Encoding Argumentation Frameworks to Propositional Logic Systems

The theory of argumentation frameworks ($AF$s) has been a useful tool for artificial intelligence. The research of the connection between $AF$s and logic is an important branch. This paper generalizes the encoding method by encoding $AF$s as logical formulas in different propositional logic systems. It studies the relationship between models of an AF by argumentation semantics, including Dung's classical semantics and Gabbay's equational semantics, and models of the encoded formulas by semantics of propositional logic systems. Firstly, we supplement the proof of the regular encoding function in the case of encoding $AF$s to the 2-valued propositional logic system. Then we encode $AF$s to 3-valued propositional logic systems and fuzzy propositional logic systems and explore the model relationship. This paper enhances the connection between $AF$s and propositional logic systems. It also provides a new way to construct new equational semantics by choosing different fuzzy logic operations.

The SCC-recursiveness Principle in Fuzzy Argumentation Frameworks

Dung's abstract argumentation theory plays a guiding role in the field of formal argumentation. The properties of argumentation semantics have been deeply explored in the previous literature. The SCC-recursiveness principle is a property of the extensions which relies on the graph-theoretical notion of strongly connected components. It provides a general recursive schema for argumentation semantics, which is an efficient and incremental algorithm for computing the argumentation semantics. However, in argumentation frameworks with uncertain arguments and uncertain attack relation, the SCC-recursive theory is absence. This paper is an exploration of the SCC-recursive theory in fuzzy argumentation frameworks (FAFs), which add numbers as fuzzy degrees to the arguments and attacks. In this paper, in order to extend the SCC-recursiveness principle to FAFs, we first modify the reinstatement principle and directionality principle to fit the FAFs. Then the SCC-recursiveness principle in FAFs is formalized by the modified principles. Additionally, some illustrating examples show that the SCC-recursiveness principle also provides an efficient and incremental algorithm for simplify the computation of argumentation semantics in FAFs.