A survey of different approaches to support in argumentation systems

Dung originally used the terminology ‘attack’ relation; however, to avoid confusions, we will refer to it as the ‘defeat’ relation since it encodes successful attacks.

Briefly, an argument $$\[--><$>{\cal A}<$><!--$$ is said to reinstate or defend an argument $$\[--><$>{\cal C}<$><!--$$ if there exists an argument $$\[--><$>{\cal B}<$><!--$$ such that $$\[--><$>{\cal B}<$><!--$$ defeats $$\[--><$>{\cal C}<$><!--$$, and $$\[--><$>{\cal A}<$><!--$$ defeats $$\[--><$>{\cal B}<$><!--$$.

Cayrol and Lagasquie-Schiex (2005) the authors use the terminology ‘indirect’ defeat; however, in later works they adopted the terminology ‘secondary’ defeat.

For additional background on graph theory see Berge (2001).

Begging the question is a type of logical fallacy that refers to its own assertion to prove the assertion.

For the sake of clarity, a unary set of arguments $$\[--><$>\{ {\cal A}\} <$><!--$$ will be referred to as $$\[--><$>{\cal A}<$><!--$$.

Martínez et al. (2006) call it an Abstract Argumentation Framework. However, to avoid confusions with the Abstract Argumentation Framework defined in Dung (1995), we have renamed it to Abstract Argumentation Framework with Subarguments.

For an overview on formal treatments of proof standards in argumentation see Atkinson and Bench-Capon (2007).