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Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated values
Journal of Applied Non-Classical Logics 29 (1):37-63 (2019)
Abstract
ABSTRACTA conditional is natural if it fulfils the three following conditions. It coincides with the classical conditional when restricted to the classical values T and F; it satisfies the Modus Ponens; and it is assigned a designated value whenever the value assigned to its antecedent is less than or equal to the value assigned to its consequent. The aim of this paper is to provide a ‘bivalent’ Belnap-Dunn semantics for all natural implicative expansions of Kleene's strong 3-valued matrix with two designated elements.Author Profiles
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Citations of this work
The Class of All Natural Implicative Expansions of Kleene’s Strong Logic Functionally Equivalent to Łkasiewicz’s 3-Valued Logic Ł3.Gemma Robles & José M. Méndez - 2020 - Journal of Logic, Language and Information 29 (3):349-374.
Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix II. Only one designated value.Gemma Robles, Francisco Salto & José M. Méndez - 2019 - Journal of Applied Non-Classical Logics 29 (3):307-325.
Note on 'Normalisation for Bilateral Classical Logic with some Philosophical Remarks'.Nils Kürbis - 2021 - Journal of Applied Logics 7 (8):2259-2261.
Proof Systems for 3-valued Logics Based on Gödel’s Implication.Arnon Avron - 2022 - Logic Journal of the IGPL 30 (3):437-453.
Partiality and its dual in natural implicative expansions of Kleene’s strong 3-valued matrix with only one designated value.Gemma Robles & José M. Méndez - 2019 - Logic Journal of the IGPL 27 (6):910-932.
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.
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