Standard

ON EXTENSIONS OF MINIMAL LOGIC WITH LINEARITY AXIOM. / Anishchenko, D. M.; Odintsov, S. P.

в: Siberian Electronic Mathematical Reports, Том 21, № 2, 2024, стр. 852-865.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Anishchenko, DM & Odintsov, SP 2024, 'ON EXTENSIONS OF MINIMAL LOGIC WITH LINEARITY AXIOM', Siberian Electronic Mathematical Reports, Том. 21, № 2, стр. 852-865. https://doi.org/10.33048/semi.2024.21.056

APA

Anishchenko, D. M., & Odintsov, S. P. (2024). ON EXTENSIONS OF MINIMAL LOGIC WITH LINEARITY AXIOM. Siberian Electronic Mathematical Reports, 21(2), 852-865. https://doi.org/10.33048/semi.2024.21.056

Vancouver

Anishchenko DM, Odintsov SP. ON EXTENSIONS OF MINIMAL LOGIC WITH LINEARITY AXIOM. Siberian Electronic Mathematical Reports. 2024;21(2):852-865. doi: 10.33048/semi.2024.21.056

Author

Anishchenko, D. M. ; Odintsov, S. P. / ON EXTENSIONS OF MINIMAL LOGIC WITH LINEARITY AXIOM. в: Siberian Electronic Mathematical Reports. 2024 ; Том 21, № 2. стр. 852-865.

BibTeX

@article{4d7b3da8336a4d14969fb05199ee1044,
title = "ON EXTENSIONS OF MINIMAL LOGIC WITH LINEARITY AXIOM",
abstract = "The Dummett logic is a superintuitionistic logic obtained by adding the linearity axiom to intuitionistic logic. This is one of the rst non-classical logics, whose lattice of axiomatic extensions was completely described. In this paper we investigate the logic JC obtained via adding the linearity axiom to minimal logic of Johansson. So JC is a natural paraconsistent analog of the Dummett logic. We describe the lattice of JC-extensions, prove that every element of this lattice is nitely axiomatizable, has the nite model property, and is decidable. Finally, we prove that JC has exactly two pretabular extensions.",
keywords = "Dummett{\textquoteright}s logic, algebraic semantics, decidability, j-algebra, lattice of extensions, linearity axiom, minimal logic, opremum, pretabularity",
author = "Anishchenko, {D. M.} and Odintsov, {S. P.}",
note = " The work is supported by State Contracts of the Sobolev Institute of Mathematics (Project FWNF-2022-0012). ",
year = "2024",
doi = "10.33048/semi.2024.21.056",
language = "English",
volume = "21",
pages = "852--865",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",
number = "2",

}

RIS

TY - JOUR

T1 - ON EXTENSIONS OF MINIMAL LOGIC WITH LINEARITY AXIOM

AU - Anishchenko, D. M.

AU - Odintsov, S. P.

N1 - The work is supported by State Contracts of the Sobolev Institute of Mathematics (Project FWNF-2022-0012).

PY - 2024

Y1 - 2024

N2 - The Dummett logic is a superintuitionistic logic obtained by adding the linearity axiom to intuitionistic logic. This is one of the rst non-classical logics, whose lattice of axiomatic extensions was completely described. In this paper we investigate the logic JC obtained via adding the linearity axiom to minimal logic of Johansson. So JC is a natural paraconsistent analog of the Dummett logic. We describe the lattice of JC-extensions, prove that every element of this lattice is nitely axiomatizable, has the nite model property, and is decidable. Finally, we prove that JC has exactly two pretabular extensions.

AB - The Dummett logic is a superintuitionistic logic obtained by adding the linearity axiom to intuitionistic logic. This is one of the rst non-classical logics, whose lattice of axiomatic extensions was completely described. In this paper we investigate the logic JC obtained via adding the linearity axiom to minimal logic of Johansson. So JC is a natural paraconsistent analog of the Dummett logic. We describe the lattice of JC-extensions, prove that every element of this lattice is nitely axiomatizable, has the nite model property, and is decidable. Finally, we prove that JC has exactly two pretabular extensions.

KW - Dummett’s logic

KW - algebraic semantics

KW - decidability

KW - j-algebra

KW - lattice of extensions

KW - linearity axiom

KW - minimal logic

KW - opremum

KW - pretabularity

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85207355453&origin=inward&txGid=597ed5ae13a24242fbd1b9ba7d91fc1e

UR - https://www.mendeley.com/catalogue/1c609356-41d9-3083-b7a2-19ae90bb50a1/

U2 - 10.33048/semi.2024.21.056

DO - 10.33048/semi.2024.21.056

M3 - Article

VL - 21

SP - 852

EP - 865

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 2

ER -

ID: 61307436