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.

Basic information

Original name

An algebraic analysis of implication in non-distributive logics

Authors

CHAJDA, Ivan, Kadir EMIR (792 Turkey, belonging to the institution), Davide FAZIO (guarantor), Helmut LANGER, Antonio LEDDA and Jan PASEKA (203 Czech Republic, belonging to the institution)

Edition

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

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United Kingdom of Great Britain and Northern Ireland

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 0.700 in 2022

RIV identification code

RIV/00216224:14310/23:00134050

Organization unit

Faculty of Science

DOI

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

UT WoS

000815515700001

Keywords in English

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

Abstract

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.

Links

GF20-09869L, research and development project

Name: Ortomodularita z různých pohledů

Investor: Czech Science Foundation, Partner Agency (Austria)

Citovat

CHAJDA, Ivan, Kadir EMIR, Davide FAZIO, Helmut LANGER, Antonio LEDDA and Jan PASEKA. An algebraic analysis of implication in non-distributive logics. Journal of logic and computation. Oxford: Oxford University Press, 2023, vol. 33, No 1, p. 47-89. ISSN 0955-792X. Available from: 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 and Jan PASEKA. An algebraic analysis of implication in non-distributive logics. \textit{Journal of logic and computation}. Oxford: Oxford University Press, 2023, vol.~33, No~1, p.~47-89. ISSN~0955-792X. Available from: https://dx.doi.org/10.1093/logcom/exac041.

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