Encoding Argumentation Frameworks to Propositional Logic Systems

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 (PL[0,1]s), 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 PL[0,1]s, including showing that Gabbay's EqₘₐₓR and EqᵢₙᵥₑᵣₛₑR 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 (EqL) 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.