Implication in Sharply Paraorthomodular and Relatively
Paraorthomodular Posets

C 2024

Implication in Sharply Paraorthomodular and Relatively Paraorthomodular Posets

CHAJDA, Ivan, Davide FAZIO, Helmut LÄNGER, Antonio LEDDA, Jan PASEKA et. al.

Basic information

Original name

Implication in Sharply Paraorthomodular and Relatively Paraorthomodular Posets

Authors

CHAJDA, Ivan, Davide FAZIO, Helmut LÄNGER, Antonio LEDDA and Jan PASEKA (203 Czech Republic, belonging to the institution)

Edition

Cham, Janusz Czelakowski on Logical Consequence, p. 419-446, 28 pp. Outstanding Contributions to Logic, volume 27, 2024

Publisher

Springer

Other information

Language

English

Type of outcome

Kapitola resp. kapitoly v odborné knize

Field of Study

10101 Pure mathematics

Country of publisher

Switzerland

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

printed version "print"

References:

URL

Organization unit

Faculty of Science

ISBN

978-3-031-44489-0

DOI

http://dx.doi.org/10.1007/978-3-031-44490-6_15

Keywords in English

Adjointness; Amalgam of Kleene lattices; Atomic amalgam; Kleene lattice; Kleene poset; Logics of quantum mechanics; Orthogonal poset; Orthomodular lattice; Orthomodular poset; Paraorthomodular poset; Relatively paraorthomodular poset; Sasaki implication

Abstract

V originále

In this paper we show that several classes of partially ordered structures having paraorthomodular reducts, or whose sections may be regarded as paraorthomodular posets, admit a quite natural notion of implication, that admits a suitable notion of adjointness. Within this framework, we propose a smooth generalization of celebrated Greechie’s theorems on amalgams of finite Boolean algebras to the realm of Kleene lattices.

Links

GF20-09869L, research and development project

Name: Ortomodularita z různých pohledů

Investor: Czech Science Foundation, Partner Agency (Austria)

Citovat

CHAJDA, Ivan, Davide FAZIO, Helmut LÄNGER, Antonio LEDDA and Jan PASEKA. Implication in Sharply Paraorthomodular and Relatively Paraorthomodular Posets. In Malinowski, J., Palczewski, R. Janusz Czelakowski on Logical Consequence. Cham: Springer, 2024, p. 419-446. Outstanding Contributions to Logic, volume 27. ISBN 978-3-031-44489-0. Available from: https://dx.doi.org/10.1007/978-3-031-44490-6_15.

@inbook{2392958,
   author = {Chajda, Ivan and Fazio, Davide and Länger, Helmut and Ledda, Antonio and Paseka, Jan},
   address = {Cham},
   booktitle = {Janusz Czelakowski on Logical Consequence},
   doi = {http://dx.doi.org/10.1007/978-3-031-44490-6_15},
   editor = {Malinowski, J., Palczewski, R.},
   keywords = {Adjointness; Amalgam of Kleene lattices; Atomic amalgam; Kleene lattice; Kleene poset; Logics of quantum mechanics; Orthogonal poset; Orthomodular lattice; Orthomodular poset; Paraorthomodular poset; Relatively paraorthomodular poset; Sasaki implication},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {Cham},
   isbn = {978-3-031-44489-0},
   pages = {419-446},
   publisher = {Springer},
   title = {Implication in Sharply Paraorthomodular and Relatively Paraorthomodular Posets},
   url = {https://link.springer.com/chapter/10.1007/978-3-031-44490-6_15},
   year = {2024}
}

TY  - CHAP
ID  - 2392958
AU  - Chajda, Ivan - Fazio, Davide - Länger, Helmut - Ledda, Antonio - Paseka, Jan
PY  - 2024
TI  - Implication in Sharply Paraorthomodular and Relatively Paraorthomodular Posets
VL  - Outstanding Contributions to Logic, volume 27
PB  - Springer
CY  - Cham
SN  - 9783031444890
KW  - Adjointness
KW  - Amalgam of Kleene lattices
KW  - Atomic amalgam
KW  - Kleene lattice
KW  - Kleene poset
KW  - Logics of quantum mechanics
KW  - Orthogonal poset
KW  - Orthomodular lattice
KW  - Orthomodular poset
KW  - Paraorthomodular poset
KW  - Relatively paraorthomodular poset
KW  - Sasaki implication
UR  - https://link.springer.com/chapter/10.1007/978-3-031-44490-6_15
N2  - In this paper we show that several classes of partially ordered structures having paraorthomodular reducts, or whose sections may be regarded as paraorthomodular posets, admit a quite natural notion of implication, that admits a suitable notion of adjointness. Within this framework, we propose a smooth generalization of celebrated Greechie’s theorems on amalgams of finite Boolean algebras to the realm of Kleene lattices.
ER  -

CHAJDA, Ivan, Davide FAZIO, Helmut LÄNGER, Antonio LEDDA and Jan PASEKA. Implication in Sharply Paraorthomodular and Relatively Paraorthomodular Posets. In Malinowski, J., Palczewski, R. \textit{Janusz Czelakowski on Logical Consequence}. Cham: Springer, 2024, p.~419-446. Outstanding Contributions to Logic, volume 27. ISBN~978-3-031-44489-0. Available from: https://dx.doi.org/10.1007/978-3-031-44490-6\_{}15.

Detailed Information on Publication Record