From User Preferences to Base Score Extraction Functions in Gradual Argumentation (with Appendix)

TL;DR

This work introduces Base Score Extraction Functions, which provide a mapping from users' preferences over arguments to base scores, and incorporates an approximation of non-linearities in human preferences to allow for better approximation of the real ones.

Abstract

Gradual argumentation is a field of symbolic AI which is attracting attention for its ability to support transparent and contestable AI systems. It is considered a useful tool in domains such as decision-making, recommendation, debate analysis, and others. The outcomes in such domains are usually dependent on the arguments' base scores, which must be selected carefully. Often, this selection process requires user expertise and may not always be straightforward. On the other hand, organising the arguments by preference could simplify the task. In this work, we introduce \emph{Base Score Extraction Functions}, which provide a mapping from users' preferences over arguments to base scores. These functions can be applied to the arguments of a \emph{Bipolar Argumentation Framework} (BAF), supplemented with preferences, to obtain a \emph{Quantitative Bipolar Argumentation Framework} (QBAF), allowing the use of well-established computational tools in gradual argumentation. We outline the desirable properties of base score extraction functions, discuss some design choices, and provide an algorithm for base score extraction. Our method incorporates an approximation of non-linearities in human preferences to allow for better approximation of the real ones. Finally, we evaluate our approach both theoretically and experimentally in a robotics setting, and offer recommendations for selecting appropriate gradual semantics in practice.

Figures (2)

• Figure 1: We introduce a methodology for converting a BAF, supplemented with a preference ordering of the arguments (top), into a QBAF (bottom). From the set of arguments and a user's preference ordering, a Base Score Extraction Function $\nu$ is applied to the preference ordering to obtain the arguments' base scores $\tau$ (middle), which allow for the QBAF to be used as normal for decision-making, i.e. comparing the decision arguments and selecting that with the highest strength. The output of the decision-making system is personalised to the user's preferences.
• Figure 2: Influence of an argument’s base score and its supporter or attacker on the final argument strength under different gradual semantics. Each subplot corresponds to a distinct semantics: DF-QuAD (left), Quadratic Energy Model (centre), and the Euler-based Semantics (right). The x-axis represents the base score of the influenced argument, and the y-axis its resulting final strength. Blue lines denote when the influencing argument is a supporter (+), while red lines denote when it is an attacker (-). Each line has assigned its aggregation ($\alpha$), with colour intensity indicating its strength.

Theorems & Definitions (29)

• Definition 1
• Example 1
• Example 2
• Definition 2
• Example 3
• Definition 3
• Definition 4
• Definition 5
• Definition 6
• Example 4