The theory of argumentation frameworks ($AF$s) has been a useful tool for artificial intelligence. The research of the connection between $AF$s and logic is an important branch. This paper generalizes the encoding method by encoding $AF$s as logical formulas in different propositional logic systems. It studies the relationship between models of an AF by argumentation semantics, including Dung's classical semantics and Gabbay's equational semantics, and models of the encoded formulas by semantics of propositional logic systems. Firstly, we supplement the proof of the regular encoding function in the case of encoding $AF$s to the 2-valued propositional logic system. Then we encode $AF$s to 3-valued propositional logic systems and fuzzy propositional logic systems and explore the model relationship. This paper enhances the connection between $AF$s and propositional logic systems. It also provides a new way to construct new equational semantics by choosing different fuzzy logic operations.

翻译：论辩框架（$AF$s）理论一直是人工智能领域的有用工具。研究$AF$s与逻辑之间的联系是一个重要分支。本文通过将$AF$s编码为不同命题逻辑系统中的逻辑公式，推广了编码方法。它研究了论辩语义（包括Dung的经典语义和Gabbay的方程语义）下AF的模型，与命题逻辑系统语义下编码公式的模型之间的关系。首先，我们补充了将$AF$s编码到二值命题逻辑系统时正则编码函数的证明。然后，我们将$AF$s编码到三值命题逻辑系统和模糊命题逻辑系统，并探讨模型关系。本文加强了$AF$s与命题逻辑系统之间的联系。它还通过选择不同的模糊逻辑运算，为构建新的方程语义提供了一种新途径。