We propose a novel method for the injection of first-order logic formulæ in Skolemised form into neural networks of any shape. Thanks to our method, a neural network can be trained by taking prior symbolic knowledge into account, and that knowledge may be exploited by data scientists willing to control what the network should (not) learn. Differently from other related works, our method for knowledge injection (i) does not require the input formulæ to be ground, (ii) it does not imposes any constraint on the NN undergoing injection, (iii) and it does not require the loss function of the network to be affected. Conversely, it acts directly at the back propagation level, by increasing the penalty to be back-propagated whenever the NN output is violating the knowledge to be injected. Experiments are reported to demonstrate the potential (and the limits) of our approach.
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