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 Lukasiewicz'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 Lukasiewicz'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.