Belnap-dunn modal logics: Truth constants VS. truth values Full article
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Review of Symbolic Logic
ISSN: 1755-0203 , E-ISSN: 1755-0211 |
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| Output data | Year: 2020, Volume: 13, Number: 2, Pages: 416-435 Pages count : 20 DOI: 10.1017/S1755020319000121 | ||||
| Tags | Algebraic logic; First-degree entailment; Many-valued modal logic; Strong negation | ||||
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Abstract:
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.
Cite:
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
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
Identifiers:
| Web of science: | WOS:000528242900009 |
| Scopus: | 2-s2.0-85062032769 |
| OpenAlex: | W2915692292 |