Zafiris, Elias and Karakostas, Vassilios (2013) A Categorial Semantic Representation of Quantum Event Structures. Foundations of Physics, 43 (9). pp. 1090-1123. ISSN 1572-9516
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Abstract
The overwhelming majority of the attempts in exploring the problems related to quantum logical structures and their interpretation have been based on an underlying set-theoretic syntactic language. We propose a transition in the involved syntactic language to tackle these problems from the set-theoretic to the category-theoretic mode, together with a study of the consequent semantic transition in the logical interpretation of quantum event structures. In the present work, this is realized by representing categorically the global structure of a quantum algebra of events (or propositions) in terms of sheaves of local Boolean frames forming Boolean localization functors. The category of sheaves is a topos providing the possibility of applying the powerful logical classiffication methodology of topos theory with reference to the quantum world. In particular, we show that the topos-theoretic representation scheme of quantum event algebras by means of Boolean localization functors incorporates an object of truth values, which constitutes the appropriate tool for the definition of quantum truth-value assignments to propositions describing the behavior of quantum systems. Effectively, this scheme induces a revised realist account of truth in the quantum domain of discourse. We also include an appendix, where we compare our topos-theoretic representation scheme of quantum event algebras with other categorial and topos-theoretic approaches.
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| Item Type: | Published Article or Volume | |||||||||
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| Keywords: | Quantum Mechanics, Category Theory, Topos Theory, Subobject Classifier, Kochen-Specker Theorem, Quantum Truth Valuation, Adjoint Functors, Realist Account | |||||||||
| Subjects: | Specific Sciences > Computation/Information > Quantum Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Quantum Mechanics General Issues > Structure of Theories |
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| Depositing User: | Prof. Vassilios Karakostas | |||||||||
| Date Deposited: | 06 Apr 2015 18:57 | |||||||||
| Last Modified: | 06 Apr 2015 18:57 | |||||||||
| Item ID: | 11401 | |||||||||
| Journal or Publication Title: | Foundations of Physics | |||||||||
| Publisher: | Springer | |||||||||
| Official URL: | http://link.springer.com/article/10.1007/s10701-01... | |||||||||
| DOI or Unique Handle: | 10.1007/s10701-013-9733-5 | |||||||||
| Subjects: | Specific Sciences > Computation/Information > Quantum Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Quantum Mechanics General Issues > Structure of Theories |
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| Date: | 10 August 2013 | |||||||||
| Page Range: | pp. 1090-1123 | |||||||||
| Volume: | 43 | |||||||||
| Number: | 9 | |||||||||
| ISSN: | 1572-9516 | |||||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/11401 |
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