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及其语义刻画，证明了LG的定理集与有效存在图集GET一一对应。研究表明，GET是皮尔斯伽马系统的扩展，但并不等同于泽曼的伽马-4系统。所有论证均以完整、严谨且详尽的方式呈现。通过构建次协调存在图系统GET4及其语义-演绎刻画，本文对该结果进行了推广。最后，证明了泽曼的伽马-4、伽马-4.2及伽马-5存在图系统均为次协调系统。