Encoding Argumentation Frameworks to Propositional Logic Systems
This work provides a framework for constructing new argumentation semantics, which is incremental for researchers in computational argumentation and logic.
The paper tackles the problem of encoding argumentation frameworks into propositional logic systems by generalizing beyond classical 2-valued logic to 3-valued and fuzzy systems, establishing model relationships between classical semantics and encoded semantics and proposing new fuzzy semantics to strengthen links between argumentation and logic.
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.