Skip to main content
Springer Nature Link
Log in

The Core Method: Connectionist Model Generation

  • Conference paper
Artificial Neural Networks – ICANN 2006 (ICANN 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4132))

Included in the following conference series:

  • 1315 Accesses

Abstract

Knowledge based artificial networks networks have been applied quite successfully to propositional knowledge representation and reasoning tasks. However, as soon as these tasks are extended to structured objects and structure-sensitive processes it is not obvious at all how neural symbolic systems should look like such that they are truly connectionist and allow for a declarative reading at the same time. The core method aims at such an integration. It is a method for connectionist model generation using recurrent networks with feed-forward core. After an introduction to the core method, this paper will focus on possible connectionist representations of structured objects and their use in structure-sensitive reasoning tasks.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Andrews, R., Diederich, J., Tickle, A.: A survey and critique of techniques for extracting rules from trained artificial neural networks. Knowledge–Based Systems 8(6) (1995)

    Google Scholar 

  2. Bader, S., Hitzler, P., Witzel, A.: Integrating first-order logic programs and connectionist systems — a constructive approach. In: Proceedings of the IJCAI 2005 Workshop on Neural-Symbolic Learning and Reasoning, NeSy 2005, Edinburgh, UK (2005)

    Google Scholar 

  3. Ballard, D.H.: Parallel logic inference and energy minimization. In: Proceedings of the AAAI National Conference on Artificial Intelligence, pp. 203–208 (1986)

    Google Scholar 

  4. Bishop, C.M.: Neural Networks for Pattern Recognition. Oxford University Press, Oxford (1995)

    Google Scholar 

  5. d’Avila Garcez, A.S., Broda, K., Gabbay, D.M.: Neural-Symbolic Learning Systems: Foundations and Applications. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  6. d’Avila Garcez, A.S., Lamb, L.C., Gabbay, D.M.: A connectionist inductive learning system for modal logic programming. In: Proceedings of the IEEE International Conference on Neural Information Processing ICONIP 2002, Singapore (2002)

    Google Scholar 

  7. d’Avila Garcez, A.S., Lamb, L.C., Gabbay, D.M.: Neural-symbolic intuitionistic reasoning. In: Design and Application of Hybrid Intelligent Systems, pp. 399–408. IOS Press, Amsterdam (2003)

    Google Scholar 

  8. d’Avila Garcez, A.S., Zaverucha, G., de Carvalho, L.A.V.: Logic programming and inductive learning in artificial neural networks. In: Herrmann, Ch., Reine, F., Strohmaier, A. (eds.) Knowledge Representation in Neural Networks, Berlin, pp. 33–46. Logos Verlag (1997)

    Google Scholar 

  9. Elman, J.L.: Structured representations and connectionist models. In: Proceedings of the Annual Conference of the Cognitive Science Society, pp. 17–25 (1989)

    Google Scholar 

  10. Fitting, M.: Metric methods – three examples and a theorem. Journal of Logic Programming, 113–127 (1994)

    Google Scholar 

  11. Fritzke, B.: Vektorbasierte Neuronale Netze. Shaker Verlag (1998)

    Google Scholar 

  12. Funahashi, K.-I.: On the approximate realization of continuous mappings by neural networks. Neural Networks 2, 183–192 (1989)

    Article  Google Scholar 

  13. Hitzler, P., Hölldobler, S., Seda, A.K.: Logic programs and connectionist networks. Journal of Applied Logic 2(3), 245–272 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  14. Hölldobler, S., Kalinke, Y.: Towards a massively parallel computational model for logic programming. In: Proceedings of the ECAI 1994 Workshop on Combining Symbolic and Connectionist Processing (ECCAI), pp. 68–77 (1994)

    Google Scholar 

  15. Hölldobler, S., Kalinke, Y., Störr, H.-P.: Approximating the semantics of logic programs by recurrent neural networks. Applied Intelligence 11, 45–59 (1999)

    Article  Google Scholar 

  16. Hölldobler, S., Kurfess, F.: CHCL – A connectionist inference system. In: Fronhöfer, B., Wrightson, G. (eds.) Dagstuhl Seminar 1990. LNCS (LNAI), vol. 590, pp. 318–342. Springer, Heidelberg (1992)

