Zero-shot learning (ZSL) is one of the most extreme forms of learning from scarce labeled data. It enables predicting that images belong to classes for which no labeled training instances are available. In this paper, we present a new ZSL framework that leverages both label attribute side information and a semantic label hierarchy. We present two methods, lifted zero-shot prediction and a custom conditional random field (CRF) model, that integrate both forms of side information. We propose benchmark tasks for this framework that focus on making predictions across a range of semantic levels. We show that lifted zero-shot prediction can dramatically outperform baseline methods when making predictions within specified semantic levels, and that the probability distribution provided by the CRF model can be leveraged to yield further performance improvements when making unconstrained predictions over the hierarchy.