- Mixing Categories and Modal Logics in the Quantum Setting
- International meeting ”Quantum Mechanics and Quantum Information: Physical, Philosophical and Logical Approaches”
- Book/source title
- Probing the Meaning of Quantum Mechanics
- Book/source subtitle
- superpositions, dynamics, semantics and identity ; Quantum Mechanics and Quantum Information: Physical, Philosophical and Logical Approaches, Cagliari, Italy, 23-25 July 2014
- Pages (from-to)
- New Jersey: World Scientific
- ISBN (electronic)
- Document type
- Conference contribution
- Interfacultary Research Institutes
Faculty of Science (FNWI)
- Institute for Logic, Language and Computation (ILLC)
The study of the foundations of Quantum Mechanics, especially after the advent of Quantum Computation and Information, has benefited from the application of category-theoretic tools and modal logics to the analysis of Quantum processes: we witness a wealth of theoretical frameworks casted in either of the two languages. This paper explores the interplay of the two formalisms in the peculiar context of Quantum Theory.
After a review of some influential abstract frameworks, we show how different modal logic frames can be extracted from the category of finite dimensional Hilbert spaces, connecting the Categorical Quantum Mechanics approach to some modal logics that have been proposed for Quantum Computing. We then apply a general version of the same technique to two other categorical frameworks, the ‘topos approach’ of Doering and Isham and the sheaf-theoretic work on contextuality by Abramsky and Brandenburger, suggesting how some key features can be expressed with modal languages.
Read More: http://www.worldscientific.com/doi/abs/10.1142/9789813146280_0003
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