An algebraic analysis of implication in non-distributive logics

J 2023

An algebraic analysis of implication in non-distributive logics

CHAJDA, Ivan, Kadir EMIR, Davide FAZIO, Helmut LANGER, Antonio LEDDA et. al.

Základní údaje

Originální název

An algebraic analysis of implication in non-distributive logics

Autoři

CHAJDA, Ivan, Kadir EMIR (792 Turecko, domácí), Davide FAZIO (garant), Helmut LANGER, Antonio LEDDA a Jan PASEKA (203 Česká republika, domácí)

Vydání

Journal of logic and computation, Oxford, Oxford University Press, 2023, 0955-792X

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Velká Británie a Severní Irsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.700 v roce 2022

Kód RIV

RIV/00216224:14310/23:00134050

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.1093/logcom/exac041

UT WoS

000815515700001

Klíčová slova anglicky

Hilbert algebras; skew Hilbert algebras; pseudocomplemented lattices; sectionally pseudocomplemented lattices; orthomodular lattices; implication algebras

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 6. 3. 2024 10:39, Mgr. Marie Šípková, DiS.

Anotace

V originále

In this paper, we introduce the concept of a (lattice) skew Hilbert algebra as a natural generalization of Hilbert algebras. This notion allows a unified treatment of several structures of prominent importance for mathematical logic, e.g. (generalized) orthomodular lattices, and MV-algebras, which admit a natural notion of implication. In fact, it turns out that skew Hilbert algebras play a similar role for (strongly) sectionally pseudocomplemented posets as Hilbert algebras do for relatively pseudocomplemented ones. We will discuss basic properties of closed, dense and weakly dense elements of skew Hilbert algebras and their applications, and we will provide some basic results on their structure theory.

Návaznosti

GF20-09869L, projekt VaV

Název: Ortomodularita z různých pohledů

Investor: Grantová agentura ČR, Ortomodularita z různých pohledů, Partnerská agentura (Rakousko)

Citovat

CHAJDA, Ivan, Kadir EMIR, Davide FAZIO, Helmut LANGER, Antonio LEDDA a Jan PASEKA. An algebraic analysis of implication in non-distributive logics. Journal of logic and computation. Oxford: Oxford University Press, 2023, roč. 33, č. 1, s. 47-89. ISSN 0955-792X. Dostupné z: https://dx.doi.org/10.1093/logcom/exac041.

@article{2250993,
   author = {Chajda, Ivan and Emir, Kadir and Fazio, Davide and Langer, Helmut and Ledda, Antonio and Paseka, Jan},
   article_location = {Oxford},
   article_number = {1},
   doi = {http://dx.doi.org/10.1093/logcom/exac041},
   keywords = {Hilbert algebras; skew Hilbert algebras; pseudocomplemented lattices; sectionally pseudocomplemented lattices; orthomodular lattices; implication algebras},
   language = {eng},
   issn = {0955-792X},
   journal = {Journal of logic and computation},
   title = {An algebraic analysis of implication in non-distributive logics},
   url = {https://doi.org/10.1093/logcom/exac041},
   volume = {33},
   year = {2023}
}

TY  - JOUR
ID  - 2250993
AU  - Chajda, Ivan - Emir, Kadir - Fazio, Davide - Langer, Helmut - Ledda, Antonio - Paseka, Jan
PY  - 2023
TI  - An algebraic analysis of implication in non-distributive logics
JF  - Journal of logic and computation
VL  - 33
IS  - 1
SP  - 47-89
EP  - 47-89
PB  - Oxford University Press
SN  - 0955792X
KW  - Hilbert algebras
KW  - skew Hilbert algebras
KW  - pseudocomplemented lattices
KW  - sectionally pseudocomplemented lattices
KW  - orthomodular lattices
KW  - implication algebras
UR  - https://doi.org/10.1093/logcom/exac041
N2  - In this paper, we introduce the concept of a (lattice) skew Hilbert algebra as a natural generalization of Hilbert algebras. This notion allows a unified treatment of several structures of prominent importance for mathematical logic, e.g. (generalized) orthomodular lattices, and MV-algebras, which admit a natural notion of implication. In fact, it turns out that skew Hilbert algebras play a similar role for (strongly) sectionally pseudocomplemented posets as Hilbert algebras do for relatively pseudocomplemented ones. We will discuss basic properties of closed, dense and weakly dense elements of skew Hilbert algebras and their applications, and we will provide some basic results on their structure theory.
ER  -

CHAJDA, Ivan, Kadir EMIR, Davide FAZIO, Helmut LANGER, Antonio LEDDA a Jan PASEKA. An algebraic analysis of implication in non-distributive logics. \textit{Journal of logic and computation}. Oxford: Oxford University Press, 2023, roč.~33, č.~1, s.~47-89. ISSN~0955-792X. Dostupné z: https://dx.doi.org/10.1093/logcom/exac041.

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