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2008 Weakening of Intuitionistic Negation for Many-valued Paraconsistent da Costa System
Zoran Majkić
Notre Dame J. Formal Logic 49(4): 401-424 (2008). DOI: 10.1215/00294527-2008-020

Abstract

In this paper we propose substructural propositional logic obtained by da Costa weakening of the intuitionistic negation. We show that the positive fragment of the da Costa system is distributive lattice logic, and we apply a kind of da Costa weakening of negation, by preserving, differently from da Costa, its fundamental properties: antitonicity, inversion, and additivity for distributive lattices. The other stronger paraconsistent logic with constructive negation is obtained by adding an axiom for multiplicative property of weak negation. After that, we define Kripke-style semantics based on possible worlds and derive from it many-valued semantics based on truth-functional valuations for these two paraconsistent logics. Finally, we demonstrate that this model-theoretic inference system is adequate—sound and complete with respect to the axiomatic da Costa-like systems for these two logics.

Citation

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Zoran Majkić. "Weakening of Intuitionistic Negation for Many-valued Paraconsistent da Costa System." Notre Dame J. Formal Logic 49 (4) 401 - 424, 2008. https://doi.org/10.1215/00294527-2008-020

Information

Published: 2008
First available in Project Euclid: 17 October 2008

zbMATH: 1180.03030
MathSciNet: MR2456656
Digital Object Identifier: 10.1215/00294527-2008-020

Subjects:
Primary: 03B53

Rights: Copyright © 2008 University of Notre Dame

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Vol.49 • No. 4 • 2008
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