Graded hyponymy for compositional distributional semantics

The categorical compositional distributional model of natural language provides a conceptually motivated procedure to compute the meaning of a sentence, given its grammatical structure and the meanings of its words. This approach has outperformed other models in mainstream empirical language processing tasks, but lacks an effective model of lexical entailment. We address this shortcoming by exploiting the freedom in our abstract categorical framework to change our choice of semantic model. This allows us to describe hyponymy as a graded order on meanings, using models of partial information used in quantum computation. Quantum logic embeds in this graded order.