Journal of Logic, Language and Information 17 (2):161-181 (2008)
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| Abstract |
In this paper, consistency is understood in the standard way, i.e. as the absence of a contradiction. The basic constructive logic BKc4, which is adequate to this sense of consistency in the ternary relational semantics without a set of designated points, is defined. Then, it is shown how to define a series of logics by extending BKc4 up to minimal intuitionistic logic. All logics defined in this paper are paraconsistent logics.
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| Keywords | Constructive negation Substructural logics Ternary relational semantics Paraconsistent logic |
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| DOI | 10.1007/s10849-007-9056-z |
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References found in this work BETA
Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview.
The Basic Constructive Logic for a Weak Sense of Consistency.Gemma Robles & José M. Méndez - 2008 - Journal of Logic, Language and Information 17 (1):89-107.
The Logic B and the Reductio Axioms.Gemma Robles & José M. Méndez - 2004 - Bulletin of the Section of Logic 33 (2):87-94.
Minimal Negation in the Ternary Relational Semantics.G. Robles, J. Mendez & F. Salto - 2005 - Reports on Mathematical Logic:47-65.
View all 6 references / Add more references
Citations of this work BETA
A Routley-Meyer Type Semantics for Relevant Logics Including B R Plus the Disjunctive Syllogism.Gemma Robles & José M. Méndez - 2010 - Journal of Philosophical Logic 39 (2):139-158.
Strong Paraconsistency and the Basic Constructive Logic for an Even Weaker Sense of Consistency.Gemma Robles & José M. Méndez - 2009 - Journal of Logic, Language and Information 18 (3):357-402.
The Basic Constructive Logic for Absolute Consistency.José M. Méndez & Gemma Robles - 2009 - Journal of Logic, Language and Information 18 (2):199-216.
The Basic Constructive Logic for Negation-Consistency Defined with a Propositional Falsity Constant.José M. Méndez, Gemma Robles & Francisco Salto - 2007 - Bulletin of the Section of Logic 36 (1-2):45-58.
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Strong Paraconsistency and the Basic Constructive Logic for an Even Weaker Sense of Consistency.Gemma Robles & José M. Méndez - 2009 - Journal of Logic, Language and Information 18 (3):357-402.
The Basic Constructive Logic for a Weak Sense of Consistency.Gemma Robles & José M. Méndez - 2008 - Journal of Logic, Language and Information 17 (1):89-107.
The Basic Constructive Logic for Absolute Consistency.José M. Méndez & Gemma Robles - 2009 - Journal of Logic, Language and Information 18 (2):199-216.
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Some Definitions of Negation Leading to Paraconsistent Logics.M. W. Bunder - 1984 - Studia Logica 43 (1-2):75 - 78.
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