argumentation screencap

args screencap 2

So the first two slides explain abstract argumentation theory and the last shows some examples.

In the second example why is {a1} not a grounded extension? There is no element in the argument graph which is a proper subset of a1, so it is minimal. A minimal set of arguments is grounded. So {a1} should be grounded.


1 Answer 1


Because the empty set { } is complete and it is a subset of both {A1} and {A2} and thus they are not grounded because not complete and minimal.

  • Then doesn’t that mean no set of arguments can be grounded? Since no matter what the empty set will always be a subset of the chosen argument set. Dec 23, 2021 at 13:39
  • @Shiny_and_Chrome - yes but... in Ex.1 the empty set is not complete while in Ex.2 it is. Dec 23, 2021 at 13:45
  • 1
    Ah... I think I just figured out why. In the first example the emtpy set is not complete because the empty set "defends" A3, as it is not attacked by anything. Meaning that defended(gamma) = gamma doesn't hold. Whereas in the second example it does, since there is not any argument which is not attacked. Dec 23, 2021 at 15:46

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