A Methodology for Incompleteness-Tolerant and Modular Gradual Semantics for Argumentative Statement Graphs

Abstract: Gradual semantics (GS) have demonstrated great potential in argumentation, in particular for deploying quantitative bipolar argumentation frameworks (QBAFs) in a number of real-world settings, from judgmental forecasting to explainable AI. In this paper, we provide a novel methodology for obtaining GS for statement graphs, a form of structured argumentation framework, where arguments and relations between them are built from logical statements. Our methodology differs from existing approaches in the literature in two main ways. First, it naturally accommodates incomplete information, so that arguments with partially specified premises can play a meaningful role in the evaluation. Second, it is modularly defined to leverage on any GS for QBAFs. We also define a set of novel properties for our GS and study their suitability alongside a set of existing properties (adapted to our setting) for two instantiations of our GS, demonstrating their advantages over existing approaches.