A Categorial Semantic Representation of Quantum Event Structures

Citation data:

Foundations of Physics, ISSN: 0015-9018, Vol: 43, Issue: 9, Page: 1090-1123

Publication Year:
2013
Usage 424
Downloads 352
Abstract Views 53
Full Text Views 19
Captures 8
Readers 5
Exports-Saves 3
Social Media 1
Tweets 1
Citations 5
Citation Indexes 5
Repository URL:
http://philsci-archive.pitt.edu/id/eprint/11401
DOI:
10.1007/s10701-013-9733-5
Author(s):
Zafiris, Elias; Karakostas, Vassilios
Publisher(s):
Springer Nature; Springer
Tags:
Physics and Astronomy
article description
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 classification 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. © 2013 Springer Science+Business Media New York.