Abstract
Compact Closed categories and Frobenius and Bi algebras have been applied to model and reason about Quantum protocols. The same constructions have also been applied to reason about natural language semantics under the name: ``categorical distributional compositional'' semantics, or in short, the ``DisCoCat'' model. This model combines the statistical vector models of word meaning with the compositional models of grammatical structure. It has been applied to natural language tasks such as disambiguation, paraphrasing and entailment of phrases and sentences. The passage from the grammatical structure to vectors is provided by a functor, similar to the Quantization functor of Quantum Field Theory. The original DisCoCat model only used compact closed categories. Later, Frobenius algebras were added to it to model long distance dependancies such as relative pronouns. Recently, bialgebras have been added to the pack to reason about quantifiers. This paper reviews these constructions and their application to natural language semantics. We go over the theory and present some of the core experimental results.
Highlights
Categorical compositional distributional semantics is a model of natural language that combines the statistical vector models of word meanings with the compositional models of grammar
This passage was generalized to abstract mathematical structures and recast in terms of functors whose co-domain was FVect by Baez and Dolan [5] and Kock [6]. This is exactly what is happening in our [DisCoCat] semantic framework: the sentence formation rules are formalized using type-logics and assigned quantitative values in terms of vector composition operations. This procedure makes our passage from grammatical structure to vector space meaning a “Quantization” functor
We review the theory of pregroup algebras and exemplify its applications to reasoning about grammatical structures in natural language
Summary
Categorical compositional distributional semantics is a model of natural language that combines the statistical vector models of word meanings with the compositional models of grammar. This passage was generalized to abstract mathematical structures and recast in terms of functors whose co-domain was FVect by Baez and Dolan [5] and Kock [6] This is exactly what is happening in our [DisCoCat] semantic framework: the sentence formation rules are formalized using type-logics and assigned quantitative values in terms of vector composition operations. This procedure makes our passage from grammatical structure to vector space meaning a “Quantization” functor. We will first review the advances made in the DisCoCat model in a chronological order; go through the the core of theoretical underpinnings of the model and present some of the main experiments performed to validate the theoretical predictions
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