Quantum Physics and Linguistics

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 natural language syntax and semantics. Her graduate studies in Computer Software Engineering, Logic, and Philosophy, were done in Universities of Sharif (in Iran), Ottawa and Quebec at Montreal (UQAM), and Oxford, where she was an academic visitor for half of the duration of her PhD and then an EPSRC Postdoctoral Fellow and where she is currently working as an EPSRC Career Acceleration Fellow. Mr Grefenstette is finishing a DPhil in Computer Science on the topic of exploiting category-theoretic methods from quantum information theory to add compositionality to distributional semantic models of natural language. He has a background in Physics (University of Sheffield, UK) and Philosophy (University of St Andrews, UK). He will be continuing his work on compositionality and semantics in Oxford as a postdoc, starting in Autumn 2012.

• 1. An alternative Gospel of structure: order, composition, processes ; 2. Some graphical aspects of Frobenius algebras ; 3. A graphical approach to measurement-based quantum com- puting ; 4. Quantum groups and braided algebra ; 5. Hopf algebrasDLVariant notions and reconstruction theorems ; 6. Modular Categories ; 7. Scalars, Monads, and Categories ; 8. Types and forgetfulness in categorical linguistics and quantum mechanics ; 9. From Sentence to Concept: Predicate Logic and Quantum Logic in Compact Closed Categories ; 10. Proof nets for the Lambek-Grishin calculus ; 11. Algebras over a field and semantics for context based reasoning ; 12. Distributional Semantic Models ; 13. Type-Driven Syntax and Semantics for Composing Mean- ing Vectors

This book will be of interest to people with a background in category theory, whether from a quantum physics background or linguistic background. It may also be useful to researchers who use the approach presented here to apply categorical ideas and compositional reasoning to another field of knowledge, resulting in further links being found between apparently unrelated field.