Sun, R. (2016). Implicit and explicit processes: Their relation, interaction, and competition. In L. Macchi, M. Bagassi, & R. Viale (Eds.), Cognitive unconscious and human rationality (pp. 27–257). Cambridge, MA: MIT Press.

    Google Scholar 

  • Tversky, B. (1981). Distortions in memory for maps. Cognitive Psychology, 13, 407–433.

    Article  Google Scholar 

  • Tversky, B. (1992). Distortions in cognitive maps. Geoforum, 23(2), 131–138.

    Article  Google Scholar 

  • Tversky, B. (2019). Mind in motion. New York, USA: Basic Books.

    Book  Google Scholar 

  • Wang, Z., Zhang, J., Feng, J., & Chen, Z. (2014). Knowledge graph embedding by translating on hyperplanes. In AAAI (pp. 1112–1119). AAAI Press.

    Google Scholar 

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Correspondence to Tiansi Dong .

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Dong, T. (2021). Spatializing Symbolic Structures for the Gap. In: A Geometric Approach to the Unification of Symbolic Structures and Neural Networks. Studies in Computational Intelligence, vol 910. Springer, Cham. https://doi.org/10.1007/978-3-030-56275-5_3

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