Valued-Based Argumentation for Tree-like Value Graphs

We consider value-based argumentation frameworks (VAFs) introduced by Bench-Capon (J. Logic Comput. 13, 2003), which has been established as a fruitful model to study abstract argumentation systems. It takes into account the relative importance among arguments which reflects the value system of an audience. The central issue in the study of VAFs is the decision problems of subjective acceptance and objective acceptance: an argument is subjectively (objectively, resp.) accepted if it is accepted with respect to one audience (all possible audiences, resp.) An important limitation for using VAFs in real-world applications is the computational intractability of the acceptance problems. We identify nontrivial classes in terms of structural restrictions on the underlying graph structure of VAFs and present a polynomial-time algorithm in the spirit of dynamic programming. We supplement the tractability by the hardness result. This extends and generalize the results of Dunne (COMMA 2010) and Kim et al. (Artificial Intelligence 175, 2011).