Semantic entailment is the problem of determining if the meaning of a given sentence entails that of another. This is a fundamental problem in natural language understanding that provides a broad framework for studying language variability and has a large number of applications. This paper presents a principled approach to this problem that builds on inducing representations of text snippets into a hierarchical knowledge representation along with a sound optimization-based inferential mechanism that makes use of it to decide semantic entailment. A preliminary evaluation on the PASCAL text collection is presented.