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Belnap-dunn modal logics: Truth constants VS. truth values Научная публикация

Журнал

Review of Symbolic Logic
ISSN: 1755-0203 , E-ISSN: 1755-0211

Вых. Данные

Год: 2020, Том: 13, Номер: 2, Страницы: 416-435 Страниц : 20 DOI: 10.1017/S1755020319000121

Ключевые слова

Algebraic logic; First-degree entailment; Many-valued modal logic; Strong negation

Авторы

Odintsov S.P. ¹ , Speranski S.O. ²

Организации

1	Sobolev Institute of Mathematics, 4 Koptyug Avenue, Novosibirsk, 630090, Russian Federation
2	St. Petersburg State University, Russian Federation

We shall be concerned with the modal logic BK-which is based on the Belnap-Dunn four-valued matrix, and can be viewed as being obtained from the least normal modal logic K by adding 'strong negation'. Though all four values 'truth', 'falsity', 'neither' and 'both' are employed in its Kripke semantics, only the first two are expressible as terms. We show that expanding the original language of BK to include constants for 'neither' or/and 'both' leads to quite unexpected results. To be more precise, adding one of these constants has the effect of eliminating the respective value at the level of BK-extensions. In particular, if one adds both of these, then the corresponding lattice of extensions turns out to be isomorphic to that of ordinary normal modal logics. © 2020 Cambridge University Press. All rights reserved.

Odintsov S.P. , Speranski S.O.
Belnap-dunn modal logics: Truth constants VS. truth values
Review of Symbolic Logic. 2020. V.13. N2. P.416-435. DOI: 10.1017/S1755020319000121 WOS Scopus OpenAlex

Web of science:	WOS:000528242900009
Scopus:	2-s2.0-85062032769
OpenAlex:	W2915692292

БД	Цитирований
Scopus	8
OpenAlex	10
Web of science	5