Extracting Formulae in Many-Valued Logic from Deep Neural Networks

We propose a new perspective on deep ReLU networks, namely as circuit counterparts of Lukasiewicz infinite-valued logic – a many-valued (MV) generalization of Boolean logic. An algorithm for extracting formulae in MV logic from deep ReLU networks is presented. As the algorithm applies to networks with general, in particular also real-valued, weights, it can be used to extract logical formulae from deep ReLU networks trained on data.