This paper presents a hybrid dialog state tracker enhanced by trainable Spoken Language Understanding (SLU) for slotfilling dialog systems. Our architecture is inspired by previously proposed neuralnetwork- based belief-tracking systems. In addition we extended some parts of our modular architecture with differentiable rules to allow end-to-end training. We hypothesize that these rules allow our tracker to generalize better than pure machinelearning based systems. For evaluation we used the Dialog State Tracking Challenge (DSTC) 2 dataset - a popular belief tracking testbed with dialogs from restaurant information system. To our knowledge, our hybrid tracker sets a new stateof- the-art result in three out of four categories within the DSTC2.