A Unifying Four-State Labelling Semantics for Bridging Abstract Argumentation Frameworks and Belief Revision

In many formalisms extending Dung's Abstract Argumentation Frameworks (AFs), arguments are not always "present". In timed AFs, for instance, arguments are only available in precise intervals of time, as they can appear and disappear in an intermittent manner; in incomplete AFs, both attacks and arguments can be absent; in constellation probabilistic AFs (attacks and) arguments have a probability to be present or not, and possible worlds are generated for the computation of the semantics. We review current approaches and propose a four-state labelling semantics to take in account such absent/unknown state of an argument. The four labels we use can be traced to the states a belief can assume, allowing us to also define operations related to belief manipulation, like expansion contraction and revision. We also discuss how labels/states of arguments in an AFs can be modified by using belief revision operations.