Efficient inference in neural networks is now one of the key research topics due to the many interesting applications. In this work, we are following the idea from [15] by applying a similar technique based on the Zadeh T-norm to enable a gradient-based neural networks training. In order to do that, we relax the discrete logic gates into a continuous form using Zadeh’s T-norm for the continuous relaxation of the logic gate operations. For each neuron, we learn a probability distribution over 16 possible Binary Logic Gates using softmax. After training, each neuron is assigned the most likely (hard) logic gate based on this learned distribution. Using the Zadeh’s T-norm provides a different, potentially more stable and efficient way to relax the logic operations compared to the Menger’s T-norm. Our work offers a significant speed-up in inference compared to the standard fully-connected neural networks similarly as the method presented in [15]. However, our logic gate networks based on Zadeh’s T-norm can achieve competitive accuracy to the original method based on Menger’s T-norm proposed in [15].