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  1. A Constructive Negation for Logics Including TW+.Gemma Robles & José M. Méndez - 2005 - Journal of Applied Non-Classical Logics 15 (4):389-404.
    The logic TW+ is positive Ticket Entailment without the contraction axiom. Constructive negation is understood in the intuitionistic sense but without paradoxes of relevance. It is shown how to introduce a constructive negation of this kind in positive logics at least as strong as TW+. Special attention is paid to the reductio axioms. Concluding remarks about relevance, modal and entailment logics are stated. Complete relational ternary semantics are provided for the logics introduced in this paper.
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  • Relevance Logics, Paradoxes of Consistency and the K Rule II. A Non-Constructive Negation.José M. Méndez & Gemma Robles - 2007 - Logic and Logical Philosophy 15 (3):175-191.
    The logic B+ is Routley and Meyer’s basic positive logic. We define the logics BK+ and BK'+ by adding to B+ the K rule and to BK+ the characteristic S4 axiom, respectively. These logics are endowed with a relatively strong non-constructive negation. We prove that all the logics defined lack the K axiom and the standard paradoxes of consistency.
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  • Relevance Logics and Intuitionistic Negation.José M. Méndez & Gemma Robles - 2008 - Journal of Applied Non-Classical Logics 18 (1):49-65.
    The logic B+ is Routley and Meyer's basic positive logic. We show how to introduce a minimal intuitionistic negation and an intuitionistic negation in B+. The two types of negation are introduced in a wide spectrum of relevance logics built up from B+. It is proved that although all these logics have the characteristic paradoxes of consistency, they lack the K rule.
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  • 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.
    In this paper, consistency is understood as the absence of the negation of a theorem, and not, in general, as the absence of any contradiction. We define the basic constructive logic BKc1 adequate to this sense of consistency in the ternary relational semantics without a set of designated points. Then we show how to define a series of logics extending BKc1 within the spectrum delimited by contractionless minimal intuitionistic logic. All logics defined in the paper are paraconsistent logics.
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