Publication details
EF4, EF4-M and EF4-Ł: A companion to BN4 and two modal four-valued systems without strong Łukasiewicz-type modal paradoxes
| Authors | |
|---|---|
| Year of publication | 2022 |
| Type | Article in Periodical |
| Magazine / Source | Logic and logical philosophy |
| MU Faculty or unit | |
| Citation | |
| Web | http://dx.doi.org/10.12775/LLP.2021.010 |
| 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 |
| Description | 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. |