Nelson’s logic ????

Logic Journal of the IGPL 28 (6):1182-1206 (2020)
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Abstract

Besides the better-known Nelson logic and paraconsistent Nelson logic, in 1959 David Nelson introduced, with motivations of realizability and constructibility, a logic called $\mathcal{S}$. The logic $\mathcal{S}$ was originally presented by means of a calculus with infinitely many rule schemata and no semantics. We look here at the propositional fragment of $\mathcal{S}$, showing that it is algebraizable, in the sense of Blok and Pigozzi, with respect to a variety of three-potent involutive residuated lattices. We thus introduce the first known algebraic semantics for $\mathcal{S}$ as well as a finite Hilbert-style calculus equivalent to Nelson’s presentation; this also allows us to clarify the relation between $\mathcal{S}$ and the other two Nelson logics $\mathcal{N}3$ and $\mathcal{N}4$.

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Author Profiles

Umberto Rivieccio
Universidad Nacional de Educación a Distancia
Joao Marcos
Universidade Federal do Rio Grande do Norte

Citations of this work

Improving Strong Negation.Satoru Niki - 2023 - Review of Symbolic Logic 16 (3):951-977.

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References found in this work

Constructible falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
Constructible falsity and inexact predicates.Ahmad Almukdad & David Nelson - 1984 - Journal of Symbolic Logic 49 (1):231-233.
Logics without the contraction rule.Hiroakira Ono & Yuichi Komori - 1985 - Journal of Symbolic Logic 50 (1):169-201.
How to be R eally Contraction-Free.Greg Restall - 1993 - Studia Logica 52 (3):381 - 391.

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