A General Notion of Equivalence for Abstract Argumentation

We introduce a parametrized equivalence notion for abstract argumentation that subsumes standard and strong equivalence as corner cases. Under this notion, two argumentation frameworks are equivalent if they deliver the same extensions under any addition of arguments and attacks that do not affect a given set of core arguments. As we will see, this notion of equivalence nicely captures the concept of local simplifications. We provide exact characterizations and complexity results for deciding our new notion of equivalence.