Advertisement

Flexible Reasoning of Boolean Constraints in Recurrent Neural Networks with Dual Representation

  • Wonil Chang
  • Hyun Ah Song
  • Soo-Young Lee
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8226)

Abstract

In this paper, we propose a recurrent neural network that can flexibly make inferences to satisfy given Boolean constraints. In our proposed network, each Boolean variable is represented in dual representation by a pair of neurons, which can handle four states of true, false, unknown, and contradiction. We successfully import Blake’s classical Boolean reasoning algorithm to recurrent neural network with hidden neurons of Boolean product terms. For symmetric Boolean functions, we designed an extended model of Boolean reasoning which can drastically reduce the hardware cost. Since our network has only excitatory connections, it does not suffer from oscillation and we can freely combine multiple Boolean constraints.

Keywords

Boolean constraint Boolean reasoning symmetric Boolean function recurrent neural network 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Beller, S., Kuhnmünch, G.: What causal conditional reasoning tells us about people’s understanding of causality. Thinking & Reasoning 13(4), 426–460 (2007)CrossRefGoogle Scholar
  2. 2.
    Blake, A.: Canonical expressions in Boolean algebra. University of Chicago (1938)Google Scholar
  3. 3.
    Brown, F.M.: Boolean reasoning: the logic of Boolean equations. Courier Dover Publications (2003)Google Scholar
  4. 4.
    Dietz, E.-A., Hölldobler, S., Ragni, M.: A computational logic approach to the suppression task. In: Proceedings of the 34th Annual Conference of the Cognitive Science Society, pp. 1500–1505 (2012)Google Scholar
  5. 5.
    Karnaugh, M.: The map method for synthesis of combinational logic circuits. Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics 72(5), 593–599 (1953)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Kowalski, R.A.: The logical way to be artificially intelligent. In: Toni, F., Torroni, P. (eds.) CLIMA 2005. LNCS (LNAI), vol. 3900, pp. 1–22. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Malik, S., Zhang, L.: Boolean satisfiability from theoretical hardness to practical success. Communications of the ACM 52(8), 76–82 (2009)CrossRefGoogle Scholar
  8. 8.
    Mandziuk, J., Macukow, B.: A neural network performing boolean logic operations. Optical Memory and Neural Networks 2(1), 17–35 (1993)Google Scholar
  9. 9.
    Mccluskey, E.J.: Minimization of Boolean functions. The Bell System Technical Journal 35(5), 1417–1444 (1956)MathSciNetCrossRefGoogle Scholar
  10. 10.
    McMullen, C., Shearer, J.: Prime implicants, minimum covers, and the complexity of logic simplification. IEEE Transactions on Computers 100(8), 761–762 (1986)CrossRefGoogle Scholar
  11. 11.
    Spears, W.M.: A nn algorithm for boolean satisfiability problems. In: IEEE International Conference on Neural Networks, vol. 2, pp. 1121–1126. IEEE (1996)Google Scholar
  12. 12.
    Stenning, K., Lambalgen, M.: Semantic interpretation as computation in nonmonotonic logic: The real meaning of the suppression task. Cognitive Science 29(6), 919–960 (2005)CrossRefGoogle Scholar
  13. 13.
    Stenning, K., Van Lambalgen, M.: Human reasoning and cognitive science. The MIT Press (2008)Google Scholar
  14. 14.
    Tan, C.L., Quah, T.S., Teh, H.H.: An artificial neural network that models human decision making. Computer 29(3), 64–70 (1996)CrossRefGoogle Scholar
  15. 15.
    Teh, H.H.: Neural Logic Networks: A New Class of Neural Networks. World Scientific (1995)Google Scholar
  16. 16.
    Wang, G., Shi, H.: Tmlnn: triple-valued or multiple-valued logic neural network. IEEE Transactions on Neural Networks 9(6), 1099–1117 (1998)CrossRefGoogle Scholar
  17. 17.
    Wegener, I.: The complexity of boolean functions (1987)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Wonil Chang
    • 1
  • Hyun Ah Song
    • 2
  • Soo-Young Lee
    • 3
  1. 1.Electronics and Telecommunications Research InstituteDaejeonRepublic of Korea
  2. 2.Korea Institute of Science and TechnologySeoulRepublic of Korea
  3. 3.Department of Electrical EngineeringKAISTDaejeonRepublic of Korea

Personalised recommendations