NEURONS OR SYMBOLS - Why Does OR Remain Exclusive?

Ekaterina Komendantskaya


Neuro-Symbolic Integration is an interdisciplinary area that endeavours to unify neural networks and symbolic logic. The goal is to create a system that combines the advantages of neural networks (adaptive behaviour, robustness, tolerance of noise and probability) and symbolic logic (validity of computations, generality, higherorder reasoning). Several different approaches have been proposed in the past. However, the existing neurosymbolic networks provide only a limited coverage of the techniques used in computational logic. In this paper, we outline the areas of neuro-symbolism where computational logic has been implemented so far, and analyse the problematic areas. We show why certain concepts cannot be implemented using the existing neuro-symbolic networks, and propose four main improvements needed to build neuro-symbolic networks of the future.


  1. Aleksander, I. and Morton, H. (1993). Neurons and Symbols. Chapman and Hall.
  2. Bader, S. and Hitzler, P. (2005). Dimensions of neural symbolic integration - a structural survey. In Artemov, S., editor, We will show them: Essays in honour of Dov Gabbay, volume 1, pages 167-194. King's College, London.
  3. Bader, S., Hitzler, P., and Hölldobler, S. (2008). Connectionist model generation: A first-order approach. Neurocomputing, 71:2420-2432.
  4. d'Avila Garcez, A., Broda, K. B., and Gabbay, D. M. (2002). Neural-Symbolic Learning Systems: Foundations and Applications. Springer-Verlag.
  5. d'Avila Garcez, A. and Gabbay, D. M. (2004). Fibring neural networks. In Proceedings of the 19th National Conference on Artificial Intelligence, pages 342-347. AAAI Press/MIT Press, San Jose, California, USA.
  6. d'Avila Garcez, A., Lamb, L., and Gabbay, D. (2007). Connectionist modal logic: Representing modalities in neural networks. Theoretical Computer Science, 1- 2(371):34-53.
  7. d'Avila Garcez, A., Lamb, L. C., and Gabbay, D. M. (2008). Neural-Symbolic Cognitive Reasoning. Cognitive Technologies. Springer-Verlag.
  8. Ding, L. (1995). Neural prolog - the concepts, construction and mechanism. In Proceedings of the 3rd Int. Conference Fuzzy Logic, Neural Nets, and Soft Computing, pages 181-192.
  9. Domingos, P. (2008). Markov logic: a unifying language for knowledge and information management. In CIKM, page 519.
  10. Güsgen, H. W. and Hölldobler, S. (1992). Connectionist inference systems. In Fronhöfer, B. and Wrightson, G., editors, Parallelization in Inference Systems, pages 82-100. Springer, LNAI 590.
  11. Hammer, B. and Hitzler, P. (2007). Perspectives of NeuralSymbolic Integration. Studies in Computational Intelligence. Springer Verlag.
  12. Hitzler, P., Hölldobler, S., and Seda, A. K. (2004). Logic programs and connectionist networks. Journal of Applied Logic, 2(3):245-272.
  13. Hölldobler, S. and Kalinke, Y. (1994). Towards a massively parallel computational model for logic programming. In Proceedings of the ECAI94 Workshop on Combining Symbolic and Connectionist Processing, pages 68-77. ECCAI.
  14. Hölldobler, S., Kalinke, Y., and Storr, H. P. (1999). Approximating the semantics of logic programs by recurrent neural networks. Applied Intelligence, 11:45-58.
  15. Indyk, P. (1995). Optimal simulation of automata by neural nets. In Mayr, E. and Puech, C., editors, Proc. of the Twelfth Annual Symposium on theoretical aspect of Computer Science, LNCS, page 337.
  16. Kilian, J. and Siegelmann, H. (1996). The dynamic universality of sigmoidal neural networks. Information and Computation, 128(1):48-56.
  17. Kleene, S. (1956). Neural nets and automata. In Automata Studies, pages 3 - 43. Princeton University Press.
