Beyond reasonable doubt: a proposal for undecidedness blocking in abstract argumentation

Abstract

In Dung’s abstract semantics, the label undecided is always propagated from the attacker to the attacked argument, unless the latter is also attacked by an accepted argument. In this work we propose undecidedness blocking abstract argumentation semantics where the undecided label is confined to the strong connected component where it was generated and it is not propagated to the other parts of the argumentation graph. We show how undecidedness blocking is a fundamental reasoning pattern absent in abstract argumentation but present in similar fashion in the ambiguity blocking semantics of Defeasible logic, in the beyond reasonable doubt legal principle or when someone gives someone else the benefit of the doubt. The resulting semantics, called SCC-void semantics, are defined using an SCC-recursive schema. The semantics are conflict-free and non-admissible, but they incorporate a more relaxed defence-based notion of admissibility. They allow reinstatement and they credulously accept what the corresponding Dung’s complete semantics accepts at least credulously