Compositional Hyponymy with Positive Operators

Language is used to describe concepts, and many of these concepts are hierarchical. Moreover, this hierarchy should be compatible with forming phrases and sentences. We use linear-algebraic methods that allow us to encode words as collections of vectors. The representations we use have an ordering, related to subspace inclusion, which we interpret as modelling hierarchical information. The word representations built can be understood within a compositional distributional semantic framework, providing methods for composing words to form phrase and sentence level representations. We show that the resulting representations give competitive results on both word-level hyponymy and sentence-level entailment datasets.