Argumentation framework

An argumentation framework, or argumentation system, is a way to deal with contentious information and draw conclusions from it.

In an abstract argumentation framework, entry-level information is a set of abstract arguments that, for instance, represent data or a proposition. Conflicts between arguments are represented by a binary relation on the set of arguments. In concrete terms, you represent an argumentation framework with a directed graph such that the nodes are the arguments, and the arrows represent the attack relation. There exist some extensions of the Dung's framework, like the logic-based argumentation frameworks or the value-based argumentation frameworks.

Abstract argumentation frameworks, also called argumentation frameworks à la Dung, are defined formally as a pair:

For instance, the argumentation system ${\displaystyle S=\langle A,R\rangle }$ with ${\displaystyle A=\{a,b,c,d\}}$ and ${\displaystyle R=\{(a,b),(b,c),(d,c)\}}$ contains four arguments (${\displaystyle a,b,c}$ and ${\displaystyle d}$) and three attacks (${\displaystyle a}$ attacks ${\displaystyle b}$, ${\displaystyle b}$ attacks ${\displaystyle c}$ and ${\displaystyle d}$ attacks ${\displaystyle c}$).

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