Skip to main content
Log in

Schemas, logics, and neural assemblies

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

To implement schemas and logics in connectionist models, some form of basic-level organization is needed. This paper proposes such an organization, which is termed a discrete neural assembly. Each discrete neural assembly is in turn made up of discrete neurons (nodes), that is, a node that processes inputs based on a discrete mapping instead of a continuous function. A group of discrete neurons (nodes) closely interconnected form an assembly and carry out a basic functionality. Some substructures and superstructures of such assemblies are developed to enable complex symbolic schemas to be represented and processed in connectionist networks. The paper shows that logical inference can be performed precisely, when necessary, in these networks and with certain genaralization, more flexible inference (fuzzy inference) can also be performed. The development of various connectionist constructs demonstrates the possibility of implementing symbolic schemas, in their full complexity, in connectionist networks.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Arbib,From schema theory to language, Oxford U. Press, New York, NY, 1987.

    Google Scholar 

  2. L. Fang and W. Wilson, “A study of Sequence Processing on Neural Networks,”Proc. IJCNN, Washington DC, pp. 588–598, IEEE Press, 1989.

  3. J. Feldman and D. Ballard, “Connectionist models and their properties,“,Cognitive Science, 205–254, 1982.

  4. J. Fodor and Z. Pylyshyn, “Connectionism and Cognitive Architecture: A Critical Analysis,”Connections and Symbols. Cambridge, MA: MIT Press, 1988.

    Google Scholar 

  5. B. Inhelder and J. Piaget,The Growth of Logical Thinking from Childhood to Adolescence, Routledge and Kegan Paul, London, England, 1958.

    Google Scholar 

  6. T. Lange and M. Dyer, “Frame selection in a connectionist model,”Proc. 11th Cognitive Science Conference, pp. 706–713. Hillsdale, NJ: Lawrence Erlba um Associates, 1989a.

    Google Scholar 

  7. T. Lange and M. Dyer, “High Level Inferencing in a Connectionist Net work,”Connection Science, pp. 181–217, 1989b.

  8. R. Miikkulainen and M. Dyer, “Natural language processing with modular PDP networks and distributed lexicons,”Cognitive Science, 15(3), pp. 343–399, 1991.

    Google Scholar 

  9. M. Minsky, “A Framework for Representing Knowledge,” in, J. Hughland (ed.)Mind Design, MIT Press, Cambridge, MA, 1983.

    Google Scholar 

  10. S. Pinker and A. Prince, “On Language and Connectionism,”Connections and Symbols, Cambridge, MA: MIT Press, 1988.

    Google Scholar 

  11. D. Rumelhart, J. McClelland, and PDP Research Group,Parallel Distributed Processing: Explorations in the Microstructures of Cognition, Cambridge, MA: MIT Press, 1986.

    Google Scholar 

  12. R. Schank,Scripts, Plans and Goals, LEA, Hillsdale, NJ, 1977.

    Google Scholar 

  13. L. Shastri and V. Ajjanagadde, “From simple association to systematic reasoning,” Tech. Report MS-CIS-90-05, University of Pennsylvania, 1990.

  14. R. Sun, “A discrete neural network model for conceptual representation and reasoning,”Proc. 11th Cognitive Science Society Conference, pp. 916–923. Hillsdale, NJ: Lawrence Erlbaum Associates, 1989.

    Google Scholar 

  15. R. Sun, “The Discrete Neuronal Models and the Probabilistic Discrete Neuronal Models,” in B. Soucek ed.Neural and Intelligent System Integration, pp. 161–178. New York, NY: John Wiley and Sons, 1991.

    Google Scholar 

  16. R. Sun, “Connectionist Models of Commonsense Reasoning Incorporating Rules and Similarities,”Knowledge Acquisition, vol. 4, pp. 293–321, 1992a.

    Google Scholar 

  17. R. Sun, “On variables binding in connectionist networks’,Connection Science, vol. 4, no. 2, pp. 93–94, 1992b.

    Google Scholar 

  18. R. Sun, “A Neural Network Model of Causality,”IEEE Transaction on Neural Networks, vol. 5, no. 4, pp. 604–611, 1994.

    Google Scholar 

  19. R. Sun,Integrating Rules and Connectionism for Robust Commonsense Reasoning, John Wiley and Sons, New York, NY. 1994.

    Google Scholar 

  20. R. Sun and L. Bookman, “How do symbols and networks fit together?”Artificial Intelligence magazine, pp. 20–23, Summer, 1993.

  21. R. Sun and D. Waltz, “Neurally Inspired Massively Parallel Model of Rule-Based Reasoning.” in B. Soucek ed.Neural and Intelligent System Integration, pp. 341–381, New York, NY: John Wiley and Sons, 1991

    Google Scholar 

  22. L. Zadeh, “Fuzzy Logic,”Computer, vol. 21, no. 4, pp. 83–93, 1988.

    Google Scholar 

  23. C. Chang and R. C. Lee,Symbolic Logic and Mechanical Theorem Proving, Academic Press, Reading, MA, 1973.

    Google Scholar 

  24. P. Smolensky, “On the proper treatment of connectionism”,Behavioral and Brain Sciences, 11, pp. 1–43, 1988.

    Google Scholar 

  25. M. R. Quillian, “Semantic memory,” in M. Minsky, (ed.)Semantic Information Processing. MIT Press, 1968.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sun, R. Schemas, logics, and neural assemblies. Appl Intell 5, 83–102 (1995). https://doi.org/10.1007/BF00877227

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00877227

Keywords

Navigation