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@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.
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