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Non-Deterministic Semantics for Quantum States
In this work, we discuss the failure of the principle of truth functionality in the quantum formalism. By exploiting this failure, we import the formalism of N-matrix theory and non-deterministic semantics to the foundations of quantum mechanics. This is done by describing quantum states as particul...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2020
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516569/ https://www.ncbi.nlm.nih.gov/pubmed/33285931 http://dx.doi.org/10.3390/e22020156 |
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author | Jorge, Juan Pablo Holik, Federico |
author_facet | Jorge, Juan Pablo Holik, Federico |
author_sort | Jorge, Juan Pablo |
collection | PubMed |
description | In this work, we discuss the failure of the principle of truth functionality in the quantum formalism. By exploiting this failure, we import the formalism of N-matrix theory and non-deterministic semantics to the foundations of quantum mechanics. This is done by describing quantum states as particular valuations associated with infinite non-deterministic truth tables. This allows us to introduce a natural interpretation of quantum states in terms of a non-deterministic semantics. We also provide a similar construction for arbitrary probabilistic theories based in orthomodular lattices, allowing to study post-quantum models using logical techniques. |
format | Online Article Text |
id | pubmed-7516569 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-75165692020-11-09 Non-Deterministic Semantics for Quantum States Jorge, Juan Pablo Holik, Federico Entropy (Basel) Article In this work, we discuss the failure of the principle of truth functionality in the quantum formalism. By exploiting this failure, we import the formalism of N-matrix theory and non-deterministic semantics to the foundations of quantum mechanics. This is done by describing quantum states as particular valuations associated with infinite non-deterministic truth tables. This allows us to introduce a natural interpretation of quantum states in terms of a non-deterministic semantics. We also provide a similar construction for arbitrary probabilistic theories based in orthomodular lattices, allowing to study post-quantum models using logical techniques. MDPI 2020-01-28 /pmc/articles/PMC7516569/ /pubmed/33285931 http://dx.doi.org/10.3390/e22020156 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Jorge, Juan Pablo Holik, Federico Non-Deterministic Semantics for Quantum States |
title | Non-Deterministic Semantics for Quantum States |
title_full | Non-Deterministic Semantics for Quantum States |
title_fullStr | Non-Deterministic Semantics for Quantum States |
title_full_unstemmed | Non-Deterministic Semantics for Quantum States |
title_short | Non-Deterministic Semantics for Quantum States |
title_sort | non-deterministic semantics for quantum states |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516569/ https://www.ncbi.nlm.nih.gov/pubmed/33285931 http://dx.doi.org/10.3390/e22020156 |
work_keys_str_mv | AT jorgejuanpablo nondeterministicsemanticsforquantumstates AT holikfederico nondeterministicsemanticsforquantumstates |