2025/03/10 by Shuai Tang, Jiachao Wu, Tang, Shuai +3 · 1 citation
Computer Science · #03B50 #03B52 #68Q55 #Artificial Intelligence (cs.AI) #F.4.1 #FOS: Computer and information sciences #FOS: Mathematics #I.2.4 #Logic (math.LO) #Logic, Reasoning, and Knowledge #Multi-Agent Systems and Negotiation #Primary 68T27 #Secondary 03B70 #Semantic Web and Ontologies
paper · pdf · doi:10.48550/arxiv.2503.07351
openalex publication_date 2025/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.