There remains a large difference between the kinds of models typical of cognitive neuroscience versus those typical of systems neuroscience. In this paper I apply the neural engineering framework (NEF) to generate a model that is both cognitive and neural. I do this by constructing a biologically realistic model of logical inference. This model consists of a large-scale, spiking neural network that learns, encodes and manipulates language-like structures. I apply this model to the well-known Wason card selection task, and demonstrate that the model performs much like human subjects for both errors and hits.