Previous theoretical studies on the interaction of excitatory and inhibitory neurons proposed to model this cortical microcircuit motif as a so-called Winner-Take-All (WTA) circuit. A recent modeling study however found that the WTA model is not adequate for data-based softer forms of divisive inhibition as found in a microcircuit motif in cortical layer 2/3. We investigate here through theoretical analysis the role of such softer divisive inhibition for the emergence of computational operations and neural codes under spike-timing dependent plasticity (STDP). We show that in contrast to WTA models - where the network activity has been interpreted as probabilistic inference in a generative mixture distribution - this network dynamics approximates inference in a noisy-OR-like generative model that explains the network input based on multiple hidden causes. Furthermore, we show that STDP optimizes the parameters of this model by approximating online the expectation maximization (EM) algorithm. This theoretical analysis corroborates a preceding modelling study which suggested that the learning dynamics of this layer 2/3 microcircuit motif extracts a specific modular representation of the input and thus performs blind source separation on the input statistics.