Concrete Quantum Logics and Delta-Logics, States and Delta-States

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F17%3A00315747" target="_blank" >RIV/68407700:21230/17:00315747 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s10773-017-3359-x" target="_blank" >http://dx.doi.org/10.1007/s10773-017-3359-x</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10773-017-3359-x" target="_blank" >10.1007/s10773-017-3359-x</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Concrete Quantum Logics and Delta-Logics, States and Delta-States

Popis výsledku v původním jazyce

By a concrete quantum logic (in short, by a logic) we mean the orthomodular poset that is set-representable. If L = (Omega, L) is a logic and L is closed under the formation of symmetric difference, Delta, we call L a Delta-logic. In the first part we situate the known results on logics and states to the context of Delta-logics and Delta-states (the Delta-states are the states that are subadditive with respect to the symmetric difference). Moreover, we observe that the rather prominent logic epsilon(even)(Omega) of all even- coeven subsets of the countable set Omega possesses only Delta-states. Then we show when a state on the logics given by the divisibility relation allows for an extension as a state. In the next paragraph we consider the so called density logic and its Delta-closure. We find that the Delta-closure coincides with the power set. Then we investigate other properties of the density logic and its factor.

Název v anglickém jazyce

Concrete Quantum Logics and Delta-Logics, States and Delta-States

Popis výsledku anglicky

By a concrete quantum logic (in short, by a logic) we mean the orthomodular poset that is set-representable. If L = (Omega, L) is a logic and L is closed under the formation of symmetric difference, Delta, we call L a Delta-logic. In the first part we situate the known results on logics and states to the context of Delta-logics and Delta-states (the Delta-states are the states that are subadditive with respect to the symmetric difference). Moreover, we observe that the rather prominent logic epsilon(even)(Omega) of all even- coeven subsets of the countable set Omega possesses only Delta-states. Then we show when a state on the logics given by the divisibility relation allows for an extension as a state. In the next paragraph we consider the so called density logic and its Delta-closure. We find that the Delta-closure coincides with the power set. Then we investigate other properties of the density logic and its factor.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10300 - Physical sciences

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

International Journal of Theoretical Physics

ISSN

0020-7748

e-ISSN

1572-9575

Svazek periodika

56

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

8

Strana od-do

3852-3859

Kód UT WoS článku

000414787000014

EID výsledku v databázi Scopus

2-s2.0-85017183334