Modal Companions for the Special Extensions of Nelson’s Constructive Logic

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Modal Companions for the Special Extensions of Nelson’s Constructive Logic. / Vishneva, A. G.; Odintsov, S. P.

в: Mathematical Notes, Том 117, № 3, 16.06.2025, стр. 366-382.

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

BibTeX

@article{5612d85bebf547dba43e5060107b1f44,

title = "Modal Companions for the Special Extensions of Nelson{\textquoteright}s Constructive Logic",

abstract = "Abstract: The Belnapian version of the normal modal logic is related to Nelson{\textquoteright}s constructive logic in approximately the same way as the logic is related to the intuitionistic logic. For this reason, it is natural to define modal companions for logics extending as extensions of the Belnapian modal logic. It is proved that, for every special extension of, the logic, where is a natural modification of the mapping assigning the least modal companion to each superintuitionistic logic, is the least modal companion of in the lattice of extensions of.",

keywords = "Belnapian modal logic, Nelson{\textquoteright}s logic, lattice of logics, modal companion, strong negation, twist structure",

author = "Vishneva, {A. G.} and Odintsov, {S. P.}",

note = "The results of Secs. and were obtained by S. P. Odintsov and the results of Sec. , by A. G. Vishneva. The work of S. P. Odintsov was financially supported by the Russian Science Foundation, project 23-11-00104, https://rscf.ru/project/23-11-00104/ , at Steklov Mathematical Institute of Russian Academy of Sciences. Vishneva, A. G. Modal Companions for the Special Extensions of Nelson's Constructive Logic / A. G. Vishneva, S. P. Odintsov // Mathematical Notes. – 2025. – Vol. 117, No. 3-4. – P. 366-382. – DOI 10.1134/S0001434625030034.",

year = "2025",

month = jun,

day = "16",

doi = "10.1134/S0001434625030034",

language = "English",

volume = "117",

pages = "366--382",

journal = "Mathematical Notes",

issn = "0001-4346",

publisher = "Pleiades Publishing",

number = "3",

}

RIS

TY - JOUR

T1 - Modal Companions for the Special Extensions of Nelson’s Constructive Logic

AU - Vishneva, A. G.

AU - Odintsov, S. P.

N1 - The results of Secs. and were obtained by S. P. Odintsov and the results of Sec. , by A. G. Vishneva. The work of S. P. Odintsov was financially supported by the Russian Science Foundation, project 23-11-00104, https://rscf.ru/project/23-11-00104/ , at Steklov Mathematical Institute of Russian Academy of Sciences. Vishneva, A. G. Modal Companions for the Special Extensions of Nelson's Constructive Logic / A. G. Vishneva, S. P. Odintsov // Mathematical Notes. – 2025. – Vol. 117, No. 3-4. – P. 366-382. – DOI 10.1134/S0001434625030034.

PY - 2025/6/16

Y1 - 2025/6/16

N2 - Abstract: The Belnapian version of the normal modal logic is related to Nelson’s constructive logic in approximately the same way as the logic is related to the intuitionistic logic. For this reason, it is natural to define modal companions for logics extending as extensions of the Belnapian modal logic. It is proved that, for every special extension of, the logic, where is a natural modification of the mapping assigning the least modal companion to each superintuitionistic logic, is the least modal companion of in the lattice of extensions of.

AB - Abstract: The Belnapian version of the normal modal logic is related to Nelson’s constructive logic in approximately the same way as the logic is related to the intuitionistic logic. For this reason, it is natural to define modal companions for logics extending as extensions of the Belnapian modal logic. It is proved that, for every special extension of, the logic, where is a natural modification of the mapping assigning the least modal companion to each superintuitionistic logic, is the least modal companion of in the lattice of extensions of.

KW - Belnapian modal logic

KW - Nelson’s logic

KW - lattice of logics

KW - modal companion

KW - strong negation

KW - twist structure

UR - https://www.mendeley.com/catalogue/d09e2ff7-411e-3a8f-8a77-c3d73d5897c8/

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UR - https://www.elibrary.ru/item.asp?id=82558356

U2 - 10.1134/S0001434625030034

DO - 10.1134/S0001434625030034

M3 - Article

VL - 117

SP - 366

EP - 382

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 3

ER -

ID: 68148821