In the framework of collective acceptability, we have to consider the acceptability of a set of arguments. This acceptability is defined with respect to some properties and the sets which satisfy these properties are called acceptable sets or extensions. An argument will be said acceptable if and only if it belongs to an extension.
 defines several semantics for collective acceptability: mainly, the admissible semantics, the preferred semantics and the stable semantics (with corresponding extensions: the admissible sets, the preferred extensions and the stable extensions).
Note that in all the above definitions, each attacker of a given argument is considered separately (the ``direct attack'' as a whole is not considered).  proves that:
Marie-Christine Lagasquie 2005-02-04