Representing and comparing large sets of extensions of abstract argumentation frameworks

In argumentation theory, some reasoning problems involve the enumeration of all extensions of an abstract argumentation framework. Abstractly speaking, extensions are simply subsets of a given domain having some special properties. The result of the enumeration is usually presented as a single text file with elements and sets separated by designated delimiters. Neither the elements within each set (a single extension), nor the extensions themselves are presented in any pre-defined order. Events such as the International Competition of Computational Models of Argumentation require the comparison of a large number of enumerations and thus performing the comparisons very efficiently has become very desirable. This paper presents and compares three different alternative representations of extensions, one of which is novel for the argumentation domain, and provides an empirical evaluation of their effectiveness in the comparison of large enumerations. We found that the newly proposed representation can perform the comparisons in a much more memory and time efficient manner than existing solutions.