We propose a novel application of Formal Concept Analysis (FCA) to neural decoding: instead of just trying to figure out which stimulus was presented, we demonstrate how to explore the semantic relationships between the neural representation of large sets of stimuli. FCA provides a way of displaying and interpreting such relationships via concept lattices. We explore the effects of neural code sparsity on the lattice. We then analyze neurophysiological data from high-level visual cortical area STSa, using an exact Bayesian approach to construct the formal context needed by FCA. Prominent features of the resulting concept lattices are discussed, including indications for a product-of-experts code in real neurons.