将论证框架编码扩展到三值与模糊逻辑系统，建立语义对应关系。
Encoding Argumentation Frameworks to Propositional Logic Systems
- 提出两种编码方法，连接论证语义与多值逻辑系统。
- 揭示经典稳定/完整语义与三值、模糊逻辑语义的对应关系。
- 为构建新论证语义提供统一逻辑框架，适合逻辑与人工智能研究者。
本文将论证框架的编码从经典的二值命题逻辑系统（PL₂）推广至三值命题逻辑系统（PL₃）和模糊命题逻辑系统（PL_{[0,1]}），采用两种关键编码方式：标准编码（ec₁）与常规编码（ec₂）。通过 ec₁ 与 ec₂，建立了杜恩经典语义（稳定与完整语义）与克莱尼三值逻辑及卢卡西维茨三值逻辑编码语义之间的模型关系。通过 ec₁，还探讨了加比的实数方程语义与模糊编码语义之间的联系，证明加比的 Eq_max^R 与 Eq_inverse^R 分别对应于模糊逻辑系统 PL_{[0,1]}^G 与 PL_{[0,1]}^P 的编码语义。此外，提出一种与卢卡西维茨模糊逻辑相关的新模糊编码语义 Eq^L，研究完整语义与模糊编码语义间的交互。本工作强化了论证框架与命题逻辑系统之间的关联，为构建新型论证语义提供了理论框架。
原文摘要 · Abstract (English)
This paper generalizes the encoding of argumentation frameworks beyond the classical 2-valued propositional logic system ($PL_2$) to 3-valued propositional logic systems ($PL_3$s) and fuzzy propositional logic systems ($PL_{[0,1]}s$), employing two key encodings: normal encoding ($ec_1$) and regular encoding ($ec_2$). Specifically, via $ec_1$ and $ec_2$, we establish model relationships between Dung's classical semantics (stable and complete semantics) and the encoded semantics associated with Kleene's $PL_3$ and Łukasiewicz's $PL_3$. Through $ec_1$, we also explore connections between Gabbay's real equational semantics and the encoded semantics of $PL_{[0,1]}s$, including showing that Gabbay's $Eq_{\text{max}}^R$ and $Eq_{\text{inverse}}^R$ correspond to the fuzzy encoded semantics of $PL_{[0,1]}^G$ and $PL_{[0,1]}^P$ respectively. Additionally, we propose a new fuzzy encoded semantics ($Eq^L$) associated with Łukasiewicz's $PL_{[0,1]}$ and investigate interactions between complete semantics and fuzzy encoded semantics. This work strengthens the links between argumentation frameworks and propositional logic systems, providing a framework for constructing new argumentation semantics.
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