The paper introduces a neural network-based model of logical connectives. The network consists of two types of generic OR and AND neurons structured into a three layer topology. The specificity of the logical connectives is captured by the network within its supervised learning. Further analysis of the connections of the network obtained in this way provides a better insight into the nature of the connectives for fuzzy sets; in particular the analysis can look at their non-monotomic and compensative properties. Numerical studies including the Zimmermann-Zysno data set illustrate the performance of the network.