The question is that if the NNs are capable of encoding logical rules? The paper proposes a neural network and proves that the network is capable of expressing any ground truth over encoded rules in the KG. The paper focuses on one class NNs as well as one class of logical rules. Investigation of capability of different class of NNs in encoding different class of logical rules is indeed an important problem which can open a new window in front of ML.
When one is sure that the KGE model has enough capability to encode a class of logical rules, deriving a formula for each of logical rules is essential. The derived formula can be used to guide the learning process.
The paper reported that injection of rules in the learning process significantly improves performance the learner (KGE model). Therefore, the prior knowledge which is encoded as logical rules significantly improves the performance of the NN.