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)
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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.



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Author Profiles

Gemma Robles
Universidad de León
José M. Méndez
Universidad de Salamanca

References found in this work

Introduction to Metamathematics.Stephen Cole Kleene - 1952 - Princeton, NJ, USA: North Holland.
The logic of paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
A useful four-valued logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
Paraconsistent logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.

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