Positiveness and Skepticism in Abstract Argumentation: A First Approach

Starting from previous work concerning the notions of consistency and reinstatement in an abstract labelling setting, we propose an enhanced model where the above mentioned notions are integrated with the one of skepticism. Skepticism makes it possible to identify the labellings prescribed by argumentation semantics involving global requirements among those satisfying a combination of local consistency and reinstatement requirements. We then consider the issue of determining argument justification by synthesizing an evaluation labelling from those prescribed by the semantics, and we analyze the evaluation function most commonly used in the literature against a number of possible desiderata. Overall, we obtain a general model, based on the foundational notions of positiveness and skepticism, able to capture a variety of instances of different reasoning stages in abstract argumentation.