Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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
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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.
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/
UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-105008234135&origin=inward&txGid=6289905ab0deaf01f42dabe9d482de13
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