On the Graded Acceptability of Arguments

The paper develops a formal theory of the degree of justification of arguments, which relies solely on the structure of an argumentation framework. The theory is based on a generalisation of Dung’s notion of acceptability, making it sensitive to the numbers of attacks and counter-attacks on arguments. Graded generalisations of argumentation semantics are then obtained and studied. The theory is applied by showing how it can arbitrate between competing preferred extensions and how it captures a specific form of accrual in instantiated argumentation.