The lattice of Belnapian modal logics: special extensions and counterparts

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The lattice of Belnapian modal logics: special extensions and counterparts. / Odintsov, Sergei P.; Speranski, Stanislav O.

In: Logic and Logical Philosophy, Vol. 25, No. 1, 2016, p. 3-33.

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

BibTeX

@article{e8da298c6ce34b129970b5a4b545fb39,

title = "The lattice of Belnapian modal logics: special extensions and counterparts",

abstract = "Let K be the least normal modal logic and BK its Belnapian version, which enriches K with 'strong negation'. We carry out a systematic study of the lattice of logics containing BK based on: • introducing the classes (or rather sublattices) of so-called explosive, complete and classical Belnapian modal logics; • assigning to every normal modal logic three special conservative extensions in these classes; • associating with every Belnapian modal logic its explosive, complete and classical counterparts. We investigate the relationships between special extensions and counterparts, provide certain handy characterisations and suggest a useful decomposition of the lattice of logics containing BK.",

keywords = "Algebraic logic, Many-valued modal logic, Paraconsistent logic, Strong negation, algebraic logic, paraconsistent logic, many-valued modal logic, strong negation",

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

year = "2016",

doi = "10.12775/LLP.2016.002",

language = "English",

volume = "25",

pages = "3--33",

journal = "Logic and Logical Philosophy",

issn = "1425-3305",

publisher = "Nicolaus Copernicus University",

number = "1",

}

RIS

TY - JOUR

T1 - The lattice of Belnapian modal logics: special extensions and counterparts

AU - Odintsov, Sergei P.

AU - Speranski, Stanislav O.

PY - 2016

Y1 - 2016

N2 - Let K be the least normal modal logic and BK its Belnapian version, which enriches K with 'strong negation'. We carry out a systematic study of the lattice of logics containing BK based on: • introducing the classes (or rather sublattices) of so-called explosive, complete and classical Belnapian modal logics; • assigning to every normal modal logic three special conservative extensions in these classes; • associating with every Belnapian modal logic its explosive, complete and classical counterparts. We investigate the relationships between special extensions and counterparts, provide certain handy characterisations and suggest a useful decomposition of the lattice of logics containing BK.

AB - Let K be the least normal modal logic and BK its Belnapian version, which enriches K with 'strong negation'. We carry out a systematic study of the lattice of logics containing BK based on: • introducing the classes (or rather sublattices) of so-called explosive, complete and classical Belnapian modal logics; • assigning to every normal modal logic three special conservative extensions in these classes; • associating with every Belnapian modal logic its explosive, complete and classical counterparts. We investigate the relationships between special extensions and counterparts, provide certain handy characterisations and suggest a useful decomposition of the lattice of logics containing BK.

KW - Algebraic logic

KW - Many-valued modal logic

KW - Paraconsistent logic

KW - Strong negation

KW - algebraic logic

KW - paraconsistent logic

KW - many-valued modal logic

KW - strong negation

UR - http://www.scopus.com/inward/record.url?scp=85007574916&partnerID=8YFLogxK

U2 - 10.12775/LLP.2016.002

DO - 10.12775/LLP.2016.002

M3 - Article

AN - SCOPUS:85007574916

VL - 25

SP - 3

EP - 33

JO - Logic and Logical Philosophy

JF - Logic and Logical Philosophy

SN - 1425-3305

IS - 1

ER -

ID: 34776042