Valued-Based Argumentation for Tree-like Value Graphs

International audienceWe consider value-based argumentation frameworks (VAFs) introducedby Bench-Capon (J. Logic Comput. 13, 2003), which has been established as a fruit-ful model to study abstract argumentation systems. It takes into account the relativeimportance among arguments which reflects the value system of an audience. Thecentral issue in the study of VAFs is the decision problems of subjective acceptanceand objective acceptance: an argument is subjectively (objectively, resp.) acceptedif it is accepted with respect to one audience (all possible audiences, resp.) An im-portant limitation for using VAFs in real-world applications is the computationalintractability of the acceptance problems. We identify nontrivial classes in termsof structural restrictions on the underlying graph structure of VAFs and present apolynomial-time algorithm in the spirit of dynamic programming. We supplementthe tractability by the hardness result. This extends and generalize the results ofDunne (COMMA 2010) and Kim et al. (Artificial Intelligence 175, 2011)