Quantum physics and linguistics : a compositional, diagrammatic discourse / edited by Chris Heunen, Mehrnoosh Sadrzadeh, and Edward Grefenstette.

Format:

Book

Contributor:

Heunen, Christiaan Johan Marie, editor.

Sadrzadeh, Mehrnoosh, editor.

Grefenstette, Edward, editor.

Language:

English

Subjects (All):

Information modeling.

Conceptual structures (Information theory).

Quantum theory.

Computational linguistics.

Physical Description:

1 online resource (430 p.)

Edition:

First edition.

Place of Publication:

Oxford : Oxford University Press, 2013.

Language Note:

English

Summary:

A growing body of literature on the use of categorical methods in quantum information theory and computational linguistics shows both the need and opportunity for new research on the relation between these categorical methods and the abstract notion of information flow. This book supplies an overview of how categorical methods are used to model information flow in both physics and linguistics.

Contents:

""Cover""; ""Contents""; ""1 An Alternative Gospel of Structure: Order, Composition, Processes""; ""1.1 Order""; ""1.2 Orders and composition""; ""1.3 Processes witnessing existence""; ""1.4 Conclusion""; ""2 Some Graphical Aspects of Frobenius Algebras""; ""2.1 Introduction""; ""2.2 Graphical calculus""; ""2.3 Frobenius and Hopf algebras""; ""2.4 A few pointers to further literature""; ""3 A Graphical Approach to Measurement-Based Quantum Computing""; ""3.1 Introduction""; ""3.2 The rudiments of quantum computing""; ""3.3 Observables and strong complementarity""; ""3.4 The zx-calculus""

""3.5 The measurement calculus""""3.6 Determinism and flow""; ""3.7 Conclusions""; ""4 Quantum Groups and Braided Algebra""; ""4.1 Introduction""; ""4.2 Braided categories""; ""4.3 Braided groups""; ""4.4 Applications of braided groups""; ""4.5 Braided-Lie algebras""; ""4.6 Diagrammatic geometry""; ""5 Hopf Algebras�Variant Notions and Reconstruction Theorems""; ""5.1 Introduction""; ""5.2 Preliminaries""; ""5.3 Bialgebras and Hopf algebras in monoidal categories""; ""5.4 Reconstruction theorems""; ""5.5 Variations on the notion of Hopf algebra""; ""6 Modular Categories""

""6.1 Introduction""""6.2 Categories""; ""6.3 Tensor categories""; ""6.4 Braided tensor categories""; ""6.5 Modular categories""; ""6.6 Modularization of pre-modular categories: generalizations""; ""6.7 The braided centre of a fusion category""; ""6.8 The Witt group of modular categories""; ""7 Scalars, Monads, and Categories""; ""7.1 Introduction""; ""7.2 Preliminaries""; ""7.3 Monoids""; ""7.4 Additive monads""; ""7.5 Semirings and monads""; ""7.6 Semirings and Lawvere theories""; ""7.7 Semirings with involutions""; ""7.8 Conclusions""

""8 Types and Forgetfulness in Categorical Linguistics and Quantum Mechanics""""8.1 Introduction""; ""8.2 Introducing typing to models of meaning""; ""8.3 What is a type?""; ""8.4 Comparing words versus comparing sentences""; ""8.5 Inner products, evaluation, and inverses""; ""8.6 Does evaluation preserve inner products?""; ""8.7 How to type connectives?""; ""8.8 Self-similarity, categorically""; ""8.9 Self-similarity and lax Frobenius algebras""; ""8.10 Classical structures""; ""8.11 A self-similar structure familiar in logic (and linguistics)""

""10.3 Proof nets and focused display calculus""

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

0-19-165031-5

0-19-174784-X

OCLC:

922972895