Argumentation frameworks (AFs) are a well-known formalism for modelling and deciding many argumentation problems. Computational issues and evaluation algorithms have been deeply investigated for static AFs, whose structure does not change over the time. However, AFs are often dynamic as a consequence of the fact that argumentation is inherently dynamic. In this paper, we tackle the problem of incrementally computing extensions for dynamic AFs: given an initial extension and an update (or a set of updates), we devise a technique for computing an extension of the updated AF under four well-known semantics (i.e., complete, preferred, stable, and grounded). The idea is to identify a reduced (updated) AF sufficient to compute an extension of the whole AF and use state-of-the-art algorithms to recompute an extension of the reduced AF only. The experiments reveal that, for all semantics considered and using different solvers, the incremental technique is on average two orders of magnitude faster than computing the semantics from scratch.
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