We presented a case study on experimental algorithms in the context of two instances of extended argument systems. The concern was to show the potential of empirical analysis in evaluating algorithms for decision problems in argument systems. Ana- lyzing algorithms is a crucial process in engineering practical algorithms. The role of experimental methodology becomes evident in cases where theoretical evaluation might fall short in discovering the performance differences between algorithms.
We projected our discussions on algorithms in value based argument systems and Modgil’s argument system. This should not be construed as giving favor to these sys- tems over other formalisms such as [1, 57]. We did not mean in this chapter to analyze the semantics of the concerned formalisms or even to show the link between them and other related argumentation theories. Although we examined the efficiency of
Figure 2.25: The effect of increase in attacks per argument.
somewhat simple algorithms, we believe that the experimental treatments introduced in this chapter are applicable to other algorithmic issues in argument systems.
Considering experiments as a means for evaluating the performance of algorithms is generally not new in the field of computer science (see e.g. [74]). However, making use of empirical investigations in the context of argument systems for the purpose of developing algorithms is, to the best of our knowledge, considered by only a few works. In [54] experiments were conducted to evaluate the effectiveness of an algorithm for constructing logic-based arguments. In [70] experiments have been conducted to examine approximation versus exact computations in the context of argument systems while [12] empirically evaluated the effect of splitting a given argument system on the computation of preferred extensions. We see these previous works as complementary to our experimental study presented in this chapter in the sense that experimental algorithmics give insights to various features according to the objectives of the research question under study. This does not imply, by no means, that experiments in the general sense have not been undertaken by other works for objectives away from designing and analyzing dedicated algorithms, see for example [53, 51, 19].
Empirical evaluation of algorithms can be taken further to several algorithmic is- sues in the context of arguments systems as we show in the coming chapters. For example, [28, 97, 95] have proposed algorithms to decide credulous/skeptical accep- tance. From an application perspective it is still an open question concerning which of these algorithms is the most efficient in practice.
Chapter 3
New Algorithms for Preferred
Semantics
Doutre and Mengin [35] and later Modgil and Caminada [78] presented algorithms for computing preferred extensions. Informally, the two algorithms are based on the notion that arguments which might be included in an extension are labeledIN while arguments which might not be in the respective extension are labeledOUT and the undecided arguments are labeledUNDEC. Both algorithms start with some initial label for all arguments and then the labels change, through what are so-calledtransitions, several times until some condition holds. At this point, the arguments labeled IN make up an admissible set. These algorithms go through different sequences of transitions, and hence, they find admissible sets in order to construct the preferred extensions. Nonetheless, the two algorithms mainly differ in two issues. Firstly, the arguments’ initial labels. Secondly, the transitions of arguments’ labels. As we show, these issues affect the performance significantly.
The contribution of this chapter can be summarized in four points. Firstly, we improve labels’ transitions by utilizing further labels, and hence, the preferred exten- sions are enumerated faster than existing algorithms. Secondly, we introduce a new mechanism for pruning the search space such that transitions leading to “dead ends” are avoided at an early stage. Thirdly, we present a cost-effective heuristic rule that selects arguments for transitions such that a goal state (i.e. a preferred extension) might be achieved earlier. Fourthly, by incorporating the three improvements, we design algorithms for answering the skeptical/credulous acceptance question without explicitly enumerating all preferred extensions.
We develop in section 3.1 a new algorithm that enumerates all preferred extensions. Supported by experiments presented in section 3.3, we argue in section 3.2 that our algorithm is faster in deciding the preferred extensions than the existing algorithms of Doutre and Mengin [35] and Modgil and Caminada [78]. Regarding the acceptance problem, the skeptically/credulously accepted arguments might be simply decided by enumerating all preferred extensions. However, in situations where the acceptance
problem is confined to a specific argument then it is more efficient to avoid enumerating all preferred extensions explicitly, especially when the underlying argument system is dynamic (i.e. changes frequently such as in a dialog setting). Adhering to this view, in section 3.4 we engineer algorithms for the acceptance problem that outperform, with respect to running time, the existing algorithms of Cayrol et al. [28], Thang et al. [95] and the algorithm of Verheij for the credulous acceptance problem [97]. With respect to the acceptance algorithms, we introduce comparisons with existing algorithms and empirical evaluation in section 3.5. Lastly, we offer further discussions, review of related works and conclusions in section 3.6.