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  1. 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.
  • 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.
    Routley-Meyer type ternary relational semantics are defined for relevant logics including Routley and Meyer’s basic logic B plus the reductio rule and the disjunctive syllogism. Standard relevant logics such as E and R (plus γ ) and Ackermann’s logics of ‘strenge Implikation’ Π and Π ′ are among the logics considered.
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  • The Basic Constructive Logic for Absolute Consistency.José M. Méndez & Gemma Robles - 2009 - Journal of Logic, Language and Information 18 (2):199-216.
    In this paper, consistency is understood as absolute consistency (i.e. non-triviality). The basic constructive logic BKc6, 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 BKc6 up to contractionless intuitionistic logic. All logics defined in this paper are paraconsistent logics.
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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.
    In a standard sense, consistency and paraconsistency are understood as the absence of any contradiction and as the absence of the ECQ (‘E contradictione quodlibet’) rule, respectively. The concepts of weak consistency (in two different senses) as well as that of F -consistency have been defined by the authors. The aim of this paper is (a) to define alternative (to the standard one) concepts of paraconsistency in respect of the aforementioned notions of weak consistency and F -consistency; (b) to define (...)
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