In memoriam José Arrazola Ramírez (1962–2018) 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 continue the study of |$\textbf{CG}^{\prime}_3$|⁠, obtaining a Hilbert-type axiomatic system and proving a soundness and completeness theorem for this logic.

中文翻译：

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一个公理方法CG ^' ₃逻辑

纪念何塞·阿拉索拉·拉米雷斯（1962–2018）逻辑| $ \ textbf {G} ^ {\ prime} _3 $ | 由Osorio等人介绍。在2008; 它是三值逻辑，与超常逻辑| $ \ textbf {CG} ^ {\ prime} _3 $ |密切相关 由Osorio等人介绍。在2014年。逻辑| $ \ textbf {CG} ^ {\ prime} _3 $ | 是根据多值语义定义的，其属性是| $ \ textbf {G} ^ {\ prime} _3 $ |中的每个定理 是| $ \ textbf {CG} ^ {\ prime} _3 $ |⁠中的一个定理。| $ \ textbf {CG} ^ {\ prime} _3 $ |被赋予了Kripke类型的语义。Borja等人以两种不同的方式。在2016年。通过这项工作，我们继续研究| $ \ textbf {CG} ^ {\ prime} _3 $ |⁠，获得了希尔伯特（Hilbert）型公理系统，并证明了该逻辑的健全性和完整性定理。