Abstract argumentation frameworks, as described in Chapter 11 are directed towards determining whether a claim that some statement is true can be coherently maintained in the context of a set of conflicting arguments. For example, if we use preferred semantics, that an argument is a member of all preferred extensions establishes that its claim must be accepted as true, and membership of at least one preferred extension shows that the claim is at least tenable. In consequence, that admissible sets of arguments are conflict free is an important requirement under all the various semantics.
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Bench-Capon, T., Atkinson, K. (2009). Abstract Argumentation and Values. In: Simari, G., Rahwan, I. (eds) Argumentation in Artificial Intelligence. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-98197-0_3
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