Belnap–Dunn modal logics: truth constants vs. truth values

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Belnap–Dunn modal logics: truth constants vs. truth values. / Odintsov, Sergei P.; Speranski, Stanislav O.

In: Review of Symbolic Logic, 2019.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{bd1be9539b58463dbe820886224a601d,

title = "Belnap–Dunn modal logics: truth constants vs. truth values",

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.",

keywords = "Many-Valued modal logic, algebraic logic, first-degree entailment, strong negation",

author = "Odintsov, {Sergei P.} and Speranski, {Stanislav O.}",

year = "2019",

doi = "10.1017/S1755020319000121",

language = "English",

journal = "Review of Symbolic Logic",

issn = "1755-0203",

publisher = "Cambridge University Press",

}

RIS

TY - JOUR

T1 - Belnap–Dunn modal logics: truth constants vs. truth values

AU - Odintsov, Sergei P.

AU - Speranski, Stanislav O.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Many-Valued modal logic

KW - algebraic logic

KW - first-degree entailment

KW - strong negation

UR - http://www.scopus.com/inward/record.url?scp=85062032769&partnerID=8YFLogxK

U2 - 10.1017/S1755020319000121

DO - 10.1017/S1755020319000121

M3 - Article

JO - Review of Symbolic Logic

JF - Review of Symbolic Logic

SN - 1755-0203

ER -

ID: 39018026