  18. Koiran, P., Cosnard, M., and M.Garzon (1994). Computability with low-dimensional dynamic systems. Theoretical Computer Science, 132:113-128.
  19. Komendantskaya, E. (2007). Learning and Deduction in Neural Networks and Logic. PhD thesis, Department of Mathematics, University College Cork, Ireland.
  20. Komendantskaya, E. (2009a). Parallel rewriting in neural networks. In Proceedings of ICNC'09.
  21. Komendantskaya, E. (2009b). Unification neural networks: Unification by error-correction learning. Submitted.
  22. Komendantskaya, E., Lane, M., and Seda, A. (2007). Connectionist representation of multi-valued logic programs. In Hammer, B. and Hizler, P., editors, Perspectives of Neural-Symbolic Integration, Computational Intelligence, pages 259-289. Springer Verlag. To appear.
  23. Lange, T. E. and Dyer, M. G. (1989). High-level inferencing in a connectionist network. Connection Science, 1:181 - 217.
  24. Lloyd, J. (1987). Foundations of Logic Programming. Springer-Verlag, 2nd edition.
  25. Markus, G. (2001). The Algebraic Mind: Integrating Connectionism and Cognitive Science. Cambridge, MA: MIT Press.
  26. McCulloch, W. and Pitts, W. (1943). A logical calculus of the ideas immanent in nervous activity. Bulletin of Math. Bio., 5:115-133.
  27. Minsky, M. (1954). Neural Nets and the Brain - Model Problem. PhD thesis, Princeton University, Princeton NJ.
  28. Minsky, M. (1969). Finite and Infinite Machines.
  29. Nauck, D., Klawonn, F., Kruse, R., and F.Klawonn (1997). Foundations of Neuro-Fuzzy Systems. John Wiley and Sons Inc., NY.
  30. Neumann, J. V. (1958). The Computer and The Brain. Yale University Press.
  31. Pollack, J. (1987). On Connectionist Models of Natural Language Processing. PhD thesis, Computer science Department, University of Illinois, Urbana.
  32. Pollack, J. (1990). Recursive distributed representations. AIJ, 46:77-105.
  33. Robinson, J. (1965). A machine-oriented logic based on resolution principle. Journal of ACM, 12(1):23-41.
  34. Shastri, L. and Ajjanagadde, V. (1993). 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.
  35. Siegelmann, H. (1999). Neural Networks and Analog Computation. Beyond the Turing Limit. Birkhauser.
  36. Siegelmann, H. and Margenstern, M. (1999). Nine switchaffine neurons suffice for Turing universality. Neural Networks, 12:593-600.
  37. Siegelmann, H. and Sontag, E. (1991). Turing computability with neural nets. Applied Mathematics Letters, 4(6):77-80.
  38. Siegelmann, H. and Sontag, E. (1995). On the computational power of neural nets. J. of Computers and System Science, 50(1):132-150.
  39. Smolensky, P. and Legendre, G. (2006). The Harmonic Mind. MIT Press.
  40. Wang, J. and Domingos, P. (2008). Hybrid markov logic networks. In AAAI, pages 1106-1111.
  41. Zadeh, L. (1992). Interpolative reasoning in fuzzy logic and neural network theory. Fuzzy Systems, pages 1-20.

Paper Citation

in Harvard Style

Komendantskaya E. (2009). NEURONS OR SYMBOLS - Why Does OR Remain Exclusive? . In Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICNC, (IJCCI 2009) ISBN 978-989-674-014-6, pages 502-507. DOI: 10.5220/0002334805020507

in Bibtex Style

author={Ekaterina Komendantskaya},
title={NEURONS OR SYMBOLS - Why Does OR Remain Exclusive?},
booktitle={Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICNC, (IJCCI 2009)},

in EndNote Style

JO - Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICNC, (IJCCI 2009)
TI - NEURONS OR SYMBOLS - Why Does OR Remain Exclusive?
SN - 978-989-674-014-6
AU - Komendantskaya E.
PY - 2009
SP - 502
EP - 507
DO - 10.5220/0002334805020507