Abstract Argumentation Framework with Conditional Preferences

Dung's abstract Argumentation Framework (AF) has emerged as a central formalism in the area of knowledge representation and reasoning. Preferences AF allow to represent comparative strength arguments simple yet expressive way. Preference-based (PAF) been proposed extend with preferences form > b, whose intuitive meaning is that argument better than b. In this paper we generalize PAF by introducing conditional b \leftarrow body informally state whenever condition expressed true. The resulting framework, namely Conditional (CPAF), extends semantics under three well-known preference criteria, i.e. democratic, elitist, KTV. After CPAF, study complexity verification problem (deciding whether set ``best'' extension) well credulous skeptical acceptance problems given belongs any or all extensions, respectively) multiple-status (that is, complete, preferred, stable, semi-stable semantics) for above-mentioned criteria.