By comparison with constraint satisfaction networks, this paper presents an essential frame of the logical theory for continuous-state neural networks, and gives the quantitative analyzing method for contradiction. The analysis indicates that the basic reason for the alternation of the logical states of the neurons is the existence of superior contradiction inside the networks. The dynamic process for a neural network to find a solution corresponds to eliminating the superior contradiction.
Montanari U, Rossi F. Constraint relaxation may be perfect[J].Artificial Intelligence.1991, 48(2):143-170[2]Touretzky D S, Hinton G E. A distributed connectionist production system[J].Cognitive Science.1988, 12(3):423-466[3]Guesgen H W, Hertzberg J. A constraint-based approach to sptiotemporal reasoning. Applied Intel-[4]ligence, 1991,3(1): 71-90.[5]Hopfield J J. Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Natl. Acad. Sci. USA, 1984, 3088-3092.[6]Sejnowski T J, Kienker P K, Hinton G E. Learning symmetry groups with hidden units: Beyond the perceptron. Physica, 1988, 22D: 260-275.[7]Grossberg S, Mingolla E, Todorovic D. A neural network architecture for preattentive vision. IEEE Trans. on BME, 1989, BME-36(1): 65-84.