# Defining argument weighing functions

**Abstract**

Dung designed abstract argumentation frameworks [8] to model attack relations among arguments. However, a common and arguably more typical form of human argumentation, where pros and cons are weighed and balanced to choose among alternative options, cannot be simply and intuitively reduced to attacks. [12] defined a new formal model of structured argument which generalizes Dung abstract argumentation frameworks to provide better support for argument weighing and balancing, enabling cumulative arguments and argument accrual to be handled without causing an exponential blowup in the number of arguments. Dung proposed a pipeline model of argument evaluation for abstract argumentation frameworks, where first all the arguments are evaluated and labeled, at the abstract level, and then, in a subsequent process, the premises and conclusions of the arguments are labeled, at the structured argument level. This pipeline model makes it impossible to make the weight of arguments depend on the labels of their premises. To overcome this problem, in the new model of [12] the weight of arguments and labels of statements can depend on each other, in a mutually recursive manner. The new model is a framework which can be instantiated with a variety of argument weighing functions. In this article, this feature is illustrated by defining a number of argument weighing functions, including: 1) simulating linked and convergent arguments, by making the weight of an argument depend on whether all or some of its premises are labeled in, respectively; 2) making the weight of an argument depend on one or more meta-level properties of the argument, such as the date or authority of the scheme instantiated by the argument; 3) modeling a simple form of cumulative argument, by making the weight of an argument depend on the percentage of its in premises; 4) making the weight of an argument depend on the percentage of its in “factors”, from a set of possible factors, where premises represent factors; and, finally 5) making the weight of an argument depend on a weighted sum of the in properties of an option, in the style of multi-criteria decision analysis, where premises model properties of an option.