When we represent logical, connective implications by directed edges, the resulting set of directed edges can be regarded as a complex network. In this article, we compose a network model that represents a deductive-logic-like structure composed solely of implications. The proposed network model grows like the BA model reported by Barabasi and Albert [Science 286, 509 (1999)]. Though the BA model references the whole of the existing network when a node is added, our model references only part of the existing network. In this view, our model is more realistic than the BA model. However, it also exhibits power law characteristics.