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International Workshop on Hybrid Neural Systems

Hybrid Neural Systems 1998: Hybrid Neural Systems pp 46–62Cite as

A Recursive Neural Network for Reflexive Reasoning

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1778))

Abstract

We formally specify a connectionist system for generating the least model of a datalogic program which uses linear time and space. The system is shown to be sound and complete if only unary relation symbols are involved and complete but unsound otherwise. For the latter case a criteria is defined which guarantees correctness. Finally, we compare our system to the forward reasoning version of Shruti.

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References

  1. Apt, K.R., Van Emden, M.H.: Contributions to the theory of logic programming. Journal of the ACM 29, 841–862 (1982)

    Article  MATH  Google Scholar 

  2. Beringer, A., Hölldobler, S.: On the adequateness of the connection method. In: Proceedings of the AAAI National Conference on Artificial Intelligence, pp. 9–14 (1993)

    Google Scholar 

  3. Bibel, W.: On matrices with connections. Journal of the ACM 28, 633–645 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bibel, W.: Advanced topics in automated deduction. In: Nossum, R.T. (ed.) ACAI 1987. LNCS, vol. 345, pp. 41–59. Springer, Heidelberg (1988)

    Google Scholar 

  5. Bibel, W.: Deduction. Academic Press, London (1993)

    Google Scholar 

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

    Google Scholar 

  7. Dowling, W.F., Gallier, J.H.: Linear-time algorithms for testing the satisfiability of propositional Horn formulae. Journal of Logic Programming 1(3), 267–284 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  8. Elcock, E.W., Hoddinott, P.: Comments on Kornfeld’s equality for Prolog: E-unification as a mechanism for argumenting the prolog search strategy. In: Proceedings of the AAAI National Conference on Artificial Intelligence, pp. 766–774 (1986)

    Google Scholar 

  9. Feldman, J.A.: Memory and change in connection networks. Technical Report TR96, Computer Science Department, University of Rochester (1981)

    Google Scholar 

  10. Feldman, J.A., Ballard, D.H.: Connectionist models and their properties. Cognitive Science 6(3), 205–254 (1982)

    Article  Google Scholar 

  11. Fitting, M.: Metric methods – three examples and a theorem. Journal of Logic Programming 21(3), 113–127 (1994)

    MATH  MathSciNet  Google Scholar 

  12. Fodor, J.A., Pylyshyn, Z.W.: Connectionism and cognitive architecture: A critical analysis. In: Pinker, Mehler (eds.) Connections and Symbols, pp. 3–71. MIT Press, Cambridge (1988)

    Google Scholar 

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

    Article  Google Scholar 

  14. Hölldobler, S.: A structured connectionist unification algorithm. In: Proceedings of the AAAI National Conference on Artificial Intelligence, pp. 587–593 (1990)

    Google Scholar 

  15. 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 

  16. Hölldobler, S., Kalinke, Y., Lehmann, H.: Designing a counter: Another case study of dynamics and activation landscapes in recurrent networks. In: Brewka, G., Habel, C., Nebel, B. (eds.) KI 1997. LNCS, vol. 1303, pp. 313–324. Springer, Heidelberg (1997)

    Google Scholar 

  17. Hölldobler, S., Kalinke, Y., Störr, H.-P.: Recurrent neural networks to approximate the semantics of acceptable logic programs. In: Antoniou, G., Slaney, J.K. (eds.) Canadian AI 1998. LNCS (LNAI), vol. 1502, Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  18. 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 

  19. Johnson-Laird, P.N., Byrne, R.M.J.: Deduction. Lawrence Erlbaum Associates, Hove and London, UK (1991)

    Google Scholar 

  20. Kalinke, Y.: Using connectionist term representation for first–order deduction – a critical view. In: Maire, F., Hayward, R., Diederich, J. (eds.) Connectionist Systems for Knowledge Representation Deduction, Queensland University of Technology, CADE–14 Workshop, Townsville, Australia (1997)

    Google Scholar 

  21. Kalinke, Y., Lehmann, H.: Computations in recurrent neural networks: From counters to iterated function systems. In: Antoniou, G., Slaney, J.K. (eds.) Canadian AI 1998. LNCS (LNAI), vol. 1502. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  22. Karp, R.M., Ramachandran, V.: Parallel algorithms for shared-memory machines. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, ch.17, pp. 869–941. Elsevier Science Publishers B.V, New York (1990)

    Google Scholar 

  23. Lloyd, J.W.: Foundations of Logic Programming. Springer, Heidelberg (1987)

    MATH  Google Scholar 

  24. 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 

  25. Newell, A.: Physical symbol systems. Cognitive Science 4, 135–183 (1980)

    Article  Google Scholar 

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

    Article  Google Scholar 

  27. Plate, T.A.: Holographic reduced representations. In: Proceedings of the International Joint Conference on Artificial Intelligence, pp. 30–35 (1991)

    Google Scholar 

  28. Pollack, J.B.: Recursive auto-associative memory: Devising compositional distributed representations. In: Proceedings of the Annual Conference of the Cognitive Science Society, pp. 33–39 (1988)

    Google Scholar 

  29. 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 

  30. Sperduti, A.: Labeling RAAM. Technical Report TR-93-029, International Computer Science Institute, Berkeley, CA (1993)

    Google Scholar 

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

    Google Scholar 

  32. Ullman, J.D.: Principles of Database Systems. Computer Science Press, Rockville (1985)

    Google Scholar 

  33. Wunderlich, J.: Erweiterung des RNN–Modells um SHRUTI–Konzepte: Vom aussagenlogischen zum Schlieβen uber prädikatenlogischen Programmen. Master’s thesis, TU Dresden, Fakultät Informatik (1998)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dresden University of Technology, Dresden, Germany

    Steffen Hölldobler

  2. Queensland University of Technology, Brisbane, Australia

    Yvonne Kalinke

  3. Neurotec Hochtechnologie GmbH, Friedrichshafen, Germany

    Jörg Wunderlich

Authors
  1. Steffen Hölldobler
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  2. Yvonne Kalinke
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  3. Jörg Wunderlich
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Editor information

Editors and Affiliations

  1. University of Sunderland, SR6 0DD, Sunderland, United Kingdom

    Stefan Wermter

  2. CECS Department, University of Missouri-Colombia , 201 Engineering Building West, MO 65211-2060, Columbia, USA

    Ron Sun

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© 2000 Springer-Verlag Berlin Heidelberg

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Hölldobler, S., Kalinke, Y., Wunderlich, J. (2000). A Recursive Neural Network for Reflexive Reasoning. In: Wermter, S., Sun, R. (eds) Hybrid Neural Systems. Hybrid Neural Systems 1998. Lecture Notes in Computer Science(), vol 1778. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10719871_4

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  • DOI: https://doi.org/10.1007/10719871_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67305-7

  • Online ISBN: 978-3-540-46417-4

  • eBook Packages: Springer Book Archive

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