Disjunctive logic programming is a powerful general-purpose reasoning system for a broader range of problems in knowledge representation and artificial intelligence. The author presents an extension of the abstract argumentation theory for representing disjunctive logic programs and their semantics. The extension, called collective argumentation, is obtained by defining the attack relation directly among sets of arguments instead of individual arguments. In other words, a set of arguments ``collectively'' attacks another set of arguments in a way that is not reducible to attacks among particular arguments from these sets. The scope and importance of collective argumentation is much wider than logic programming. Collective argumentation is purported to describe reasoning situation in which the conflict between incompatible views or theories is global and cannot be reduced to particular claims made by these theories. The suggested collective argumentation theory is shown to be adequate for representing any ``well-behaved'' semantics for disjunctive logic programs. As an application of the general theory, the author considers two special kinds of collective argumentation: negative and positive argumentation. Negative argumentation will be shown to be especially appropriate for analysing stable sets of arguments. Positive argumentation also generalizes some known semantics suggested for logic programs.