Abstract

Abstract argumentation frameworks are formal systems that facilitate obtaining conclusions from non-monotonic knowledge systems. Within such a system, an argumentation semantics is defined as a set of arguments with some desired qualities, for example, that the elements are not in conflict with each other. Splitting an argumentation framework can efficiently speed up the computation of argumentation semantics. With respect to stable semantics, two methods have been proposed to split an argumentation framework either in a unidirectional or bidirectional fashion. The advantage of bidirectional splitting is that it is not structure-dependent and, unlike unidirectional splitting, it can be used for frameworks consisting of a single strongly connected component. Bidirectional splitting makes use of a minimum cut. In this paper, we implement and test the performance of the bidirectional splitting method, along with two types of graph cut algorithms. Experimental data suggest that using a minimum cut will not improve the performance of computing stable semantics in most cases. Hence, instead of a minimum cut, we propose to use a balanced cut, where the framework is split into two sub-frameworks of equal size. Experimental results conducted on bidirectional splitting using the balanced cut show a significant improvement in the performance of computing semantics.

Highlights

  • Nowadays, much research in the field of argumentation relates to the notion of an abstract argumentation framework (AF) introduced by Phan Minh Dung in 1995 [1,2,3,4]

  • Our experimental results demonstrate that bidirectional splitting has a good potential to speed up the computation of stable semantics in argumentation frameworks

  • If we want the speedup to be reliable at all, the balanced cut method should be used instead of a minimum cut proposed in [14], as the results suggest that the k parameter does not play a role in the speedup

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Summary

Introduction

Much research in the field of argumentation relates to the notion of an abstract argumentation framework (AF) introduced by Phan Minh Dung in 1995 [1,2,3,4]. Being dissociated from any specific instance, an abstract framework is able to cover a variety of situations and can be instantiated for use in various empirical fields. It allows for various extensions to improve its expressiveness and performance. Some of the proposed extensions include e.g. value-based argumentation frameworks by Bench-Capon et al [5], logic-based argumentation frameworks by Besnard and Hunter [6], probabilistic argumentation frameworks by Li et al [7,8], or preference-based argumentation frameworks by Amgoud and Cayrol [9]

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