2. If an argument is labeled rejected then there must be at least one argument that attacks it and is labeled accepted.

3. If an argument is labeled abstained then it must not be the case that all arguments that attack it are labeled rejected, and it must not be the case that there is an argument that attacks it and is labeled accepted.
A labeling is called complete iff it satisfies each of the above three constraints. As an example, the argumentation framework of eq. 1 has exactly one complete labeling, in which A and C
are labeled accepted and B is labeled rejected. In general, an argumentation framework has one or more complete labelings. Furthermore, the arguments labeled accepted in a complete labeling form a complete extension in the sense of [7]. Other standard argumentation concepts, like preferred, grounded and stable extensions can also be expressed in terms of labelings [2].

In essence, one can see a complete labeling as a reasonable position one can take in the presence of the imperfect and conflicting information expressed in the argumentation framework. An interesting question is whether an argument can be accepted (that is, whether the argument is labeled accepted in at least one complete labeling) and whether an argument has to be accepted (that is, whether the argument is labeled accepted in each complete labeling). These two questions can be answered using formal discussion games [9, 11, 1, 6]. For instance, in the argumentation framework of eq. 1, a possible discussion would go as follows.

Proponent: Argument A has to be accepted.

Opponent: But perhaps A's attacker B does not have to be rejected.

Proponent: B has to be rejected because B's attacker C has to be accepted.

The precise rules which such discussions have to follow are described in [9, 11, 1, 6]. We say that argument A can be *defended* iff the proponent has a winning strategy for A. We say that argument A can be *denied* iff the opponent has a winning strategy against A.

If informedness is defined as justified belief, and justified is being interpreted as defensible in a rational discussion, then formal discussion games can serve as a way to examine whether an agent is informed with respect to proposition p, even in cases where one cannot directly determine the truth or falsity of p in the objective world. An agent is informed on p iff it has an argument for p that it is able to defend in the face of criticism.

The dialectical approach to knowledge also allows for the distinction of various grades of informedness. That is, an agent X can be perceived to be at least as informed as agent Y
w.r.t. argument A iff either X and Y originally disagreed on the status of A but combining their information the position of X is confirmed, or X and Y originally agreed on the status of A and in every case where Y is able to maintain its position in the presence of criticism from agent Z, X is also able to maintain its position in the presence of the same criticism.

When AF1 = (Ar 1, att1) and AF2 = (Ar 2, att2) are argumentation frameworks, we write AF1 t AF2 as a shorthand for (Ar 1 ∪ Ar 2, att1 ∪ att2), and AF1 v AF2 as a shorthand for Ar 1 ⊆ Ar 2 ∧ att1 ⊆ att2. Formally, agent X is at least as knowledgeable about argument A
as agent Y iff:
1. A can be defended using AFX (that is, if X assumes the role of the proponent of A then it has a winning strategy using the argumentation framework of X), A can be denied using AFY (that is, if Y assumes the role of the opponent than it has a winning strategy using the argumentation framework of Y ), but A can be defended using AFX t AFY ,
or