A characterization of collective conflict for defeasible argumentation

In this paper we define a recursive semantics for warrant in a general defeasible argumentation framework by formalizing a notion of collective (non-binary) con- flict among arguments. This allows us to ensure direct and indirect consistency (in the sense of Caminada and Amgoud) without distinguishing between direct and in- direct conflicts. Then, the general defeasible argumentation framework is extended by allowing to attach levels of preference to defeasible knowledge items and by providing a level-wise definition of warranted and blocked conclusions. Finally, we formalize the warrant recursive semantics for the particular framework of Pos- sibilistic Defeasible Logic Programming, characterize the unique output program property and design an efficient algorithm for computing warranted conclusions in polynomial space.