Abstract: We consider the problem of zero-shot learning, where the goal is to learn a classifier $f: X \rightarrow Y$ that must predict novel values of $Y$ that were omitted from the training set. To achieve this, we define the notion of a semantic output code classifier (SOC) which utilizes a knowledge base of semantic properties of $Y$ to extrapolate to novel classes. We provide a formalism for this type of classifier and study its theoretical properties in a PAC framework, showing conditions under which the classifier can accurately predict novel classes. As a case study, we build a SOC classifier for a neural decoding task and show that it can often predict words that people are thinking about from functional magnetic resonance images (fMRI) of their neural activity, even without training examples for those words.