  Distributional semantics creates vector-space representations that capture
many forms of semantic similarity, but their relation to semantic entailment
has been less clear. We propose a vector-space model which provides a formal
foundation for a distributional semantics of entailment. Using a mean-field
approximation, we develop approximate inference procedures and entailment
operators over vectors of probabilities of features being known (versus
unknown). We use this framework to reinterpret an existing
distributional-semantic model (Word2Vec) as approximating an entailment-based
model of the distributions of words in contexts, thereby predicting lexical
entailment relations. In both unsupervised and semi-supervised experiments on
hyponymy detection, we get substantial improvements over previous results.
