Holistic Type Extension for Classical Logic via Toffoli Quantum Gate

A holistic extension of classical propositional logic is introduced via Toffoli quantum gate. This extension is based on the framework of the so-called “quantum computation with mixed states”, where also irreversible transformations are taken into account. Formal aspects of this new logical system a...

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Detalles Bibliográficos
Autores principales: Freytes, Hector, Giuntini, Roberto, Sergioli, Giuseppe
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2019
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7515129/
https://www.ncbi.nlm.nih.gov/pubmed/33267350
http://dx.doi.org/10.3390/e21070636
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author Freytes, Hector
Giuntini, Roberto
Sergioli, Giuseppe
author_facet Freytes, Hector
Giuntini, Roberto
Sergioli, Giuseppe
author_sort Freytes, Hector
collection PubMed
description A holistic extension of classical propositional logic is introduced via Toffoli quantum gate. This extension is based on the framework of the so-called “quantum computation with mixed states”, where also irreversible transformations are taken into account. Formal aspects of this new logical system are detailed: in particular, the concepts of tautology and contradiction are investigated in this extension. These concepts turn out to receive substantial changes due to the non-separability of some quantum states; as an example, Werner states emerge as particular cases of “holistic” contradiction.
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spelling pubmed-75151292020-11-09 Holistic Type Extension for Classical Logic via Toffoli Quantum Gate Freytes, Hector Giuntini, Roberto Sergioli, Giuseppe Entropy (Basel) Article A holistic extension of classical propositional logic is introduced via Toffoli quantum gate. This extension is based on the framework of the so-called “quantum computation with mixed states”, where also irreversible transformations are taken into account. Formal aspects of this new logical system are detailed: in particular, the concepts of tautology and contradiction are investigated in this extension. These concepts turn out to receive substantial changes due to the non-separability of some quantum states; as an example, Werner states emerge as particular cases of “holistic” contradiction. MDPI 2019-06-27 /pmc/articles/PMC7515129/ /pubmed/33267350 http://dx.doi.org/10.3390/e21070636 Text en © 2019 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
Freytes, Hector
Giuntini, Roberto
Sergioli, Giuseppe
Holistic Type Extension for Classical Logic via Toffoli Quantum Gate
title Holistic Type Extension for Classical Logic via Toffoli Quantum Gate
title_full Holistic Type Extension for Classical Logic via Toffoli Quantum Gate
title_fullStr Holistic Type Extension for Classical Logic via Toffoli Quantum Gate
title_full_unstemmed Holistic Type Extension for Classical Logic via Toffoli Quantum Gate
title_short Holistic Type Extension for Classical Logic via Toffoli Quantum Gate
title_sort holistic type extension for classical logic via toffoli quantum gate
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7515129/
https://www.ncbi.nlm.nih.gov/pubmed/33267350
http://dx.doi.org/10.3390/e21070636
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