The principle of counter-transitivity plays a vital role in argumentation. It states that an argument is strong when its attackers are weak, and is weak when its attackers are strong. In this work, we develop a formal theory about the argument ranking semantics based on this principle. Three approaches, quantity-based, quality-based and the unity of them, are defined to implement the principle. Then, we show an iterative refinement algorithm for capturing the ranking on arguments based on the recursive nature of the principle.

Dung's abstract argumentation framework consists of a set of interacting arguments and a series of semantics for evaluating them. Those semantics partition the powerset of the set of arguments into two classes: extensions and non-extensions. In order to reason with a specific semantics, one needs to take a credulous or skeptical approach, i.e. an argument is eventually accepted, if it is accepted in one or all extensions, respectively. In our previous work [1], we have proposed a novel semantics, called counting semantics, which allows for a more fine-grained assessment to arguments by counting the number of their respective attackers and defenders based on argument graph and argument game. In this paper, we continue our previous work by presenting some supplementaries about how to choose the damaging factor for the counting semantics, and what relationships with some existing approaches, such as Dung's classical semantics, generic gradual valuations. Lastly, an axiomatic perspective on the ranking semantics induced by our counting semantics are presented.

The knowledgebase uncertainty and the argument preferences are considered in this paper. The uncertainty is captured by weighted satisfiability degree, while a preference relation over arguments is derived by the beliefs of an agent.