Incremental computation of grounded semantics for dynamic abstract argumentation frameworks

Abstract argumentation has emerged as a central field in Artificial Intelligence. Although the underlying idea is very simple and intuitive, most of the semantics proposed so far suffer from a high computational complexity. For this reason, in recent years, an increasing amount of work has been done to define efficient algorithms. However, so far, the research has concentrated on the definition of algorithms for static frameworks, whereas argumentation frameworks (AFs) are highly dynamic in practice. Surprisingly, the definition of evaluation algorithms taking into account such dynamic aspects has been mostly neglected. In this paper, we address the problem of efficiently recomputing the extensions of AFs which are updated by adding/deleting arguments or attacks. In particular, after identifying some properties that hold for updates of AFs under several well-known semantics, we focus on the most popular unique-status semantics (namely, the grounded semantics) and present an algorithm for its incremental computation, well-suited to dynamic applications where updates to an initial AF are frequently performed to take into account new available knowledge.