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

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.