Subsymbolic Computation Theory for the Human Intuitive Processor

  • Paul Smolensky
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7318)


The classic theory of computation initiated by Turing and his contemporaries provides a theory of effective procedures—algorithms that can be executed by the human mind, deploying cognitive processes constituting the conscious rule interpreter. The cognitive processes constituting the human intuitive processor potentially call for a different theory of computation. Assuming that important functions computed by the intuitive processor can be described abstractly as symbolic recursive functions and symbolic grammars, we ask which symbolic functions can be computed by the human intuitive processor, and how those functions are best specified—given that these functions must be computed using neural computation. Characterizing the automata of neural computation, we begin the construction of a class of recursive symbolic functions computable by these automata, and the construction of a class of neural networks that embody the grammars defining formal languages.


Binary Tree Symbolic Function Human Language Neural Computation Grid State 
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  1. 1.
    Hofstadter, D.R.: Waking up from the Boolean dream, or, subcognition as computation. In: Hofstadter, D.R. (ed.) Metamagical Themas: Questing for the Essence of Mind and Pattern, pp. 631–665. Bantam Books (1986)Google Scholar
  2. 2.
    Kimoto, M., Takahashi, M.: On Computable Tree Functions. In: He, J., Sato, M. (eds.) ASIAN 2000. LNCS, vol. 1961, pp. 273–289. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  3. 3.
    McClelland, J., Botvinick, M., Noelle, D., Plaut, D., Rogers, T., Seidenberg, M., Smith, L.: Letting structure emerge: Connectionist and dynamical systems approaches to cognition. Trends in Cognitive Sciences 14(8), 348–356 (2010)CrossRefGoogle Scholar
  4. 4.
    McCulloch, W., Pitts, W.: A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biology 5(4), 115–133 (1943)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Newell, A.: Physical symbol systems. Cognitive Science 4(2), 135–183 (1980)CrossRefGoogle Scholar
  6. 6.
    Prince, A., Smolensky, P.: Optimality Theory: Constraint interaction in generative grammar. Blackwell (1993/2004)Google Scholar
  7. 7.
    Prince, A., Smolensky, P.: Optimality: From neural networks to universal grammar. Science 275(5306), 1604–1610 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Rumelhart, D., McClelland, J., The PDP Research Group: Parallel distributed processing: Explorations in the microstructure of cognition. Foundations, vol. 1. MIT Press, Cambridge (1986)Google Scholar
  9. 9.
    Rutgers Optimality Archive,
  10. 10.
    Smolensky, P.: On the proper treatment of connectionism. Behavioral and Brain Sciences 11(01), 1–23 (1988)CrossRefGoogle Scholar
  11. 11.
    Smolensky, P.: Cognition: Discrete or continuous computation? In: Cooper, S., van Leeuwen, J. (eds.) Alan Turing — His Work and Impact. Elsevier (2012)Google Scholar
  12. 12.
    Smolensky, P.: Symbolic functions from neural computation. Philosophical Transactions of the Royal Society – A: Mathematical, Physical and Engineering Sciences (in press, 2012)Google Scholar
  13. 13.
    Smolensky, P., Goldrick, M., Mathis, D.: Optimization and quantization in gradient symbol systems: A framework for integrating the continuous and the discrete in cognition. Cognitive Science (in press, 2012)Google Scholar
  14. 14.
    Smolensky, P., Legendre, G.: The harmonic mind: From neural computation to Optimality-Theoretic grammar, vol. 1: Cognitive architecture, vol. 2: Linguistic and philosophical implications. MIT Press, Cambridge (2006)Google Scholar
  15. 15.
    Turing, A.M.: On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society 42, 230–265 (1936)CrossRefGoogle Scholar
  16. 16.
    Turing, A.M.: Intelligent machinery: A report by Turing, A.M. National Physical Laboratory (1948)Google Scholar
  17. 17.
    Turing, A.M.: Computing machinery and intelligence. Mind 59(236), 433–460 (1950)MathSciNetCrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Paul Smolensky
    • 1
  1. 1.Department of Cognitive ScienceJohns Hopkins UniversityBaltimoreUnited States of America

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