Varieties of Orthocomplemented Lattices Induced by Lukasiewicz-Groupoid-Valued Mappings

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F17%3A00315746" target="_blank" >RIV/68407700:21230/17:00315746 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1007/s10773-017-3411-x" target="_blank" >http://dx.doi.org/10.1007/s10773-017-3411-x</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10773-017-3411-x" target="_blank" >10.1007/s10773-017-3411-x</a>

Result language

angličtina

Original language name

Varieties of Orthocomplemented Lattices Induced by Lukasiewicz-Groupoid-Valued Mappings

Original language description

In the logico-algebraic approach to the foundation of quantum mechanics we sometimes identify the set of events of the quantum experiment with an orthomodular lattice ("quantum logic"). The states are then usually associated with (normalized) finitely additive measures ("states"). The conditions imposed on states then define classes of orthomodular lattices that are sometimes found to be universal-algebraic varieties. In this paper we adopt a conceptually different approach, we relax orthomodular to orthocomplemented and we replace the states with certain subadditive mappings that range in the Aukasiewicz groupoid. We then show that when we require a type of "fulness" of these mappings, we obtain varieties of orthocomplemented lattices. Some of these varieties contain the projection lattice in a Hilbert space so there is a link to quantum logic theories. Besides, on the purely algebraic side, we present a characterization of orthomodular lattices among the orthocomplemented ones. - The intention of our approach is twofold. First, we recover some of the Mayet varieties in a principally different way (indeed, we also obtain many other new varieties). Second, by introducing an interplay of the lattice, measure-theoretic and fuzzy-set notions we intend to add to the concepts of quantum axiomatics.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10300 - Physical sciences

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2017

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

International Journal of Theoretical Physics

ISSN

0020-7748

e-ISSN

1572-9575

Volume of the periodical

56

Issue of the periodical within the volume

12

Country of publishing house

US - UNITED STATES

Number of pages

13

Pages from-to

4004-4016

UT code for WoS article

000414787000028

EID of the result in the Scopus database

2-s2.0-85019717696