    Google Scholar 

  17. Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2, 359–366 (1989)

    Article  Google Scholar 

  18. Kalinke, Y.: Ein massiv paralleles Berechnungsmodell für normale logische Programme. Master’s thesis, TU Dresden, Fakultät Informatik (1994) (in German)

    Google Scholar 

  19. Lange, T.E., Dyer, M.G.: High-level inferencing in a connectionist network. Connection Science 1, 181–217 (1989)

    Article  Google Scholar 

  20. Lloyd, J.W.: Foundations of Logic Programming. Springer, Berlin (1993)

    MATH  Google Scholar 

  21. McCarthy, J.: Epistemological challenges for connectionism. Behavioural and Brain Sciences 11, 44 (1988)

    Article  Google Scholar 

  22. McCulloch, W.S., Pitts, W.: A logical calculus and the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics 5, 115–133 (1943)

    Article  MATH  MathSciNet  Google Scholar 

  23. Pinkas, G.: Symmetric neural networks and logic satisfiability. Neural Computation 3, 282–291 (1991)

    Article  Google Scholar 

  24. Plate, T.A.: Holographic reduced networks. In: Giles, C.L., Hanson, S.J., Cowan, J.D. (eds.) Advances in Neural Information Processing Systems, vol. 5, Morgan Kaufmann, San Francisco (1992)

    Google Scholar 

  25. Pollack, J.B.: Recursive distributed representations. Artificial Intelligence 46, 77–105 (1990)

    Article  Google Scholar 

  26. Seda, A.K., Lane, M.: Some aspects of the integration of connectionist and logic-based systems. In: Proceedings of the Third International Conference on Information, pp. 297–300. International Information Institute, Tokyo (2004)

    Google Scholar 

  27. Shastri, L., Ajjanagadde, V.: From associations to systematic reasoning: A connectionist representation of rules, variables and dynamic bindings using temporal synchrony. Behavioural and Brain Sciences 16(3), 417–494 (1993)

    Article  Google Scholar 

  28. Smolensky, P.: On variable binding and the representation of symbolic structures in connectionist systems. Technical Report CU-CS-355-87, Department of Computer Science & Institute of Cognitive Science, University of Colorado, Boulder, CO 80309-0430 (1987)

    Google Scholar 

  29. Towell, G.G., Shavlik, J.W.: Extracting refined rules from knowledge–based neural networks. Machine Learning 131, 71–101 (1993)

    Google Scholar 

  30. Willard, S.: General Topology. Addison Wesley, Reading (1970)

    MATH  Google Scholar 

  31. Witzel, A.: Integrating first-order logic programs and connectionist networks. Project Thesis, Technische Universität Dresden, Informatik (2005)

    Google Scholar 

  32. Witzel, A.: Neural-symbolic integration – constructive approaches. Master’s thesis, Technische Universit”at Dresden, Informatik (2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. International Center for Computational Logic, Technische Universität Dresden, 01062, Dresden, Germany

    Sebastian Bader & Steffen Hölldobler

Authors
  1. Sebastian Bader
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Steffen Hölldobler
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Electrical and Computer Engineering, Image, Video and Multimedia Systems Laboratory, National Technical University of Athens, 157 80, Zographou, GR, Greece

    Stefanos Kollias

  2. Department of Electrical and Computer Engineering, National Technical University of Athens, 15780, Zographou, Greece

    Andreas Stafylopatis

  3. Department of Informatics, Nicolaus Copernicus University, Toruń, Poland

    Włodzisław Duch

  4. Adaptive Informatics Research Centre, Helsinki University of Technology, P.O. Box 5400, 02015, HUT, Finland

    Erkki Oja

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bader, S., Hölldobler, S. (2006). The Core Method: Connectionist Model Generation. In: Kollias, S., Stafylopatis, A., Duch, W., Oja, E. (eds) Artificial Neural Networks – ICANN 2006. ICANN 2006. Lecture Notes in Computer Science, vol 4132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11840930_1

Download citation

  • DOI: https://doi.org/10.1007/11840930_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38871-5

  • Online ISBN: 978-3-540-38873-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics