Studia Logica 103 (4):825-851 (2015)

Authors
Michael De
Utrecht University
Abstract
We investigate the notion of classical negation from a non-classical perspective. In particular, one aim is to determine what classical negation amounts to in a paracomplete and paraconsistent four-valued setting. We first give a general semantic characterization of classical negation and then consider an axiomatic expansion BD+ of four-valued Belnap–Dunn logic by classical negation. We show the expansion complete and maximal. Finally, we compare BD+ to some related systems found in the literature, specifically a four-valued modal logic of Béziau and the logic of classical implication and a paraconsistent de Morgan negation of Zaitsev
Keywords First-degree entailment  Belnap–Dunn logic  Classical negation  Many-valued logic  Paraconsistency  Paracompleteness  Maximality
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DOI 10.1007/s11225-014-9595-7
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References found in this work BETA

On the Theory of Inconsistent Formal Systems.Newton C. A. Costa - 1972 - Recife, Universidade Federal De Pernambuco, Instituto De Matemática.
On the Theory of Inconsistent Formal Systems.Newton C. A. Da Costa - 1974 - Notre Dame Journal of Formal Logic 15 (4):497-510.
Natural 3-Valued Logics—Characterization and Proof Theory.Arnon Avron - 1991 - Journal of Symbolic Logic 56 (1):276-294.
Can Contradictions Be True?Timothy Smiley & Graham Priest - 1993 - Aristotelian Society Supplementary Volume 67 (1):17 - 54.

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Citations of this work BETA

Defining LFIs and LFUs in Extensions of Infectious Logics.Szmuc Damian Enrique - 2016 - Journal of Applied Non-Classical Logics 26 (4):286-314.
Disjoint Logics.Federico Pailos - forthcoming - Logic and Logical Philosophy:1.

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