Balancing Open-Mindedness and Conservativeness in Quantitative Bipolar Argumentation (and How to Prove Semantical from Functional Properties)

Quantitative bipolar argumentation frameworks (QBAFs) have various

applications in areas like product recommendation, review aggregation

and explaining machine learning models. QBAF semantics assign a

strength to every argument that is based on an a priori belief and the

strength of its attackers and supporters. Intuitively, a QBAF semantics

is open-minded when it is unbiased in the sense that a priori beliefs

can be given up eventually when sufficient arguments to the contrary

are presented. While this behaviour is desirable in many applications,

existing open-minded semantics also have the property that even very

weak arguments will eventually eliminate the a priori beliefs. In this

paper, we will study notions of conservativeness that demand that the deviation

from the a priori beliefs is bounded by the strength of pro and contra

arguments. We will discuss compatibility and conflicts with existing

properties and present two new semantics with interesting semantical

guarantees. To do so, we will build up on the framework of modular semantics

and prove some general relationships between functional and semantical properties

that are useful to simplify the study of new modular semantics.