Quantum Physics and Linguistics: A Compositional, Diagrammatic Discourse

Hardcover | April 7, 2013

EditorChris Heunen, Mehrnoosh Sadrzadeh, Edward Grefenstette

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New scientific paradigms typically consist of an expansion of the conceptual language with which we describe the world. Over the past decade, theoretical physics and quantum information theory have turned to category theory to model and reason about quantum protocols. This new use ofcategorical and algebraic tools allows a more conceptual and insightful expression of elementary events such as measurements, teleportation and entanglement operations, that were obscured in previous formalisms. Recent work in natural language semantics has begun to use these categorical methods to relate grammatical analysis and semantic representations in a unified framework for analysing language meaning, and learning meaning from a corpus. A growing body of literature on the use of categorical methodsin 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. It serves as an introduction to this interdisciplinary research, and provides a basis for future research and collaboration between the different communities interested inapplying category theoretic methods to their domain's open problems.

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From the Publisher

New scientific paradigms typically consist of an expansion of the conceptual language with which we describe the world. Over the past decade, theoretical physics and quantum information theory have turned to category theory to model and reason about quantum protocols. This new use ofcategorical and algebraic tools allows a more concept...

Dr. Heunen is a mathematical physicist with an interest in logic. He obtained his PhD in mathematics and computer science at the University of Nijmegen in 2009. Currently he works as a postdoctoral researcher at the University of Oxford. Dr Sadrzadeh works on computational logical modelling and reasoning and their applications to natu...
Format:HardcoverDimensions:424 pages, 9.21 × 6.14 × 0.1 inPublished:April 7, 2013Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199646295

ISBN - 13:9780199646296

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Table of Contents

1. Bob Coecke: An alternative Gospel of structure: order, composition, processes2. Bertfried Fauser: Some graphical aspects of Frobenius algebras3. Ross Duncan: A graphical approach to measurement-based quantum com- puting4. Shahn Majid: Quantum groups and braided algebra5. Joost Vercruysse: Hopf algebras - Variant notions and reconstruction theorems6. Michael Muger: Modular Categories7. Dion Coumans and Bart Jacobs: Scalars, Monads, and Categories8. Peter Hines: Types and forgetfulness in categorical linguistics and quantum mechanics9. Anne Preller: From Sentence to Concept: Predicate Logic and Quantum Logic in Compact Closed Categories10. Michael Moortgat and Richard Moot: Proof nets for the Lambek-Grishin calculus11. Daoud Clarke: Algebras over a field and semantics for context based reasoning12. Stephen Pulman: Distributional Semantic Models13. Stephen Clark: Type-Driven Syntax and Semantics for Composing Mean- ing Vectors