Skip to main content

Logics and Networks for Human Reasoning

  • Conference paper
Artificial Neural Networks – ICANN 2009 (ICANN 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5769))

Included in the following conference series:

  • 3853 Accesses

Abstract

We propose to model human reasoning tasks using completed logic programs interpreted under the three-valued Łukasiewicz semantics. Given an appropriate immediate consequence operator, completed logic programs admit a least model, which can be computed by iterating the consequence operator. Reasoning is then performed with respect to the least model. The approach is realized in a connectionist setting.

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

Access this chapter

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. Bader, S., Hitzler, P., Hölldobler, S., Witzel, A.: A fully connectionist model generator for covered first-order logic programs. In: Veloso, M.M. (ed.) Proceedings of the Twentieth International Joint Conference on Artificial Intelligence, January 2007, pp. 666–671. AAAI Press, Menlo Park (2007)

    Google Scholar 

  2. Bader, S., Hölldobler, S.: The core method: Connectionist model generation. In: Kollias, S.D., Stafylopatis, A., Duch, W., Oja, E. (eds.) ICANN 2006. LNCS, vol. 4132, pp. 1–13. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  3. Byrne, R.M.J.: Suppressing valid inferences with conditionals. Cognition 31, 61–83 (1989)

    Article  Google Scholar 

  4. Clark, K.L.: Negation as failure. In: Gallaire, H., Minker, J. (eds.) Logic and Databases, pp. 293–322. Plenum, New York (1978)

    Google Scholar 

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

    Book  MATH  Google Scholar 

  6. d’Avila Garcez, A.S., Gabbay, D.M., Ray, O., Woods, J.: Abductive reasoning in neural-symbolic learning systems. TOPOI 26, 37–49 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. 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), Singapore (2002)

    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, C., Reine, F., Strohmaier, A. (eds.) Knowledge Representation in Neural Networks, pp. 33–46. Logos Verlag, Berlin (1997)

    Google Scholar 

  9. Fitting, M.: A Kripke–Kleene semantics for logic programs. Journal of Logic Programming 2(4), 295–312 (1985)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  12. 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, pp. 68–77, ECCAI (1994)

    Google Scholar 

  13. 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 

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

    Article  Google Scholar 

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

    Google Scholar 

  16. Kleene, S.C.: Introduction to Metamathematics. North-Holland, Amsterdam (1952)

    MATH  Google Scholar 

  17. Łukasiewicz, J.: O logice trójwartościowej. Ruch Filozoficzny 5, 169–171 (1920); English translation: On Three-Valued Logic. In: Borkowski, L. (ed.) Jan Łukasiewicz Selected Works, pp. 87–88. North Holland, Amsterdam (1990)

    Google Scholar 

  18. 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 

  19. Stenning, K., van Lambalgen, M.: Human Reasoning and Cognitive Science. MIT Press, Cambridge (2008)

    Google Scholar 

  20. Stoy, J.E.: Denotational Semantics. MIT Press, Cambridge (1977)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hölldobler, S., Kencana Ramli, C.D.P. (2009). Logics and Networks for Human Reasoning. In: Alippi, C., Polycarpou, M., Panayiotou, C., Ellinas, G. (eds) Artificial Neural Networks – ICANN 2009. ICANN 2009. Lecture Notes in Computer Science, vol 5769. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04277-5_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-04277-5_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04276-8

  • Online ISBN: 978-3-642-04277-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics