The many-valued logic of quantum mechanics

Jarosław Pykacz

Abstract

It is shown that any quantum logic in the Birkhoff - von Neumann sense that possesses anordering set of probability measures can be isomorphically represented as a particular kindof infinite-valued Łukasiewicz logic with partially defined conjunction and disjunction. Itis argued that such non-classical features of BvN quantum logic as lack of distributivity orvalidity of the orthomodular law follow from properties of Łukasiewicz conjunction anddisjunction.
Publication typeIn press (online first, early view)
Author Jarosław Pykacz (FMPI / IM)
Jarosław Pykacz,,
- Institute of Mathematics
Journal seriesInternational Journal of Theoretical Physics, ISSN 0020-7748, e-ISSN 1572-9575, (N/A 40 pkt)
Issue year2020
Noonline first
Pages1-10
Publication size in sheets0.5
Keywords in Englishquantum logic, many-valued logic, Łukasiewicz logic
ASJC Classification2600 General Mathematics; 3101 Physics and Astronomy (miscellaneous)
DOIDOI:10.1007/s10773-019-04050
URL https://link.springer.com/content/pdf/10.1007/s10773-019-04050-6.pdf
Languageen angielski
LicenseOther; published final; Uznanie Autorstwa (CC-BY); with publication
Score (nominal)40
Score sourcejournalList
ScoreMinisterial score = 40.0, 29-02-2020, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2018 = 0.541; WoS Impact Factor: 2018 = 1.121 (2) - 2018=0.971 (5)
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