  Despite their great success in recent years, deep neural networks (DNN) are
mainly black boxes where the results obtained by running through the network
are difficult to understand and interpret. Compared to e.g. decision trees or
bayesian classifiers, DNN suffer from bad interpretability where we understand
by interpretability, that a human can easily derive the relations modeled by
the network. A reasonable way to provide interpretability for humans are
logical rules. In this paper we propose neural logic rule layers (NLRL) which
are able to represent arbitrary logic rules in terms of their conjunctive and
disjunctive normal forms. Using various NLRL within one layer and
correspondingly stacking various layers, we are able to represent arbitrary
complex rules by the resulting neural network architecture. The NLRL are
end-to-end trainable allowing to learn logic rules directly from available data
sets. Experiments show that NLRL-enhanced neural networks can learn to model
arbitrary complex logic and perform arithmetic operation over the input values.
