A general notion of equivalence for abstract argumentation

Abstract

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. We also provide exact characterizations and complexity results. The proposed notion of equivalence is motivated by its capability to capture the concept of local simplifications. In fact, our equivalence notion allows to decide whether a sub-framework can be replaced by another one without changing the extensions in the framework which undergoes this change. Moreover, as our characterizations demonstrate deciding this form of equivalence does not require an analysis of the entire framework. This makes it an appealing formal underpinning for establishing general replacement patterns in argumentation frameworks.