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A Categorial Semantic Representation of Quantum Event Structures

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
Creators:
CreatorsEmailORCID
Zafiris, Eliasezafiris@math.uoa.gr
Karakostas, Vassilioskarakost@phs.uoa.gr
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
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: https://doi.org/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
Date: 10 August 2013
Page Range: pp. 1090-1123
Volume: 43
Number: 9
ISSN: 1572-9516
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/11401

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