A weak-inference theory and a contradictory analysis for binary neural
networks (BNNs). are presented. The analysis indicates that the essen
tial reason why a neural network is changing its states is the existen
ce of superior contradiction inside the network, and that the process
by which a neural network seeks a solution corresponds to eliminating
the superior contradiction. Different from general constraint satisfac
tion networks, the solutions found by BNNs may contain inferior contra
diction but not superior contradiction.