Gradual Acceptability for Structured Argumentation in ASPIC+

Abstract

Argumentation is a reasoning approach in Artificial Intelligence, which is approached by extension-based methods as well as gradual approaches. In the literature one is often vague about the type of argument strength that is studied and it is mostly approached avoiding structured argumentation. Thereby, assumptions are made on abstract level that do not always hold at the structural level. In this work we answer the question how a semantics for dialectical argument strength in structured approaches to argumentation can be developed and evaluated. To that end two new semantics will be proposed using ASPIC+, one for argumentation frameworks with only attacks, one for argumentation frameworks with only supports. Both of these semantics will be evaluated by the postulates proposed in the literature as well as by postulates proposed in this work. Existing semantics will also be evaluated by the new postulates.