Extension-based Semantics of Abstract Dialectical Frameworks
This work addresses foundational issues in computational argumentation for researchers in AI and logic, but it is incremental as it builds on existing ADF enrichments.
The paper tackles the problem of support cycles in abstract dialectical frameworks (ADFs) by introducing a new method to ensure acyclicity of arguments and developing a family of extension-based semantics based on it, while also extending research on semantics that permit cycles and providing ADF versions of properties from Dung's frameworks.
One of the most prominent tools for abstract argumentation is the Dung's framework, AF for short. It is accompanied by a variety of semantics including grounded, complete, preferred and stable. Although powerful, AFs have their shortcomings, which led to development of numerous enrichments. Among the most general ones are the abstract dialectical frameworks, also known as the ADFs. They make use of the so-called acceptance conditions to represent arbitrary relations. This level of abstraction brings not only new challenges, but also requires addressing existing problems in the field. One of the most controversial issues, recognized not only in argumentation, concerns the support cycles. In this paper we introduce a new method to ensure acyclicity of the chosen arguments and present a family of extension-based semantics built on it. We also continue our research on the semantics that permit cycles and fill in the gaps from the previous works. Moreover, we provide ADF versions of the properties known from the Dung setting. Finally, we also introduce a classification of the developed sub-semantics and relate them to the existing labeling-based approaches.