Dung’s abstract argumentation provides us with a general framework to deal with argumentation, non-monotonic reasoning and logic programming. For the extension-based semantics, one of the basic principles is I-maximality which is in particular related with the notion of skeptical justification. Another one is directionality which can be employed for the study of dynamics of argumentation. In this paper, we introduce two new extension-based semantics into Dung’s abstract argumentation, called grounded-like semantics and initial semantics which satisfy the I-maximality and directionality principles. (...) The initial semantics has many good properties and can be expected to play a central role in studying other extension-based semantics, such as admissible, complete and preferred semantics. (shrink)