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.

本研究解决了论证框架（$AF$s）与逻辑之间的连接问题，通过将$AF$s编码为不同命题逻辑系统中的逻辑公式，提出了一种新的编码方法。研究表明，实现$AF$s到不同值和模糊命题逻辑系统的编码，可以加强$AF$s与命题逻辑系统的连接，并为构建新的方程语义提供了一种新思路。

将论证框架编码为命题逻辑系统