Bisimulation between base argumentation and premise-conclusion argumentation

The structured argumentation system that represents arguments by premise-conclusion pairs is called premise-conclusion argumentation (PA) and the one that represents arguments by their premises is called base argumentation (BA). To assess whether BA and PA have the same ability in argument evaluation by extensional semantics, this paper defines the notion of extensional equivalence between BA and PA. It also defines the notion of bisimulation between BA and PA and shows that bisimulation implies extensional equivalence. To illustrate how base argumentation, bisimulation and extensional equivalence can contribute to the study of PA, we prove some new results about PA by investigating the extensional properties of a base argumentation framework and exporting them to two premise-conclusion argumentation frameworks via bisimulation and extensional equivalence. We show that there are essentially three kinds of extensions in these frameworks and that the extensions in the two premise-conclusion argumentation frameworks are identical.