Neighbourhood Semantics for FDE-Based Modal Logics

S. Drobyshevich; D. Skurt

doi:10.1007/s11225-021-09948-z

Neighbourhood Semantics for FDE-Based Modal Logics

S. Drobyshevich, D. Skurt

Кафедра алгебры и математической логики ММФ

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

Аннотация

We investigate some non-normal variants of well-studied paraconsistent and paracomplete modal logics that are based on N. Belnap’s and M. Dunn’s four-valued logic. Our basic non-normal modal logics are characterized by a weak extensionality rule, which reflects the four-valued nature of underlying logics. Aside from introducing our basic framework of bi-neighbourhood semantics, we develop a correspondence theory in order to prove completeness results with respect to our neighbourhood semantics for non-normal variants of BK, BK^FS and MBL.

Язык оригинала	английский
Страницы (с-по)	1273-1309
Число страниц	37
Журнал	Studia Logica
Том	109
Номер выпуска	6
DOI	https://doi.org/10.1007/s11225-021-09948-z
Состояние	Опубликовано - дек 2021

Предметные области OECD FOS+WOS

1.01.QL ЛОГИКА
6.01.MQ ИСТОРИЯ И ФИЛОСОФИЯ НАУКИ
1.01 МАТЕМАТИКА
6.03.UA ФИЛОСОФИЯ

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02 ФИЛОСОФИЯ

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10.1007/s11225-021-09948-z

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title = "Neighbourhood Semantics for FDE-Based Modal Logics",

abstract = "We investigate some non-normal variants of well-studied paraconsistent and paracomplete modal logics that are based on N. Belnap{\textquoteright}s and M. Dunn{\textquoteright}s four-valued logic. Our basic non-normal modal logics are characterized by a weak extensionality rule, which reflects the four-valued nature of underlying logics. Aside from introducing our basic framework of bi-neighbourhood semantics, we develop a correspondence theory in order to prove completeness results with respect to our neighbourhood semantics for non-normal variants of BK, BKFS and MBL.",

keywords = "Correspondence theory, FDE, Many-valued logic, Modal logic, Neighbourhood semantics",

author = "S. Drobyshevich and D. Skurt",

note = "Funding Information: The work reported in this paper has been carried out as part of the research project “ FDE -based Modal Logics”, supported by the Deutsche Forschungsgemeinschaft, DFG, grant WA 936/13-1, and the Russian Foundation for Basic Research, RFBR, grant No. 18-501-12019. We gratefully acknowledge this support. We also thank an anonymous reviewer for some useful comments which helped improve the presentation of the paper. Publisher Copyright: {\textcopyright} 2021, Springer Nature B.V. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",

year = "2021",

month = dec,

doi = "10.1007/s11225-021-09948-z",

language = "English",

volume = "109",

pages = "1273--1309",

journal = "Studia Logica",

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TY - JOUR

T1 - Neighbourhood Semantics for FDE-Based Modal Logics

AU - Drobyshevich, S.

AU - Skurt, D.

N1 - Funding Information: The work reported in this paper has been carried out as part of the research project “ FDE -based Modal Logics”, supported by the Deutsche Forschungsgemeinschaft, DFG, grant WA 936/13-1, and the Russian Foundation for Basic Research, RFBR, grant No. 18-501-12019. We gratefully acknowledge this support. We also thank an anonymous reviewer for some useful comments which helped improve the presentation of the paper. Publisher Copyright: © 2021, Springer Nature B.V. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/12

Y1 - 2021/12

N2 - We investigate some non-normal variants of well-studied paraconsistent and paracomplete modal logics that are based on N. Belnap’s and M. Dunn’s four-valued logic. Our basic non-normal modal logics are characterized by a weak extensionality rule, which reflects the four-valued nature of underlying logics. Aside from introducing our basic framework of bi-neighbourhood semantics, we develop a correspondence theory in order to prove completeness results with respect to our neighbourhood semantics for non-normal variants of BK, BKFS and MBL.

AB - We investigate some non-normal variants of well-studied paraconsistent and paracomplete modal logics that are based on N. Belnap’s and M. Dunn’s four-valued logic. Our basic non-normal modal logics are characterized by a weak extensionality rule, which reflects the four-valued nature of underlying logics. Aside from introducing our basic framework of bi-neighbourhood semantics, we develop a correspondence theory in order to prove completeness results with respect to our neighbourhood semantics for non-normal variants of BK, BKFS and MBL.

KW - Correspondence theory

KW - FDE

KW - Many-valued logic

KW - Modal logic

KW - Neighbourhood semantics

UR - http://www.scopus.com/inward/record.url?scp=85104962238&partnerID=8YFLogxK

UR - https://elibrary.ru/item.asp?id=46057209

U2 - 10.1007/s11225-021-09948-z

DO - 10.1007/s11225-021-09948-z

M3 - Article

AN - SCOPUS:85104962238

VL - 109

SP - 1273

EP - 1309

JO - Studia Logica

JF - Studia Logica

SN - 0039-3215

IS - 6

ER -

Neighbourhood Semantics for FDE-Based Modal Logics

Аннотация

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