Ambiguity in Categorical Models of Meaning
Robin Piedeleu · 2014
Building on existing categorical accounts of natural language semantics, we propose a compositional distributional model of ambiguous meaning. Originally inspired by the high-level category theoretic language of quantum information protocols, the compositional, distributional categorical model provides a conceptually motivated procedure to compute the meaning of a sentence, given its grammatical structure and an empirical derivation of the meaning of its parts. Grammar is given a type-logical description in a compact closed category while the meaning of words is represented in a finite inner product space model. Since the category of finite-dimensional Hilbert spaces is also compact closed, the type-checking deduction process lifts to a concrete meaning-vector computation via a strong monoidal functor between the two categories. The advantage of reasoning with these structures is that grammatical composition admits an interpretation in terms of flow of meaning between words. Pushing the analogy with quantum mechanics further, we describe ambiguous words as statistical ensembles of unambiguous concepts and extend the semantics of the previous model to a category that supports probabilistic mixing. We introduce two different Frobenius algebras representing different ways of composing the meaning of words, and discuss their properties. We conclude with a range of applications to the case of definitions, including a meaning update rule that reconciles the meaning of an ambiguous word with that of its definition.