This paper generalizes the encoding of argumentation frameworks beyond the classical 2-valued propositional logic system (PL₂) to 3-valued propositional logic systems (PL₃s) and fuzzy propositional logic systems (PL₀, ₁s), employing two key encodings: normal encoding (ec₁) and regular encoding (ec₂). Specifically, via ec₁ and ec₂, we establish model relationships between Dung's classical semantics (stable and complete semantics) and the encoded semantics associated with Kleene's PL₃ and Łukasiewicz's PL₃. Through ec₁, we also explore connections between Gabbay's real equational semantics and the encoded semantics of PL₀, ₁s, including showing that Gabbay's Eq₌₀ₗR and Eq₈₍ₕ₄ₑₒ₄R correspond to the fuzzy encoded semantics of PL₀, ₁G and PL₀, ₁P respectively. Additionally, we propose a new fuzzy encoded semantics (EqL) associated with Łukasiewicz's PL₀, 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.
Tang et al. (Mon,) studied this question.
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