Affiliations: Department of Informatics, Modeling, Electronics and System Engineering (DIMES), University of Calabria, Italy
Correspondence:
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Corresponding author: Francesco Parisi, Department of Informatics, Modeling, Electronics and System Engineering (DIMES), University of Calabria, Italy. E-mail: fparisi@dimes.unical.it.
Abstract: Bipolar argumentation frameworks (BAFs) extend Dung’s argumentation frameworks to explicitly represent the notion of support between arguments, in addition to that of attack. BAFs can be profitably used to model disputes between two or more agents, with the aim of deciding the sets of arguments that should be accepted to support a point of view in a discussion. However, since new arguments, attacks, and supports are often introduced to take into account new available knowledge, BAFs as well as the set of accepted arguments (under a given semantics) change over the time. In this paper we first tackle the problem of efficiently recomputing sets of accepted arguments of dynamic BAFs (under the preferred and stable semantics). Focusing on a deductive interpretation of the support relation, we introduce an incremental approach that, given an initial BAF, an initial extension for it, and an update, computes an extension of the updated BAF. This is achieved by introducing a meta-argumentation transformation according to which an initial BAF, as well as its extension and an update, are transformed into a plain argumentation framework (AF) with a suitable initial extension and update. Thanks to the use of the meta-argumentation intermediate level, our approach is able to incorporate existing AF-solvers and an incremental technique for plain AFs in order to compute an extension of the updated BAF. Moreover, our approach can be seamlessly applied to a more general form of BAFs, namely Extended Bipolar Argumentation Frameworks (EAFs), where defeasible supports and defeats are modelled by means of second-order attacks (i.e., attacks toward elements of the support or attack relation). We experimentally validated our approach on both BAFs and EAFs. The experiments showed that, on average, our technique is almost 100 times faster than computing extensions of updated BAFs or EAFs from scratch.
