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In this paper, we present a neural network structure and a fast incremental learning algorithm using this network. The proposed network structure, named evolving logic networks for real-valued inputs (ELN-R), is a data structure for storing and using the knowledge. A distinctive feature of ELN-R is that the previously learned knowledge stored in ELN-R can be used as a kind of building block in constructing new knowledge. Using this feature, the proposed learning algorithm can enhance the stability and plasticity at the same time, and as a result, the fast incremental learning can be realized. The performance of the proposed scheme is shown by a theoretical analysis and an experimental study on two benchmark problems.