Quantization, Frobenius and Bi Algebras from the Categorical Framework of Quantum Mechanics to Natural Language Semantics

Frontiers in Physics

Sadrzadeh, Mehrnoosh¹ 

[1] Theory Group and Computational Linguistics Lab, School of Electronic Engineering and Computer Science, Queen Mary University, London, United Kingdom

关键词: Compact closed categories;    Frobenius algebras;    Bialgebras;    Quantisation Functor;    Categorical quantum mechanics;    Vector Space Models;    distributional semantics;    Pregroup grammars;    compositionality;    Natural Language Processing;   

DOI  :  10.3389/fphy.2017.00018

学科分类：物理（综合）

来源: Frontiers

【 摘 要 】

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.

【 授权许可】

CC BY