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EF4, EF4-M and EF4-Ł: A companion to BN4 and two modal four-valued systems without strong Łukasiewicz-type modal paradoxes [Book Review]
Logic and Logical Philosophy:75-104 (forthcoming)
Abstract
The logic BN4 was defined by R.T. 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 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 w.r.t. their respective semantics and that EF4-M and EF4-Ł are free from strong Łukasiewicz-type modal paradoxes.Links
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Citations of this work
A Class of Implicative Expansions of Belnap-Dunn Logic in which Boolean Negation is Definable.Gemma Robles & José M. Méndez - 2023 - Journal of Philosophical Logic 52 (3):915-938.
The lattice of all 4-valued implicative expansions of Belnap–Dunn logic containing Routley and Meyer’s basic logic Bd.Gemma Robles & José M. Méndez - forthcoming - Logic Journal of the IGPL.
References found in this work
A useful four-valued logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
Intuitive semantics for first-degree entailments and 'coupled trees'.J. Michael Dunn - 1976 - Philosophical Studies 29 (3):149-168.
How a computer should think.Nuel Belnap - 1977 - In Gilbert Ryle (ed.), Contemporary aspects of philosophy. Boston: Oriel Press.
Modal logics with Belnapian truth values.Serge P. Odintsov & Heinrich Wansing - 2010 - Journal of Applied Non-Classical Logics 20 (3):279-304.
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