With computers to handle more and more complicated things in variable environments, it becomes an urgent requirement that the artificial intelligence has the ability of automatic judging and deciding according to numerous specific conditions so as to deal with the complicated and variable cases. ANNs inspired by brain is a good candidate. However, most of current numeric ANNs are not good at representing logical relations because these models still try to represent logical relations in the form of ratio based on functional approximation. On the other hand, researchers have been trying to design novel neural network models to make neural network model represent logical relations. In this work, a novel neural network model specified for representing logical relations is proposed and applied. New neurons and multiple kinds of links are defined. Inhibitory links are introduced besides exciting links. Different from current numeric ANNs, one end of an inhibitory link connects an exciting link rather than a neuron. Inhibitory links inhibit the connected exciting links conditionally to make this neural network model represent logical relations correctly. This model can simulate the operations of Boolean logic gates, and construct complex logical relations with the advantages of simpler neural network structures than recent works in this area. This work provides some ideas to make neural networks represent logical relations more directly and efficiently, and the model could be used as the complement to current numeric ANN to deal with logical issues and expand the application areas of ANN.