Quantum Implications in Orthomodular Posets

J 2025

Quantum Implications in Orthomodular Posets

EMIR, Kadir and Jan PASEKA

Basic information

Original name

Quantum Implications in Orthomodular Posets

Authors

EMIR, Kadir (792 Turkey, belonging to the institution) and Jan PASEKA (203 Czech Republic, belonging to the institution)

Edition

Journal of Multiple-Valued Logic and Soft Computing, Old City Publishing Inc, 2025, 1542-3980

Other information

Language

English

Type of outcome

Article in a journal

Field of Study

10101 Pure mathematics

Country of publisher

United States of America

Confidentiality degree

is not subject to a state or trade secret

References:

URL

Impact factor

Impact factor: 0.700 in 2024

Organization unit

Faculty of Science

UT WoS

001439942900004

EID Scopus

2-s2.0-105005833402

Keywords in English

Multiple-valued implication; classical implication; Kalmbach implication; non-tollens implication; Dishkant implication; Sasaki implication; orthomodular poset; modus ponens rule

Abstract

In the original language

We show that, for every orthogonal lub-complete poset P, we can introduce multiple-valued implications sharing properties with quantum implications presented by Kalmbach for orthomodular lattices. We call them classical implication, Kalmbach implication, non-tollens implication, Dishkant implication and Sasaki implication. If the classical implication satisfies the order property, then the corresponding orthologic becomes classical and vice versa. If the Kalmbach or non-tollens or Dishkant or Sasaki implication meets the order property, then the corresponding orthologic becomes quantum and vice versa. A related result for the modus ponens rule is obtained.

Links

GF20-09869L, research and development project

Name: Ortomodularita z různých pohledů

Investor: Czech Science Foundation, Partner Agency (Austria)

MUNI/A/1099/2022, interní kód MU

Name: Specifický výzkum v odborné a učitelské matematice 2023

Investor: Masaryk University

Cite

EMIR, Kadir and Jan PASEKA. Quantum Implications in Orthomodular Posets. Journal of Multiple-Valued Logic and Soft Computing. Old City Publishing Inc, 2025, vol. 44, No 4, p. 385-405. ISSN 1542-3980.

@article{2485380,
   author = {Emir, Kadir and Paseka, Jan},
   article_number = {4},
   keywords = {Multiple-valued implication; classical implication; Kalmbach implication; non-tollens implication; Dishkant implication; Sasaki implication; orthomodular poset; modus ponens rule},
   language = {eng},
   issn = {1542-3980},
   journal = {Journal of Multiple-Valued Logic and Soft Computing},
   title = {Quantum Implications in Orthomodular Posets},
   url = {https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-44-number-4-2025/mvlsc-44-4-p-385-405/},
   volume = {44},
   year = {2025}
}

TY  - JOUR
ID  - 2485380
AU  - Emir, Kadir - Paseka, Jan
PY  - 2025
TI  - Quantum Implications in Orthomodular Posets
JF  - Journal of Multiple-Valued Logic and Soft Computing
VL  - 44
IS  - 4
SP  - 385-405
EP  - 385-405
PB  - Old City Publishing Inc
SN  - 15423980
KW  - Multiple-valued implication
KW  - classical implication
KW  - Kalmbach implication
KW  - non-tollens implication
KW  - Dishkant implication
KW  - Sasaki implication
KW  - orthomodular poset
KW  - modus ponens rule
UR  - https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-44-number-4-2025/mvlsc-44-4-p-385-405/
N2  - We show that, for every orthogonal lub-complete poset P, we can introduce multiple-valued implications sharing properties with quantum implications presented by Kalmbach for orthomodular lattices. We call them classical implication, Kalmbach implication, non-tollens implication, Dishkant implication and Sasaki implication. If the classical implication satisfies the order property, then the corresponding orthologic becomes classical and vice versa. If the Kalmbach or non-tollens or Dishkant or Sasaki implication meets the order property, then the corresponding orthologic becomes quantum and vice versa. A related result for the modus ponens rule is obtained.
ER  -

EMIR, Kadir and Jan PASEKA. Quantum Implications in Orthomodular Posets. \textit{Journal of Multiple-Valued Logic and Soft Computing}. Old City Publishing Inc, 2025, vol.~44, No~4, p.~385-405. ISSN~1542-3980.

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