Collective Argumentation and Disjunctive Logic Programming

An extension of an abstract argumentation framework is introduced that provides a direct representation of global conflicts between sets of arguments. The extension, called collective argumentation, turns out to be suitable for representing semantics of disjunctive logic programs. Collective argumentation theories are shown to possess a four-valued semantics, and are closely related to multiple-conclusion (Scott) consequence relations. Two special kinds of collective argumentation, positive and negative argumentation, are considered in which the opponents can share their arguments. Negative argumentation turns out to be especially appropriate for analyzing stable sets of arguments. Positive argumentation generalizes certain alternative semantics for logic programs.