Computing Extensions of Dynamic Abstract Argumentation Frameworks with Second-Order Attacks

Extended argumentation frameworks (EAFs) extend Dung's argumentation frameworks (AFs) to represent a kind of defeasible attack (by relying on the concept of second-order attack), in addition to the Dung's classical notion of attack between arguments. EAFs can be profitably used to model disputes between agents, with the aim of deciding the sets of arguments (called extensions) that should be accepted to support a point of view in a discussion. However, since new arguments and attacks are often introduced to take into account new available knowledge, EAFs as well as their extensions change over the time. In this paper we tackle the problem of efficiently recomputing extensions of dynamic EAFs under two well-known semantics (i.e., preferred and stable semantics). We introduce an incremental approach that, given an initial EAF, an initial extension for it, and an update, computes an extension of the updated EAF. This is achieved by introducing a meta-argumentation transformation according to which an initial EAF, as well as a given initial extension and an update, is transformed into a plain argumentation framework with a corresponding extension and update. The proposed approach is able to incorporate existing AF-solvers to compute an extension of the updated EAF. The experimental analysis showed that our technique is significantly faster than computing extensions of updated EAFs from scratch.