Identifying the Core of Logic-Based Argumentation Systems

We are interested by argumentation systems which build their arguments from a propositional knowledge base (KB), and evaluate them using Dung´s acceptability semantics. We start by showing that such systems are infinite, i.e. from a finite KB, an infinite set of arguments and an infinite set of attacks among them are generated. While the construction of arguments under propositional logic is costly even in the finite case, the fact that those systems are infinite makes them completely useless. Then, we provide a procedure which, given an argumentation system, computes its finite sub-system, called core. A core considers a finite subset of arguments and a finite subset of attacks, and returns all the results of the original system. This means that a finite subset of arguments is sufficient to draw all the expected conclusions from a KB.