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A Learning Multiple-Valued Logic Network: Algebra, Algorithm, and Applications
February 1998 (vol. 47 no. 2)
pp. 247-251

Abstract—We propose a multiple-valued logic (MVL) network with functional completeness and develop its learning capability. The MVL network consists of layered arithmetic piecewise linear processors. Since the arithmetic operations of the network are basically a wired-sum and a piecewise linear operation, their implementations should be rather simple and straightforward. Furthermore, the MVL network can be trained by the traditional backpropagation algorithm directly. The algorithm trains the networks using examples and appears to be available for most MVL problems of interest.

[1] G. Epstein, G. Frieder, and D.C. Rine, "The Development of Multiple-Valued Logic as Related to Computer Science," Computer, vol. 7, pp. 20-32, 1974.
[2] K.C. Smith, "The Prospects for Multivalued Logic: A Technology and Application View," IEEE Trans. Computers, vol. 30, pp. 619-634, 1981.
[3] S.L. Hurst, "Multiple-Valued Logic—Its Status and Its Future," IEEE Trans. Computers, vol. 33, no. 12, pp. 1,160-1,179, Dec. 1984.
[4] M. Kameyama, T. Hanyu, and T. Higuchi, "Design and Implementation of Quaternary NMOS Integrated Circuits for Pipe-Line Image Processing," IEEE J. Solid-State Circuits, vol. 12, no. 1, pp. 20-27, 1987.
[5] K.C. Smith, "A Multiple-Valued Logic: A Tutorial and Appreciation," Computer, vol. 21, no. 4, pp. 17-27, Apr. 1988.
[6] J.J. Hopfield and D.W. Tank, "Simple Neural Optimization Networks: An A/D Converter, Signal Decision Circuit, and a Linear Programming Circuit," IEEE Trans. Circuits and Systems, vol. 33, pp. 533-541, May 1986.
[7] Z. Tang, O. Ishizuka, and H. Matsumoto, "Implementing Nerual Architecture Using CMOS Current-Mode VLSI Circuits," IEICE Trans. Fundamentals, vol. 74, no. 5, pp. 1,329-1,336, May 1991.
[8] Z. Tang, O. Ishizuka, and H. Matsumoto, "Multiple-Valued Neuro-Algebra," IEICE Trans. Fundamentals, vol. 76A, no. 9, pp. 1,541-1,543, Sept. 1993.
[9] H.R. Berenji and P. Khedkar, "Learning and Training Fuzzy Logic Controllers Through Reinforcements," IEEE Trans. Neural Networks, vol. 3, no. 5, pp. 724-740, 1992.
[10] R. Rosenblatt, Principles of Neurodynamics.New York: Spartan Book, 1959.
[11] A. Kramer and A. Sangiovanni-Vincentelli, "Efficient Parallel Learning Algorithm for Neural Networks," Advances in Neural Information Systems, vol. 1, pp. 40-48.San Mateo, Calif.: Morgan Kaufmann, 1989.

Index Terms:
Multiple-valued logic, learning capability, functional completeness, backpropagation algorithm.
Citation:
Zheng Tang, Qi-ping Cao, Okihiko Ishizuka, "A Learning Multiple-Valued Logic Network: Algebra, Algorithm, and Applications," IEEE Transactions on Computers, vol. 47, no. 2, pp. 247-251, Feb. 1998, doi:10.1109/12.663773
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