EF4, EF4-M and EF4-Ł: A companion to BN4 and two modal
four-valued systems without strong Łukasiewicz-type modal
paradoxes

J 2022

EF4, EF4-M and EF4-Ł: A companion to BN4 and two modal four-valued systems without strong Łukasiewicz-type modal paradoxes

BLANCO SÁNCHEZ, José Miguel

Základní údaje

Originální název

EF4, EF4-M and EF4-Ł: A companion to BN4 and two modal four-valued systems without strong Łukasiewicz-type modal paradoxes

Autoři

BLANCO SÁNCHEZ, José Miguel (724 Španělsko, garant, domácí)

Vydání

Logic and logical philosophy, Toruń, Poland, Nicholas Copernicus University Press, 2022, 1425-3305

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10201 Computer sciences, information science, bioinformatics

Stát vydavatele

Polsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.500

Kód RIV

RIV/00216224:14330/22:00125040

Organizační jednotka

Fakulta informatiky

DOI

http://dx.doi.org/10.12775/LLP.2021.010

UT WoS

000708879400001

Klíčová slova anglicky

relevant logics; modal logics; many-valued logics; Belnap-Dunn semantics; modal paradoxes; 4-valued modal logics

Změněno: 6. 4. 2023 11:16, RNDr. Pavel Šmerk, Ph.D.

Anotace

V originále

The logic BN4 was defined by RT Brady as a four-valued extension of Routley and Meyer’s basic logic B. The system EF4 is defined as a companion to BN4 to represent the four-valued system of (relevant) implication. The system Ł was defined by J. Łukasiewicz and it is a four-valued modal logic that validates what is known as strong Łukasiewicz-type modal paradoxes. The systems EF4-M and EF4-Ł are defined as alternatives to Ł without modal paradoxes. This paper aims to define a Belnap-Dunn semantics for EF4, EF4-M and EF4-Ł. It is shown that EF4, EF4-M and EF4-Ł are strongly sound and complete wrt their respective semantics and that EF4-M and EF4-Ł are free from strong Łukasiewicz-type modal paradoxes.

Citovat

BLANCO SÁNCHEZ, José Miguel. EF4, EF4-M and EF4-Ł: A companion to BN4 and two modal four-valued systems without strong Łukasiewicz-type modal paradoxes. Logic and logical philosophy. Toruń, Poland: Nicholas Copernicus University Press, 2022, roč. 31, č. 1, s. 75-104. ISSN 1425-3305. Dostupné z: https://dx.doi.org/10.12775/LLP.2021.010.

@article{1802045,
   author = {Blanco Sánchez, José Miguel},
   article_location = {Toruń, Poland},
   article_number = {1},
   doi = {http://dx.doi.org/10.12775/LLP.2021.010},
   keywords = {relevant logics; modal logics; many-valued logics; Belnap-Dunn semantics; modal paradoxes; 4-valued modal logics},
   language = {eng},
   issn = {1425-3305},
   journal = {Logic and logical philosophy},
   title = {EF4, EF4-M and EF4-Ł: A companion to BN4 and two modal four-valued systems without strong Łukasiewicz-type modal paradoxes},
   url = {http://dx.doi.org/10.12775/LLP.2021.010},
   volume = {31},
   year = {2022}
}

TY  - JOUR
ID  - 1802045
AU  - Blanco Sánchez, José Miguel
PY  - 2022
TI  - EF4, EF4-M and EF4-Ł: A companion to BN4 and two modal four-valued systems without strong Łukasiewicz-type modal paradoxes
JF  - Logic and logical philosophy
VL  - 31
IS  - 1
SP  - 75-104
EP  - 75-104
PB  - Nicholas Copernicus University Press
SN  - 14253305
KW  - relevant logics
KW  - modal logics
KW  - many-valued logics
KW  - Belnap-Dunn semantics
KW  - modal paradoxes
KW  - 4-valued modal logics
UR  - http://dx.doi.org/10.12775/LLP.2021.010
N2  - The logic BN4 was defined by RT Brady as a four-valued extension of Routley and Meyer’s basic logic B. The system EF4 is defined as a companion to BN4 to represent the four-valued system of (relevant) implication. The system Ł was defined by J. Łukasiewicz and it is a four-valued modal logic that validates what is known as strong Łukasiewicz-type modal paradoxes. The systems EF4-M and EF4-Ł are defined as alternatives to Ł without modal paradoxes. This paper aims to define a Belnap-Dunn semantics for EF4, EF4-M and EF4-Ł. It is shown that EF4, EF4-M and EF4-Ł are strongly sound and complete wrt their respective semantics and that EF4-M and EF4-Ł are free from strong Łukasiewicz-type modal paradoxes.
ER  -

BLANCO SÁNCHEZ, José Miguel. EF4, EF4-M and EF4-Ł: A companion to BN4 and two modal four-valued systems without strong Łukasiewicz-type modal paradoxes. \textit{Logic and logical philosophy}. Toru\'n, Poland: Nicholas Copernicus University Press, 2022, roč.~31, č.~1, s.~75-104. ISSN~1425-3305. Dostupné z: https://dx.doi.org/10.12775/LLP.2021.010.

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