In this paper, the paraconsistent propositional logic LG is presented, along with its semantic characterization. It is shown that LG's set of theorems corresponds to the set of valid existential graphs, GET, which turns out to be an extension of Peirce's Gamma system, without becoming Zeman's gamma-4 system. All evidence is presented in a complete, rigorous, and detailed manner. This result is generalized by constructing the paraconsistent system of existential graphs GET4, and its semantic-deductive characterization. Finally, Zeman's Gamma-4, Gamma-4.2, and Gamma-5 existential graph systems are proven to be paraconsistent.

翻译：本文提出了次协调命题逻辑系统LG，并给出了其语义刻画。证明了LG的定理集与有效存在图集GET相对应，而GET是皮尔斯伽玛系统的一个扩展，但并非泽曼伽玛-4系统。所有证据均以完整、严谨且详尽的方式呈现。通过构建存在图系统GET4的次协调版本及其语义-演绎刻画，对上述结果进行了推广。最后，证明了泽曼的伽玛-4、伽玛-4.2和伽玛-5存在图系统具有次协调性。