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.