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  1.  17
    The Pursuit of an Implication for the Logics L3A and L3B.Alejandro Hernández-Tello, José Arrazola Ramírez & Mauricio Osorio Galindo - 2017 - Logica Universalis 11 (4):507-524.
    The authors of Beziau and Franceschetto work with logics that have the property of not satisfying any of the formulations of the principle of non contradiction, Béziau and Franceschetto also analyze, among the three-valued logics, which of these logics satisfy this property. They prove that there exist only four of such logics, but only two of them are worthwhile to study. The language of these logics does not consider implication as a connective. However, the enrichment of a language with an (...)
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  2.  10
    Axiomatisations of the Genuine Three-Valued Paraconsistent Logics $$Mathbf {L3AG}$$ L 3 A G and $$Mathbf {L3BG}$$ L 3 B G.Alejandro Hernández-Tello, Miguel Pérez-Gaspar & Verónica Borja Macías - 2021 - Logica Universalis 15 (1):87-121.
    Genuine Paraconsistent logics \ and \ were defined in 2016 by Béziau et al, including only three logical connectives, namely, negation disjunction and conjunction. Afterwards in 2017 Hernández-Tello et al, provide implications for both logics and define the logics \ and \. In this work we continue the study of these logics, providing sound and complete Hilbert-type axiomatic systems for each logic. We prove among other properties that \ and \ satisfy a restricted version of the Substitution Theorem, and that (...)
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  3. An Axiomatic Approach to CG′3 Logic.Miguel Pérez-Gaspar, Alejandro Hernández-Tello, José Arrazola Ramírez & Mauricio Osorio Galindo - forthcoming - Logic Journal of the IGPL.
    In memoriam José Arrazola Ramírez The logic $\textbf{G}^{\prime}_3$ was introduced by Osorio et al. in 2008; it is a three-valued logic, closely related to the paraconsistent logic $\textbf{CG}^{\prime}_3$ introduced by Osorio et al. in 2014. The logic $\textbf{CG}^{\prime}_3$ is defined in terms of a multi-valued semantics and has the property that each theorem in $\textbf{G}^{\prime}_3$ is a theorem in $\textbf{CG}^{\prime}_3$. Kripke-type semantics has been given to $\textbf{CG}^{\prime}_3$ in two different ways by Borja et al. in 2016. In this work, we (...)
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