Recently there has been an increasing interest in frameworks extending Dung’s abstract Argumentation Framework (AF). Popular extensions include bipolar AFs and AFs with recursive attacks and necessary supports. Although the relationships between AF semantics and Partial Stable Models (PSMs) of logic programs has been deeply investigated, this is not the case for more general frameworks extending AF.In this paper we explore the relationships between AF-based frameworks and PSMs. We show that every AF-based framework Δ can be translated into a logic program P_Δ so that the extensions prescribed by different semantics of Δ coincide with subsets of the PSMs of P_Δ. We provide a logic programming approach that characterizes, in an elegant and uniform way, the semantics of several AF-based frameworks. This result allows also to define the semantics for new AF-based frameworks, such as AFs with recursive attacks and recursive deductive supports.

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.

Dealing with controversial information is a challenging and important task for intelligent systems. Formal argumentation enables reasoning on arguments for and against a claim to decide on an outcome. An argumentation framework often models a dynamic situation where arguments as well as the way they interact frequently change over the time. As a consequence, the sets of accepted arguments (i.e., extensions under a given semantics) often need to be computed again after performing an update. In this paper, we address the problem of efficiently recomputing extensions of dynamic argumentation frameworks. We present an incremental algorithmic solution whose main idea is that of using an initial extension and the update to identify a (potentially small) portion of the argumentation framework which is sufficient to compute an extension of the whole updated framework.

In this paper, we tackle the problem of efficiently recomputing the skeptical acceptance of dynamic argumentation frameworks under the well-known preferred semantics. We discuss an incremental algorithmic solution whose main idea is that of exploiting the initial knowledge (including the update to perform) in order to identify a potentially small portion of the argumentation framework. Such a portion is sufficient to compute the skeptical preferred acceptance of a goal argument w.r.t. the whole updated framework. We also discuss on how similar ideas extend to more general argumentation frameworks.