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.
We introduce two ways to detect entailment using distributional semantic representations of phrases. Our first experiment shows that the entailment relation between adjective-noun constructions and their head nouns (big cat|= cat), once represented as semantic vector pairs, generalizes to lexical entailment among nouns (dog|= animal). Our second experiment shows that a classifier fed semantic vector pairs can similarly generalize the entailment relation among quantifier phrases (many dogs|= some dogs) to entailment involving unseen quantifiers (all cats|= several cats). Moreover, nominal and quantifier phrase entailment appears to be cued by different distributional correlates, as predicted by the type-based view of entailment in formal semantics.