Abstract
Abstract Argumentation is a key formalism to resolve conflicts in incomplete or inconsistent knowledge bases. Argumentation Frameworks (AFs) and extended versions thereof turned out to be a fruitful approach to reason in a flexible and intuitive setting. The addition of collective attacks, we refer to this class of frameworks as SETAFs, enriches the expressiveness and allows for compacter instantiations from knowledge bases, while maintaining the computational complexity of standard argumentation frameworks. This means, however, that standard reasoning tasks are intractable and worst-case runtimes for known standard algorithms can be exponential. In order to still obtain manageable runtimes, we exploit graph properties of these frameworks. In this paper, we initiate a parameterized complexity analysis of SETAFs in terms of the popular graph parameter treewidth. While treewidth is well studied in the context of AFs with their graph structure, it cannot be directly applied to the (directed) hypergraphs representing SETAFs. We thus introduce two generalizations of treewidth based on different graphs that can be associated with SETAFs, i.e., the primal graph and the incidence graph. We show that while some of these notions allow for parameterized tractability results, reasoning remains intractable for other notions, even if we fix the parameter to a small constant.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.